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#Visual Studio Code
.vscode

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GNU LESSER GENERAL PUBLIC LICENSE
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Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
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#ProjectEuler/Python/Problem1.py
#Matthew Ellison
# Created: 01-26-19
#Modified: 03-28-19
#What is the sum of all the multiples of 3 or 5 that are less than 1000
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
def Problem1():
#Setup your variables
fullSum = 0 #Holds the sum of all the correct numbers
#Start at 3 and start counting up, checking if any of the numbers are divisible by 3 or 5
#This method skips the problem of numbers that are divisible by both, like 15, being added twice
num = 3
while(num < 1000):
if((num % 3) == 0): #3 Will be triggered more often, putting it first makes the algorithm more efficient
fullSum += num
elif((num % 5) == 0):
fullSum += num
num += 1
#Print the results
print("The sum of all the multiples of 3 or 5 is " + str(fullSum))
#If you are running this file, automatically start the correct function
if(__name__ == "__main__"):
timer = Stopwatch() #Used to determine the algorithm's run time
timer.start() #Start the timer
Problem1() #Call the function that answers the problem
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The sum of all the multiples of 3 or 5 is 233168
It took 114.142 microseconds to run this algorithm
"""

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#Project Euler/Python/Problem10.py
#Matthew Ellison
# Created: 01-30-19
#Modified: 03-28-19
#Find the sum of all the primes below two million
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
from Algorithms import getPrimes
__numberGreaterThanPrimes = 2000000 #Get all primes <= this number
def Problem10():
#Get all of the primes < 2000000
primes = getPrimes(__numberGreaterThanPrimes - 1)
#Get the sum of the list
primeSum = sum(primes)
#Print the results
print("The sum of all the prime numbers less than " + str(__numberGreaterThanPrimes) + " is " + str(primeSum))
#If you are running this file, automatically start the correct function
if __name__ == "__main__":
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem10() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The sum of all the prime numbers less than 2000000 is 142913828922
It took 5.926 seconds to run this algorithm
"""

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#ProjectEuler/Python/Problem11.py
#Matthew Ellison
# Created: 01-31-19
#Modified: 03-28-19
#What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid?
"""
08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
"""
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
from Algorithms import prod
__grid = [[8, 2, 22, 97, 38, 15, 00, 40, 00, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8],
[49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 00],
[81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65],
[52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91],
[22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80],
[24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50],
[32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70],
[67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21],
[24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],
[21, 36, 23, 9, 75, 00, 76, 44, 20, 45, 35, 14, 00, 61, 33, 97, 34, 31, 33, 95],
[78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92],
[16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57],
[86, 56, 00, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
[19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40],
[4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],
[88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],
[4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36],
[20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16],
[20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54],
[1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]]
def Problem11():
#Setup the variables
greatestNumbers = [0, 0, 0, 0] #Holds the numbers that give the greatest product
currentNumbers = [0, 0, 0, 0] #Holds the numbers that you are currently working with
row = 0 #Holds the row in the grid that you are currently working on
col = 0 #Holds the column in the grid that you are currently working on
#Loop through every location in the grid
while(row < len(__grid)): #This loops through every row
col = 0 #Reset the column variable
while(col < len(__grid[row])): #This loops through every column
#Setup variables for knowing what direction you can move
moveLeft = False
moveRight = False
moveDown = False
#Check which directions you will be able to move
if((col - 3) >= 0):
moveLeft = True
if((col + 3) < len(__grid[row])):
moveRight = True
if((row + 3) < 20):
moveDown = True
#With these movements check for the greatest product of 4 adjacent numebrs
#Move Right
if moveRight:
currentNumbers[0] = __grid[row][col]
currentNumbers[1] = __grid[row][col + 1]
currentNumbers[2] = __grid[row][col + 2]
currentNumbers[3] = __grid[row][col + 3]
if(prod(currentNumbers) > prod(greatestNumbers)):
greatestNumbers = currentNumbers.copy()
#Move Down
if moveDown:
currentNumbers[0] = __grid[row][col]
currentNumbers[1] = __grid[row + 1][col]
currentNumbers[2] = __grid[row + 2][col]
currentNumbers[3] = __grid[row + 3][col]
if(prod(currentNumbers) > prod(greatestNumbers)):
greatestNumbers = currentNumbers.copy()
#Move Down & Left
if(moveDown and moveLeft):
currentNumbers[0] = __grid[row][col]
currentNumbers[1] = __grid[row + 1][col - 1]
currentNumbers[2] = __grid[row + 2][col - 2]
currentNumbers[3] = __grid[row + 3][col - 3]
if(prod(currentNumbers) > prod(greatestNumbers)):
greatestNumbers = currentNumbers.copy()
#Move Down & Right
if(moveDown and moveRight):
currentNumbers[0] = __grid[row][col]
currentNumbers[1] = __grid[row + 1][col + 1]
currentNumbers[2] = __grid[row + 2][col + 2]
currentNumbers[3] = __grid[row + 3][col + 3]
if(prod(currentNumbers) > prod(greatestNumbers)):
greatestNumbers = currentNumbers.copy()
#Move to the next column
col += 1
#Move to the next row
row += 1
#Print the results
print("The greatest product of 3 numbers in a line is " + str(prod(greatestNumbers)))
#If you are running this file, automatically start the correct function
if __name__ == "__main__":
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem11() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The greatest product of 3 numbers in a line is 70600674
It took 1.162 milliseconds to run this algorithm
"""

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#ProjectEuler/Python/Problem12.py
#Matthew Ellison
# Created: 01-31-19
#Modified: 03-28-19
#What is the value of the first triangle number to have over five hundred divisors?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
from Algorithms import getDivisors
__goalDivisors = 500 #The number of divisors a number needs to reach
def Problem12():
#Setup the variables
triangularNumber = 1 #Holds the triangular numbers
nextNumber = 2 #The next number to be added to the triangular number
foundNumber = False #A flag for when the triangular number has over __goalDivisors divisors
#Start at the first triangular number and loop around, moving to the next, until you find one with the appropriate number of divisors
while((not foundNumber) and (triangularNumber > 0)): #Make sure you haven't caused an overflow and made trianularNumber negative
#See how many divisors this triangular number has
divisors = getDivisors(triangularNumber)
#If it did have enough raise a flag to stop the loop
if(len(divisors) > __goalDivisors):
foundNumber = True
else:
triangularNumber += nextNumber #Add the next number to continue the triangular sequence
nextNumber += 1 #Advance to the next number in the triangular sequence
#Print the results
if(triangularNumber <= 0):
print("There was an error. Could not find a triangular number with " + str(__goalDivisors) + " divisors before overflow")
else:
print("The first triangular number with more than " + str(__goalDivisors) + " divisors is " + str(triangularNumber))
#If you are running this file, automatically start the correct function
if __name__ == "__main__":
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem12() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The first triangular number with more than 500 divisors is 76576500
It took 2.898 seconds to run this algorithm
"""

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#ProjectEuler/Python/Problem13.py
#Matthew Ellison
# Created: 01-31-19
#Modified: 03-28-19
#Work out the first ten digits of the sum of the following one-hundred 50-digit numbers
"""
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46376937677490009712648124896970078050417018260538
74324986199524741059474233309513058123726617309629
91942213363574161572522430563301811072406154908250
23067588207539346171171980310421047513778063246676
89261670696623633820136378418383684178734361726757
28112879812849979408065481931592621691275889832738
44274228917432520321923589422876796487670272189318
47451445736001306439091167216856844588711603153276
70386486105843025439939619828917593665686757934951
62176457141856560629502157223196586755079324193331
64906352462741904929101432445813822663347944758178
92575867718337217661963751590579239728245598838407
58203565325359399008402633568948830189458628227828
80181199384826282014278194139940567587151170094390
35398664372827112653829987240784473053190104293586
86515506006295864861532075273371959191420517255829
71693888707715466499115593487603532921714970056938
54370070576826684624621495650076471787294438377604
53282654108756828443191190634694037855217779295145
36123272525000296071075082563815656710885258350721
45876576172410976447339110607218265236877223636045
17423706905851860660448207621209813287860733969412
81142660418086830619328460811191061556940512689692
51934325451728388641918047049293215058642563049483
62467221648435076201727918039944693004732956340691
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55037687525678773091862540744969844508330393682126
18336384825330154686196124348767681297534375946515
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59959406895756536782107074926966537676326235447210
69793950679652694742597709739166693763042633987085
41052684708299085211399427365734116182760315001271
65378607361501080857009149939512557028198746004375
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38298203783031473527721580348144513491373226651381
34829543829199918180278916522431027392251122869539
40957953066405232632538044100059654939159879593635
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41698116222072977186158236678424689157993532961922
62467957194401269043877107275048102390895523597457
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82959174767140363198008187129011875491310547126581
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75506164965184775180738168837861091527357929701337
62177842752192623401942399639168044983993173312731
32924185707147349566916674687634660915035914677504
99518671430235219628894890102423325116913619626622
73267460800591547471830798392868535206946944540724
76841822524674417161514036427982273348055556214818
97142617910342598647204516893989422179826088076852
87783646182799346313767754307809363333018982642090
10848802521674670883215120185883543223812876952786
71329612474782464538636993009049310363619763878039
62184073572399794223406235393808339651327408011116
66627891981488087797941876876144230030984490851411
60661826293682836764744779239180335110989069790714
85786944089552990653640447425576083659976645795096
66024396409905389607120198219976047599490197230297
64913982680032973156037120041377903785566085089252
16730939319872750275468906903707539413042652315011
94809377245048795150954100921645863754710598436791
78639167021187492431995700641917969777599028300699
15368713711936614952811305876380278410754449733078
40789923115535562561142322423255033685442488917353
44889911501440648020369068063960672322193204149535
41503128880339536053299340368006977710650566631954
81234880673210146739058568557934581403627822703280
82616570773948327592232845941706525094512325230608
22918802058777319719839450180888072429661980811197
77158542502016545090413245809786882778948721859617
72107838435069186155435662884062257473692284509516
20849603980134001723930671666823555245252804609722
53503534226472524250874054075591789781264330331690
"""
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
#The numbers that need to be summed
__numbers = [37107287533902102798797998220837590246510135740250,
46376937677490009712648124896970078050417018260538,
74324986199524741059474233309513058123726617309629,
91942213363574161572522430563301811072406154908250,
23067588207539346171171980310421047513778063246676,
89261670696623633820136378418383684178734361726757,
28112879812849979408065481931592621691275889832738,
44274228917432520321923589422876796487670272189318,
47451445736001306439091167216856844588711603153276,
70386486105843025439939619828917593665686757934951,
62176457141856560629502157223196586755079324193331,
64906352462741904929101432445813822663347944758178,
92575867718337217661963751590579239728245598838407,
58203565325359399008402633568948830189458628227828,
80181199384826282014278194139940567587151170094390,
35398664372827112653829987240784473053190104293586,
86515506006295864861532075273371959191420517255829,
71693888707715466499115593487603532921714970056938,
54370070576826684624621495650076471787294438377604,
53282654108756828443191190634694037855217779295145,
36123272525000296071075082563815656710885258350721,
45876576172410976447339110607218265236877223636045,
17423706905851860660448207621209813287860733969412,
81142660418086830619328460811191061556940512689692,
51934325451728388641918047049293215058642563049483,
62467221648435076201727918039944693004732956340691,
15732444386908125794514089057706229429197107928209,
55037687525678773091862540744969844508330393682126,
18336384825330154686196124348767681297534375946515,
80386287592878490201521685554828717201219257766954,
78182833757993103614740356856449095527097864797581,
16726320100436897842553539920931837441497806860984,
48403098129077791799088218795327364475675590848030,
87086987551392711854517078544161852424320693150332,
59959406895756536782107074926966537676326235447210,
69793950679652694742597709739166693763042633987085,
41052684708299085211399427365734116182760315001271,
65378607361501080857009149939512557028198746004375,
35829035317434717326932123578154982629742552737307,
94953759765105305946966067683156574377167401875275,
88902802571733229619176668713819931811048770190271,
25267680276078003013678680992525463401061632866526,
36270218540497705585629946580636237993140746255962,
24074486908231174977792365466257246923322810917141,
91430288197103288597806669760892938638285025333403,
34413065578016127815921815005561868836468420090470,
23053081172816430487623791969842487255036638784583,
11487696932154902810424020138335124462181441773470,
63783299490636259666498587618221225225512486764533,
67720186971698544312419572409913959008952310058822,
95548255300263520781532296796249481641953868218774,
76085327132285723110424803456124867697064507995236,
37774242535411291684276865538926205024910326572967,
23701913275725675285653248258265463092207058596522,
29798860272258331913126375147341994889534765745501,
18495701454879288984856827726077713721403798879715,
38298203783031473527721580348144513491373226651381,
34829543829199918180278916522431027392251122869539,
40957953066405232632538044100059654939159879593635,
29746152185502371307642255121183693803580388584903,
41698116222072977186158236678424689157993532961922,
62467957194401269043877107275048102390895523597457,
23189706772547915061505504953922979530901129967519,
86188088225875314529584099251203829009407770775672,
11306739708304724483816533873502340845647058077308,
82959174767140363198008187129011875491310547126581,
97623331044818386269515456334926366572897563400500,
42846280183517070527831839425882145521227251250327,
55121603546981200581762165212827652751691296897789,
32238195734329339946437501907836945765883352399886,
75506164965184775180738168837861091527357929701337,
62177842752192623401942399639168044983993173312731,
32924185707147349566916674687634660915035914677504,
99518671430235219628894890102423325116913619626622,
73267460800591547471830798392868535206946944540724,
76841822524674417161514036427982273348055556214818,
97142617910342598647204516893989422179826088076852,
87783646182799346313767754307809363333018982642090,
10848802521674670883215120185883543223812876952786,
71329612474782464538636993009049310363619763878039,
62184073572399794223406235393808339651327408011116,
66627891981488087797941876876144230030984490851411,
60661826293682836764744779239180335110989069790714,
85786944089552990653640447425576083659976645795096,
66024396409905389607120198219976047599490197230297,
64913982680032973156037120041377903785566085089252,
16730939319872750275468906903707539413042652315011,
94809377245048795150954100921645863754710598436791,
78639167021187492431995700641917969777599028300699,
15368713711936614952811305876380278410754449733078,
40789923115535562561142322423255033685442488917353,
44889911501440648020369068063960672322193204149535,
41503128880339536053299340368006977710650566631954,
81234880673210146739058568557934581403627822703280,
82616570773948327592232845941706525094512325230608,
22918802058777319719839450180888072429661980811197,
77158542502016545090413245809786882778948721859617,
72107838435069186155435662884062257473692284509516,
20849603980134001723930671666823555245252804609722,
53503534226472524250874054075591789781264330331690]
def Problem13():
#Get the sum of all of the numbers in the list
sumOfNums = sum(__numbers)
#Print the results
print("The sum of all " + str(len(__numbers)) + " numbers is " + str(sumOfNums))
print("The first 10 digits are: " + str(sumOfNums)[0:10])
#If you are running this file, automatically start the correct function
if __name__ == "__main__":
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem13() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The sum of all 100 numbers is 5537376230390876637302048746832985971773659831892672
The first 10 digits are: 5537376230
It took 23.015 microseconds to run this algorithm
"""

80
Problem14.py Normal file
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#ProjectEuler/Python/Problem14.py
#Matthew Ellison
# Created: 01-31-19
#Modified: 03-28-19
"""
The following iterative sequence is defined for the set of positive integers:
n → n/2 (n is even)
n → 3n + 1 (n is odd)
Which starting number, under one million, produces the longest chain?
"""
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
__topNum = 1000000 #The largest number that you will check against the chain
#This function returns a list of numbers created by the chain
def getChain(startNum: int) -> list:
#Put the starting number in the list
chain = [startNum]
#Starting with the current number perform the correct opperations on the numbers until that number reaches 1
while(startNum > 1):
#Determine if the number is odd or even and perform the correct operation and add the new number to the list
if((startNum % 2) == 0):
startNum /= 2
else:
startNum = (3 * startNum) + 1
#Add the new number to the chain
chain.append(startNum)
#Return the list
return chain
def Problem14():
#Setup your variables
largestChain = [] #Holds the longest chain of numbers
#Start at 1 and run up to 1000000, checking how long the chain is when started with each number
for startingNumber in range(1, __topNum):
currentChain = getChain(startingNumber) #Get the chain
#If the new chain is longer than the current longest chain replace it
if(len(currentChain) > len(largestChain)):
largestChain = currentChain.copy()
#Print the results
print("The longest chain with a starting number < " + str(__topNum) + " is " + str(largestChain[0]) + " with a length of " + str(len(largestChain)))
#If you are running this file, automatically start the correct function
if __name__ == "__main__":
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem14() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The longest chain with a starting number < 1000000 is 837799 with a length of 525
It took 28.893 seconds to run this algorithm
"""

66
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#ProjectEuler/Python/Problem15.py
#Matthew Ellison
# Created: 01-31-19
#Modified: 03-28-19
#How many routes from the top left corner to the bottom right corner are there through a 20×20 grid if you can only move right and down?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
#There must be a better way than this. This is untested. I let it run for about 14 hours and it still hadn't spit an answer out for me
#But it is programed exactly as I programmed the C++ solution, so the eventual answer should be correct
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
__gridWidth = 20 #The height of the grid
__gridHeight = 20 #The width of the grid
def movement(currentX: int, currentY: int) -> int:
#Return 1 if you are at the finish location
if((currentX == __gridWidth) and (currentY == __gridHeight)):
return 1
numberMoves = 0
#Otherwise move one right if you can and recurse
if(currentX < __gridWidth):
numberMoves = movement(currentX + 1, currentY)
#Then move one down and recurse
if(currentY < __gridHeight):
numberMoves += movement(currentX, currentY + 1)
return numberMoves
def Problem15():
#Start the recursion at the right location and catch what is returned
numberMoves = movement(0, 0)
#Print the results
print("The number of paths from 1 corner of a " + str(__gridWidth) + " x " + str(__gridHeight) + " grid to the opposite corner is " + str(numberMoves))
#If you are running this file, automatically start the correct function
if __name__ == "__main__":
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem15() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
"""

60
Problem16.py Normal file
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#Project Euler/Python/Problem16.py
#Matthew Ellison
# Created: 02-03-19
#Modified: 03-28-19
#What is the sum of the digits of the number 2^1000?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
def Problem16():
#Setup the variables
sumOfNum = 0 #Holds the sum of the numbers
#Get the number
num = 2 ** 1000
#Change the number to a string
stringOfNum = str(num)
#Step through the string one element at a time
for cnt in range(0, len(stringOfNum)):
#Change the character to an int and add it to the sum
sumOfNum += int(stringOfNum[cnt])
#Print the result
print("2^1000 = " + stringOfNum)
print("The sum of the digits is: " + str(sumOfNum))
#If you are running this file, automatically start the correct function
if __name__ == "__main__":
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem16() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
2^1000 = 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376
The sum of the digits is: 1366
It took 86.206 microseconds to run this algorithm
"""

173
Problem17.py Normal file
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#ProjectEuler/Python/Problem17.py
#Matthew Ellison
# Created: 02-04-19
#Modified: 03-28-19
#If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
import math
__startNum = 1
__stopNum = 1000
#This function only works for numbers -1,000,000 < num < 1,000,000
def getStringFromNum(number: int) -> str:
numberString = ""
#Starting with the largest digit create a string based on the number passed in
#Check for negative
if(number < 0):
numberString += "negative "
#Check if the number is zero
if(number == 0):
numberString += "zero"
#Start with the thousands place
if((number / 1000) >= 1):
numberString += getStringFromNum(math.floor(number / 1000))
numberString += " thousand"
number -= (math.floor(number / 1000) * 1000)
#Check for hundreds place
if((number / 100) >= 1):
numberString += getStringFromNum(math.floor(number / 100))
numberString += " hundred"
number -= (math.floor(number / 100) * 100)
#Insert an and if there is need
if((numberString != "") and (number > 0)):
numberString += " and "
#Check for tens place
if((number / 10) >= 2):
#For the tens you need to do something special
tensPlace = math.floor(number / 10)
if(tensPlace == 9):
numberString += "ninety"
elif(tensPlace == 8):
numberString += "eighty"
elif(tensPlace == 7):
numberString += "seventy"
elif(tensPlace == 6):
numberString += "sixty"
elif(tensPlace == 5):
numberString += "fifty"
elif(tensPlace == 4):
numberString += "forty"
elif(tensPlace == 3):
numberString += "thirty"
elif(tensPlace == 2):
numberString += "twenty"
number -= (tensPlace * 10)
#If there is something left in the number you will need a space to separate it
if(number > 0):
numberString += ' '
#Check for teens
elif((number / 10) >= 1):
onesPlace = (number % 10)
if(onesPlace == 9):
numberString += "nineteen"
elif(onesPlace == 8):
numberString += "eighteen"
elif(onesPlace == 7):
numberString += "seventeen"
elif(onesPlace == 6):
numberString += "sixteen"
elif(onesPlace == 5):
numberString += "fifteen"
elif(onesPlace == 4):
numberString += "fourteen"
elif(onesPlace == 3):
numberString += "thirteen"
elif(onesPlace == 2):
numberString += "twelve"
elif(onesPlace == 1):
numberString += "eleven"
elif(onesPlace == 0):
numberString += "ten"
#If this if was hit number was used up
number = 0
#Check for ones place
if(number >= 1):
if(number == 9):
numberString += "nine"
elif(number == 8):
numberString += "eight"
elif(number == 7):
numberString += "seven"
elif(number == 6):
numberString += "six"
elif(number == 5):
numberString += "five"
elif(number == 4):
numberString += "four"
elif(number == 3):
numberString += "three"
elif(number == 2):
numberString += "two"
elif(number == 1):
numberString += "one"
#If this if was hit number was used up
number = 0
#Return the string
return numberString
def getNumberChars(number: str) -> int:
sumOfLetters = 0
#Start at location 0 and count the number of letters, ignoring punctuation and whitespace
for location in range(0, len(number)):
tempString = number[location]
if(tempString.isalpha()):
sumOfLetters += 1
#Return the number
return sumOfLetters
def Problem17():
sumOfLetters = 0
#Start with 1 and increment
for num in range(__startNum, __stopNum + 1):
#Pass the number to a function that will create a string for the number
currentNumString = getStringFromNum(num)
#Pass the string to a function that will count the number of letters in a string, ignoring whitespace and punctuation and add the amount to the running tally
sumOfLetters += getNumberChars(currentNumString)
#Print the results
print("The sum of all the letters in all the numbers " + str(__startNum) + '-' + str(__stopNum) + " is " + str(sumOfLetters))
#If you are running this file, automatically start the correct function
if __name__ == "__main__":
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem17() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The sum of all the letters in all the numbers 1-1000 is 21124
It took 4.107 milliseconds to run this algorithm
"""

139
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#ProjectEuler/Python/Problem18.py
#Matthew Ellison
# Created: 03-12-19
#Modified: 03-28-19
#Find the maximum total from top to bottom
"""
75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23
"""
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
from collections import namedtuple
location = namedtuple("location", "xLocation yLocation total fromRight")
NUM_ROWS = 15
def invert(listNum):
for rowCnt in range(0, NUM_ROWS):
for colCnt in range(0, len(listNum[rowCnt])):
listNum[rowCnt][colCnt] = 100 - listNum[rowCnt][colCnt]
def removeIf(listNum: list, loc):
location = 0
while(location < len(listNum)):
if((listNum[location].xLocation == loc.xLocation) and (listNum[location].yLocation == loc.yLocation)):
del listNum[location]
else:
location += 1
def Problem18():
listNum = [[75],
[95, 64],
[17, 47, 82],
[18, 35, 87, 10],
[20, 4, 82, 47, 65],
[19, 1, 23, 75, 3, 34],
[88, 2, 77, 73, 7, 63, 67],
[99, 65, 4, 28, 6, 16, 70, 92],
[41, 41, 26, 56, 83, 40, 80, 70, 33],
[41, 48, 72, 33, 47, 32, 37, 16, 94, 29],
[53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14],
[70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57],
[91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48],
[63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
[ 4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]]
#Invert the list so that each element = 100 - element
invert(listNum)
#Holds points we know are of the shortest route
foundPoints = []
#Add the tip of the pyramid because everything has to go through that
foundPoints.append(location(0, 0, listNum[0][0], True))
#Holds points that might be the shortest route
possiblePoints = []
#Add the second row as possible points because everything must pass through the second row
possiblePoints.append(location(0, 1, (listNum[0][0] + listNum[1][0]), True))
possiblePoints.append(location(1, 1, (listNum[0][0] + listNum[1][1]), False))
foundBottom = False
#Loop until you find the bottom
while(not foundBottom):
#Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one
minLoc = possiblePoints[0]
for loc in possiblePoints:
if(loc.total < minLoc.total):
minLoc = loc
#Remove it from the list of possible points
removeIf(possiblePoints, minLoc)
foundPoints.append(minLoc)
#Add to the list of possible points from the point we just found and
#If you are at the bottom raise the flag to end the program
xLoc = minLoc.xLocation
yLoc = minLoc.yLocation + 1
if(yLoc >= NUM_ROWS):
foundBottom = True
else:
possiblePoints.append(location(xLoc, yLoc, minLoc.total + listNum[yLoc][xLoc], True))
xLoc += 1
possiblePoints.append(location(xLoc, yLoc, minLoc.total + listNum[yLoc][xLoc], False))
#Get the real total of the journey
actualTotal = ((100 * NUM_ROWS) - foundPoints[len(foundPoints) - 1].total)
#Invert the list so it can be read again
invert(listNum)
#Print the results
print("The value of the longest path is " + str(actualTotal))
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem18()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The value of the longest path is 1074
It took 654.691 microseconds to run this algorithm
"""

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#ProjectEuler/Python/Problem19.py
#Matthew Ellison
# Created: 03-13-19
#Modified: 03-28-19
#How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?
"""
You are given the following information, but you may prefer to do some research for yourself.
1 Jan 1900 was a Monday.
Thirty days has September,
April, June and November.
All the rest have thirty-one,
Saving February alone,
Which has twenty-eight, rain or shine.
And on leap years, twenty-nine.
A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.
"""
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
class DAYS:
SUNDAY = 0
MONDAY = 1
TUESDAY = 2
WEDNESDAY = 3
THURSDAY = 4
FRIDAY = 5
SATURDAY = 6
NUMBER_OF_DAYS = 7
ERROR = 8
START_YEAR = 1901 #The year we start counting sundays
END_YEAR = 2000 #The year we stop counting sundays
#Return the day of the week that the date you pass into it is on
def getDay(month: int, day: int, year: int) -> DAYS:
#Make sure the numebrs are within propper bounds
if((month < 1) or (month > 12) or (day < 1) or (day > 31) or (year < 1)):
return DAYS.ERROR
numDays = 0 #The number of days between 01-01-0001 and the date given
currentYear = 1
currentMonth = 1
currentDay = DAYS.SATURDAY
day -= 1
#Add the correct number of days for every year
while(currentYear < year):
if(isLeapYear(currentYear)):
numDays += 366
else:
numDays += 365
currentYear += 1
#Add the correct number of days for eveyr month
while(currentMonth < month):
#February
if(currentMonth == 2):
if(isLeapYear(currentYear)):
numDays += 29
else:
numDays += 28
elif((currentMonth == 1) or (currentMonth == 3) or (currentMonth == 5) or (currentMonth == 7) or (currentMonth == 8) or (currentMonth == 10) or (currentMonth == 12)):
numDays += 31
#For 30 day months
else:
numDays += 30
currentMonth += 1
#Account for the weird year of 1752
if(year > 1752):
numDays -= 11
elif(year == 1752):
if(month > 9):
numDays -= 11
elif(month == 9):
if(day >= 14):
numDays -= 11
#Days 3-13 were skipped that year
elif((day > 2) and (day < 14)):
return DAYS.ERROR
#Add the correct number of days for every day
numDays += day
currentDay += numDays
currentDay = currentDay % DAYS.NUMBER_OF_DAYS
if(currentDay == DAYS.SUNDAY):
return DAYS.SUNDAY
elif(currentDay == DAYS.MONDAY):
return DAYS.MONDAY
elif(currentDay == DAYS.TUESDAY):
return DAYS.TUESDAY
elif(currentDay == DAYS.WEDNESDAY):
return DAYS.WEDNESDAY
elif(currentDay == DAYS.THURSDAY):
return DAYS.THURSDAY
elif(currentDay == DAYS.FRIDAY):
return DAYS.FRIDAY
elif(currentDay == DAYS.SATURDAY):
return DAYS.SATURDAY
else:
return DAYS.ERROR
#Returns true if the year passed to it is a leap year
def isLeapYear(year: int) -> bool:
if(year < 1):
return False
elif((year % 100) == 0):
#This rule only applies at and after 1800
if(year <= 1700):
return True
elif((year % 400) == 0):
return True
elif((year % 4) == 0):
return True
return False
def Problem19():
totalSundays = 0 #Keep track of the number of sundays
#Run for all years from start to end
for year in range(START_YEAR, END_YEAR + 1):
#Run for all months in the year
for month in range(1, 13):
day = getDay(month, 1, year)
if(day == DAYS.ERROR):
print("There was an error with the day")
return
elif(day == DAYS.SUNDAY):
totalSundays += 1
#Print the results
print("There are " + str(totalSundays) + " Sundays that landed on the first of the month from " + str(START_YEAR) + " to " + str(END_YEAR))
#Run automatically if the script was called stand alone
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem19()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
There are 171 Sundays that landed on the first of the month from 1901 to 2000
It took 724.930 milliseconds to run this algorithm
"""

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#ProjectEuler/Python/Problem2.py
#Matthew Ellison
# Created: 01-26-19
#Modified: 03-28-19
#The sum of the even Fibonacci numbers less than 4,000,000
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
from Algorithms import getAllFib
__topNumber = 4000000
def Problem2():
#Setup your variables
fibSum = 0 #Holds the sum of the Fibonacci numbers
fibNums = [] #An array that holds the Fibonacci numbers
#Get all of the fibonacci numbers
fibNums = getAllFib(__topNumber - 1) #Send it - 1 because it is < __topNumber
#Determine if each number is odd or even
for num in fibNums:
#If it is even add it to the running sum
if((num % 2) == 0):
fibSum += num
#Print the results
print("The sum of all even Fibonacci numbers less than " + str(__topNumber) + " is " + str(fibSum))
#If you are running this file, automatically start the correct function
if __name__ == '__main__':
timer = Stopwatch() #Use to determine the algorithm's run time
timer.start() #Start the timer
Problem2() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The sum of all even Fibonacci numbers less than 4000000 is 4613732
It took 27.621 microseconds to run this algorithm
"""

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#ProjectEuler/Python/Problem20.py
#Matthew Ellison
# Created: 03-14-19
#Modified: 03-28-19
#What is the sum of the digits of 100!
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
__TOP_NUM = 100 #The number that you are trying to find the factorial of
def Problem20():
num = 1 #Holds the number being calculated
sumOfNum = 0 #Holds the sum of the digits of num
#Run through every number from 1 to 100 and multiply it by the current num to get 100!
for cnt in range(1, __TOP_NUM + 1):
num *= cnt
#Get a string of the number because it is easier to pull appart the individual charaters for the sum
numString = str(num)
#Run through every character in the string, convert it back to an integer and add it to the running sum
for char in numString:
sumOfNum += int(char)
#Print the results
print("100! = " + numString)
print("The sum of the digits is: " + str(sumOfNum))
#This starts the correct function if called directly
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem20()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
The sum of the digits is: 648
It took 99.670 microseconds to run this algorithm
"""

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#ProjectEuler/Python/Problem21.py
#Matthew Ellison
# Created: 03-18-19
#Modified: 03-28-19
#Evaluate the sum of all the amicable numbers under 10000
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
import Algorithms
__limit = 10000 #The top number that will be evaluated
def Problem21():
#Setup the variables
divisorSum = [] #Holds the sum of the divisors of the subscript number
divisorSum.append(0) #Start with a 0 in the [0] location
#Generate the divisors of all the numbers < 10000, get their sum, and add it to the list
for cnt in range(1, __limit):
divisors = Algorithms.getDivisors(cnt) #Get all the divisors of a number
if(len(divisors) > 1):
divisors.pop() #Remove the last entry because it will be the number itself
divisorSum.append(int(sum(divisors)))
#Check every sum of divisors in the list for a matching sum
amicable = []
for cnt in range(1, len(divisorSum)):
currentSum = divisorSum[cnt]
#If the sum is greater than the number of divisors then it is impossible to be amicable. Skip the number and continue
if(currentSum >= len(divisorSum)):
continue
#We know that divisorSum[cnt] == currentSum, so if divisorSum[currentSum] == cnt we found an amicable number
if(divisorSum[currentSum] == cnt):
#A number can't be amicable with itself
if(currentSum == cnt):
continue
#Add the number to the amicable vector
amicable.append(cnt)
#Print the results
print("All amicable numbers less than 10000 are")
for num in amicable:
print(str(num))
print("The sum of all of these amicable numbers is " + str(sum(amicable)))
#Run the correct function if this script is called stand along
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem21()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
All amicable numbers less than 10000 are
220
284
1184
1210
2620
2924
5020
5564
6232
6368
The sum of all of these amicable numbers is 31626
It took 59.496 milliseconds to run this algorithm
"""

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Problem22.py Normal file
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#ProjectEuler/Python/Problem22.py
#Matthew Ellison
# Created: 03-20-19
#Modified: 03-28-19
#What is the total of all the name scores in the file?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
import Algorithms
__NAMES = ["MARY","PATRICIA","LINDA","BARBARA","ELIZABETH","JENNIFER","MARIA","SUSAN","MARGARET","DOROTHY","LISA","NANCY","KAREN",
"BETTY","HELEN","SANDRA","DONNA","CAROL","RUTH","SHARON","MICHELLE","LAURA","SARAH","KIMBERLY","DEBORAH","JESSICA","SHIRLEY",
"CYNTHIA","ANGELA","MELISSA","BRENDA","AMY","ANNA","REBECCA","VIRGINIA","KATHLEEN","PAMELA","MARTHA","DEBRA","AMANDA","STEPHANIE",
"CAROLYN","CHRISTINE","MARIE","JANET","CATHERINE","FRANCES","ANN","JOYCE","DIANE","ALICE","JULIE","HEATHER","TERESA","DORIS",
"GLORIA","EVELYN","JEAN","CHERYL","MILDRED","KATHERINE","JOAN","ASHLEY","JUDITH","ROSE","JANICE","KELLY","NICOLE","JUDY",
"CHRISTINA","KATHY","THERESA","BEVERLY","DENISE","TAMMY","IRENE","JANE","LORI","RACHEL","MARILYN","ANDREA","KATHRYN","LOUISE",
"SARA","ANNE","JACQUELINE","WANDA","BONNIE","JULIA","RUBY","LOIS","TINA","PHYLLIS","NORMA","PAULA","DIANA","ANNIE","LILLIAN",
"EMILY","ROBIN","PEGGY","CRYSTAL","GLADYS","RITA","DAWN","CONNIE","FLORENCE","TRACY","EDNA","TIFFANY","CARMEN","ROSA","CINDY",
"GRACE","WENDY","VICTORIA","EDITH","KIM","SHERRY","SYLVIA","JOSEPHINE","THELMA","SHANNON","SHEILA","ETHEL","ELLEN","ELAINE",
"MARJORIE","CARRIE","CHARLOTTE","MONICA","ESTHER","PAULINE","EMMA","JUANITA","ANITA","RHONDA","HAZEL","AMBER","EVA","DEBBIE",
"APRIL","LESLIE","CLARA","LUCILLE","JAMIE","JOANNE","ELEANOR","VALERIE","DANIELLE","MEGAN","ALICIA","SUZANNE","MICHELE","GAIL",
"BERTHA","DARLENE","VERONICA","JILL","ERIN","GERALDINE","LAUREN","CATHY","JOANN","LORRAINE","LYNN","SALLY","REGINA","ERICA",
"BEATRICE","DOLORES","BERNICE","AUDREY","YVONNE","ANNETTE","JUNE","SAMANTHA","MARION","DANA","STACY","ANA","RENEE","IDA","VIVIAN",
"ROBERTA","HOLLY","BRITTANY","MELANIE","LORETTA","YOLANDA","JEANETTE","LAURIE","KATIE","KRISTEN","VANESSA","ALMA","SUE","ELSIE",
"BETH","JEANNE","VICKI","CARLA","TARA","ROSEMARY","EILEEN","TERRI","GERTRUDE","LUCY","TONYA","ELLA","STACEY","WILMA","GINA",
"KRISTIN","JESSIE","NATALIE","AGNES","VERA","WILLIE","CHARLENE","BESSIE","DELORES","MELINDA","PEARL","ARLENE","MAUREEN","COLLEEN",
"ALLISON","TAMARA","JOY","GEORGIA","CONSTANCE","LILLIE","CLAUDIA","JACKIE","MARCIA","TANYA","NELLIE","MINNIE","MARLENE","HEIDI",
"GLENDA","LYDIA","VIOLA","COURTNEY","MARIAN","STELLA","CAROLINE","DORA","JO","VICKIE","MATTIE","TERRY","MAXINE","IRMA","MABEL",
"MARSHA","MYRTLE","LENA","CHRISTY","DEANNA","PATSY","HILDA","GWENDOLYN","JENNIE","NORA","MARGIE","NINA","CASSANDRA","LEAH","PENNY",
"KAY","PRISCILLA","NAOMI","CAROLE","BRANDY","OLGA","BILLIE","DIANNE","TRACEY","LEONA","JENNY","FELICIA","SONIA","MIRIAM","VELMA",
"BECKY","BOBBIE","VIOLET","KRISTINA","TONI","MISTY","MAE","SHELLY","DAISY","RAMONA","SHERRI","ERIKA","KATRINA","CLAIRE","LINDSEY",
"LINDSAY","GENEVA","GUADALUPE","BELINDA","MARGARITA","SHERYL","CORA","FAYE","ADA","NATASHA","SABRINA","ISABEL","MARGUERITE",
"HATTIE","HARRIET","MOLLY","CECILIA","KRISTI","BRANDI","BLANCHE","SANDY","ROSIE","JOANNA","IRIS","EUNICE","ANGIE","INEZ","LYNDA",
"MADELINE","AMELIA","ALBERTA","GENEVIEVE","MONIQUE","JODI","JANIE","MAGGIE","KAYLA","SONYA","JAN","LEE","KRISTINE","CANDACE",
"FANNIE","MARYANN","OPAL","ALISON","YVETTE","MELODY","LUZ","SUSIE","OLIVIA","FLORA","SHELLEY","KRISTY","MAMIE","LULA","LOLA",
"VERNA","BEULAH","ANTOINETTE","CANDICE","JUANA","JEANNETTE","PAM","KELLI","HANNAH","WHITNEY","BRIDGET","KARLA","CELIA","LATOYA",
"PATTY","SHELIA","GAYLE","DELLA","VICKY","LYNNE","SHERI","MARIANNE","KARA","JACQUELYN","ERMA","BLANCA","MYRA","LETICIA","PAT",
"KRISTA","ROXANNE","ANGELICA","JOHNNIE","ROBYN","FRANCIS","ADRIENNE","ROSALIE","ALEXANDRA","BROOKE","BETHANY","SADIE","BERNADETTE",
"TRACI","JODY","KENDRA","JASMINE","NICHOLE","RACHAEL","CHELSEA","MABLE","ERNESTINE","MURIEL","MARCELLA","ELENA","KRYSTAL",
"ANGELINA","NADINE","KARI","ESTELLE","DIANNA","PAULETTE","LORA","MONA","DOREEN","ROSEMARIE","ANGEL","DESIREE","ANTONIA","HOPE",
"GINGER","JANIS","BETSY","CHRISTIE","FREDA","MERCEDES","MEREDITH","LYNETTE","TERI","CRISTINA","EULA","LEIGH","MEGHAN","SOPHIA",
"ELOISE","ROCHELLE","GRETCHEN","CECELIA","RAQUEL","HENRIETTA","ALYSSA","JANA","KELLEY","GWEN","KERRY","JENNA","TRICIA","LAVERNE",
"OLIVE","ALEXIS","TASHA","SILVIA","ELVIRA","CASEY","DELIA","SOPHIE","KATE","PATTI","LORENA","KELLIE","SONJA","LILA","LANA","DARLA",
"MAY","MINDY","ESSIE","MANDY","LORENE","ELSA","JOSEFINA","JEANNIE","MIRANDA","DIXIE","LUCIA","MARTA","FAITH","LELA","JOHANNA",
"SHARI","CAMILLE","TAMI","SHAWNA","ELISA","EBONY","MELBA","ORA","NETTIE","TABITHA","OLLIE","JAIME","WINIFRED","KRISTIE","MARINA",
"ALISHA","AIMEE","RENA","MYRNA","MARLA","TAMMIE","LATASHA","BONITA","PATRICE","RONDA","SHERRIE","ADDIE","FRANCINE","DELORIS",
"STACIE","ADRIANA","CHERI","SHELBY","ABIGAIL","CELESTE","JEWEL","CARA","ADELE","REBEKAH","LUCINDA","DORTHY","CHRIS","EFFIE",
"TRINA","REBA","SHAWN","SALLIE","AURORA","LENORA","ETTA","LOTTIE","KERRI","TRISHA","NIKKI","ESTELLA","FRANCISCA","JOSIE","TRACIE",
"MARISSA","KARIN","BRITTNEY","JANELLE","LOURDES","LAUREL","HELENE","FERN","ELVA","CORINNE","KELSEY","INA","BETTIE","ELISABETH",
"AIDA","CAITLIN","INGRID","IVA","EUGENIA","CHRISTA","GOLDIE","CASSIE","MAUDE","JENIFER","THERESE","FRANKIE","DENA","LORNA",
"JANETTE","LATONYA","CANDY","MORGAN","CONSUELO","TAMIKA","ROSETTA","DEBORA","CHERIE","POLLY","DINA","JEWELL","FAY","JILLIAN",
"DOROTHEA","NELL","TRUDY","ESPERANZA","PATRICA","KIMBERLEY","SHANNA","HELENA","CAROLINA","CLEO","STEFANIE","ROSARIO","OLA",
"JANINE","MOLLIE","LUPE","ALISA","LOU","MARIBEL","SUSANNE","BETTE","SUSANA","ELISE","CECILE","ISABELLE","LESLEY","JOCELYN",
"PAIGE","JONI","RACHELLE","LEOLA","DAPHNE","ALTA","ESTER","PETRA","GRACIELA","IMOGENE","JOLENE","KEISHA","LACEY","GLENNA",
"GABRIELA","KERI","URSULA","LIZZIE","KIRSTEN","SHANA","ADELINE","MAYRA","JAYNE","JACLYN","GRACIE","SONDRA","CARMELA","MARISA",
"ROSALIND","CHARITY","TONIA","BEATRIZ","MARISOL","CLARICE","JEANINE","SHEENA","ANGELINE","FRIEDA","LILY","ROBBIE","SHAUNA",
"MILLIE","CLAUDETTE","CATHLEEN","ANGELIA","GABRIELLE","AUTUMN","KATHARINE","SUMMER","JODIE","STACI","LEA","CHRISTI","JIMMIE",
"JUSTINE","ELMA","LUELLA","MARGRET","DOMINIQUE","SOCORRO","RENE","MARTINA","MARGO","MAVIS","CALLIE","BOBBI","MARITZA","LUCILE",
"LEANNE","JEANNINE","DEANA","AILEEN","LORIE","LADONNA","WILLA","MANUELA","GALE","SELMA","DOLLY","SYBIL","ABBY","LARA","DALE",
"IVY","DEE","WINNIE","MARCY","LUISA","JERI","MAGDALENA","OFELIA","MEAGAN","AUDRA","MATILDA","LEILA","CORNELIA","BIANCA","SIMONE",
"BETTYE","RANDI","VIRGIE","LATISHA","BARBRA","GEORGINA","ELIZA","LEANN","BRIDGETTE","RHODA","HALEY","ADELA","NOLA","BERNADINE",
"FLOSSIE","ILA","GRETA","RUTHIE","NELDA","MINERVA","LILLY","TERRIE","LETHA","HILARY","ESTELA","VALARIE","BRIANNA","ROSALYN",
"EARLINE","CATALINA","AVA","MIA","CLARISSA","LIDIA","CORRINE","ALEXANDRIA","CONCEPCION","TIA","SHARRON","RAE","DONA","ERICKA",
"JAMI","ELNORA","CHANDRA","LENORE","NEVA","MARYLOU","MELISA","TABATHA","SERENA","AVIS","ALLIE","SOFIA","JEANIE","ODESSA","NANNIE",
"HARRIETT","LORAINE","PENELOPE","MILAGROS","EMILIA","BENITA","ALLYSON","ASHLEE","TANIA","TOMMIE","ESMERALDA","KARINA","EVE",
"PEARLIE","ZELMA","MALINDA","NOREEN","TAMEKA","SAUNDRA","HILLARY","AMIE","ALTHEA","ROSALINDA","JORDAN","LILIA","ALANA","GAY",
"CLARE","ALEJANDRA","ELINOR","MICHAEL","LORRIE","JERRI","DARCY","EARNESTINE","CARMELLA","TAYLOR","NOEMI","MARCIE","LIZA",
"ANNABELLE","LOUISA","EARLENE","MALLORY","CARLENE","NITA","SELENA","TANISHA","KATY","JULIANNE","JOHN","LAKISHA","EDWINA",
"MARICELA","MARGERY","KENYA","DOLLIE","ROXIE","ROSLYN","KATHRINE","NANETTE","CHARMAINE","LAVONNE","ILENE","KRIS","TAMMI",
"SUZETTE","CORINE","KAYE","JERRY","MERLE","CHRYSTAL","LINA","DEANNE","LILIAN","JULIANA","ALINE","LUANN","KASEY","MARYANNE",
"EVANGELINE","COLETTE","MELVA","LAWANDA","YESENIA","NADIA","MADGE","KATHIE","EDDIE","OPHELIA","VALERIA","NONA","MITZI","MARI",
"GEORGETTE","CLAUDINE","FRAN","ALISSA","ROSEANN","LAKEISHA","SUSANNA","REVA","DEIDRE","CHASITY","SHEREE","CARLY","JAMES","ELVIA",
"ALYCE","DEIRDRE","GENA","BRIANA","ARACELI","KATELYN","ROSANNE","WENDI","TESSA","BERTA","MARVA","IMELDA","MARIETTA","MARCI",
"LEONOR","ARLINE","SASHA","MADELYN","JANNA","JULIETTE","DEENA","AURELIA","JOSEFA","AUGUSTA","LILIANA","YOUNG","CHRISTIAN",
"LESSIE","AMALIA","SAVANNAH","ANASTASIA","VILMA","NATALIA","ROSELLA","LYNNETTE","CORINA","ALFREDA","LEANNA","CAREY","AMPARO",
"COLEEN","TAMRA","AISHA","WILDA","KARYN","CHERRY","QUEEN","MAURA","MAI","EVANGELINA","ROSANNA","HALLIE","ERNA","ENID","MARIANA",
"LACY","JULIET","JACKLYN","FREIDA","MADELEINE","MARA","HESTER","CATHRYN","LELIA","CASANDRA","BRIDGETT","ANGELITA","JANNIE",
"DIONNE","ANNMARIE","KATINA","BERYL","PHOEBE","MILLICENT","KATHERYN","DIANN","CARISSA","MARYELLEN","LIZ","LAURI","HELGA","GILDA",
"ADRIAN","RHEA","MARQUITA","HOLLIE","TISHA","TAMERA","ANGELIQUE","FRANCESCA","BRITNEY","KAITLIN","LOLITA","FLORINE","ROWENA",
"REYNA","TWILA","FANNY","JANELL","INES","CONCETTA","BERTIE","ALBA","BRIGITTE","ALYSON","VONDA","PANSY","ELBA","NOELLE","LETITIA",
"KITTY","DEANN","BRANDIE","LOUELLA","LETA","FELECIA","SHARLENE","LESA","BEVERLEY","ROBERT","ISABELLA","HERMINIA","TERRA","CELINA",
"TORI","OCTAVIA","JADE","DENICE","GERMAINE","SIERRA","MICHELL","CORTNEY","NELLY","DORETHA","SYDNEY","DEIDRA","MONIKA","LASHONDA",
"JUDI","CHELSEY","ANTIONETTE","MARGOT","BOBBY","ADELAIDE","NAN","LEEANN","ELISHA","DESSIE","LIBBY","KATHI","GAYLA","LATANYA",
"MINA","MELLISA","KIMBERLEE","JASMIN","RENAE","ZELDA","ELDA","MA","JUSTINA","GUSSIE","EMILIE","CAMILLA","ABBIE","ROCIO","KAITLYN",
"JESSE","EDYTHE","ASHLEIGH","SELINA","LAKESHA","GERI","ALLENE","PAMALA","MICHAELA","DAYNA","CARYN","ROSALIA","SUN","JACQULINE",
"REBECA","MARYBETH","KRYSTLE","IOLA","DOTTIE","BENNIE","BELLE","AUBREY","GRISELDA","ERNESTINA","ELIDA","ADRIANNE","DEMETRIA",
"DELMA","CHONG","JAQUELINE","DESTINY","ARLEEN","VIRGINA","RETHA","FATIMA","TILLIE","ELEANORE","CARI","TREVA","BIRDIE","WILHELMINA",
"ROSALEE","MAURINE","LATRICE","YONG","JENA","TARYN","ELIA","DEBBY","MAUDIE","JEANNA","DELILAH","CATRINA","SHONDA","HORTENCIA",
"THEODORA","TERESITA","ROBBIN","DANETTE","MARYJANE","FREDDIE","DELPHINE","BRIANNE","NILDA","DANNA","CINDI","BESS","IONA","HANNA",
"ARIEL","WINONA","VIDA","ROSITA","MARIANNA","WILLIAM","RACHEAL","GUILLERMINA","ELOISA","CELESTINE","CAREN","MALISSA","LONA",
"CHANTEL","SHELLIE","MARISELA","LEORA","AGATHA","SOLEDAD","MIGDALIA","IVETTE","CHRISTEN","ATHENA","JANEL","CHLOE","VEDA","PATTIE",
"TESSIE","TERA","MARILYNN","LUCRETIA","KARRIE","DINAH","DANIELA","ALECIA","ADELINA","VERNICE","SHIELA","PORTIA","MERRY","LASHAWN",
"DEVON","DARA","TAWANA","OMA","VERDA","CHRISTIN","ALENE","ZELLA","SANDI","RAFAELA","MAYA","KIRA","CANDIDA","ALVINA","SUZAN",
"SHAYLA","LYN","LETTIE","ALVA","SAMATHA","ORALIA","MATILDE","MADONNA","LARISSA","VESTA","RENITA","INDIA","DELOIS","SHANDA",
"PHILLIS","LORRI","ERLINDA","CRUZ","CATHRINE","BARB","ZOE","ISABELL","IONE","GISELA","CHARLIE","VALENCIA","ROXANNA","MAYME",
"KISHA","ELLIE","MELLISSA","DORRIS","DALIA","BELLA","ANNETTA","ZOILA","RETA","REINA","LAURETTA","KYLIE","CHRISTAL","PILAR",
"CHARLA","ELISSA","TIFFANI","TANA","PAULINA","LEOTA","BREANNA","JAYME","CARMEL","VERNELL","TOMASA","MANDI","DOMINGA","SANTA",
"MELODIE","LURA","ALEXA","TAMELA","RYAN","MIRNA","KERRIE","VENUS","NOEL","FELICITA","CRISTY","CARMELITA","BERNIECE","ANNEMARIE",
"TIARA","ROSEANNE","MISSY","CORI","ROXANA","PRICILLA","KRISTAL","JUNG","ELYSE","HAYDEE","ALETHA","BETTINA","MARGE","GILLIAN",
"FILOMENA","CHARLES","ZENAIDA","HARRIETTE","CARIDAD","VADA","UNA","ARETHA","PEARLINE","MARJORY","MARCELA","FLOR","EVETTE",
"ELOUISE","ALINA","TRINIDAD","DAVID","DAMARIS","CATHARINE","CARROLL","BELVA","NAKIA","MARLENA","LUANNE","LORINE","KARON","DORENE",
"DANITA","BRENNA","TATIANA","SAMMIE","LOUANN","LOREN","JULIANNA","ANDRIA","PHILOMENA","LUCILA","LEONORA","DOVIE","ROMONA","MIMI",
"JACQUELIN","GAYE","TONJA","MISTI","JOE","GENE","CHASTITY","STACIA","ROXANN","MICAELA","NIKITA","MEI","VELDA","MARLYS","JOHNNA",
"AURA","LAVERN","IVONNE","HAYLEY","NICKI","MAJORIE","HERLINDA","GEORGE","ALPHA","YADIRA","PERLA","GREGORIA","DANIEL","ANTONETTE",
"SHELLI","MOZELLE","MARIAH","JOELLE","CORDELIA","JOSETTE","CHIQUITA","TRISTA","LOUIS","LAQUITA","GEORGIANA","CANDI","SHANON",
"LONNIE","HILDEGARD","CECIL","VALENTINA","STEPHANY","MAGDA","KAROL","GERRY","GABRIELLA","TIANA","ROMA","RICHELLE","RAY",
"PRINCESS","OLETA","JACQUE","IDELLA","ALAINA","SUZANNA","JOVITA","BLAIR","TOSHA","RAVEN","NEREIDA","MARLYN","KYLA","JOSEPH",
"DELFINA","TENA","STEPHENIE","SABINA","NATHALIE","MARCELLE","GERTIE","DARLEEN","THEA","SHARONDA","SHANTEL","BELEN","VENESSA",
"ROSALINA","ONA","GENOVEVA","COREY","CLEMENTINE","ROSALBA","RENATE","RENATA","MI","IVORY","GEORGIANNA","FLOY","DORCAS","ARIANA",
"TYRA","THEDA","MARIAM","JULI","JESICA","DONNIE","VIKKI","VERLA","ROSELYN","MELVINA","JANNETTE","GINNY","DEBRAH","CORRIE","ASIA",
"VIOLETA","MYRTIS","LATRICIA","COLLETTE","CHARLEEN","ANISSA","VIVIANA","TWYLA","PRECIOUS","NEDRA","LATONIA","LAN","HELLEN",
"FABIOLA","ANNAMARIE","ADELL","SHARYN","CHANTAL","NIKI","MAUD","LIZETTE","LINDY","KIA","KESHA","JEANA","DANELLE","CHARLINE",
"CHANEL","CARROL","VALORIE","LIA","DORTHA","CRISTAL","SUNNY","LEONE","LEILANI","GERRI","DEBI","ANDRA","KESHIA","IMA","EULALIA",
"EASTER","DULCE","NATIVIDAD","LINNIE","KAMI","GEORGIE","CATINA","BROOK","ALDA","WINNIFRED","SHARLA","RUTHANN","MEAGHAN",
"MAGDALENE","LISSETTE","ADELAIDA","VENITA","TRENA","SHIRLENE","SHAMEKA","ELIZEBETH","DIAN","SHANTA","MICKEY","LATOSHA","CARLOTTA",
"WINDY","SOON","ROSINA","MARIANN","LEISA","JONNIE","DAWNA","CATHIE","BILLY","ASTRID","SIDNEY","LAUREEN","JANEEN","HOLLI","FAWN",
"VICKEY","TERESSA","SHANTE","RUBYE","MARCELINA","CHANDA","CARY","TERESE","SCARLETT","MARTY","MARNIE","LULU","LISETTE","JENIFFER",
"ELENOR","DORINDA","DONITA","CARMAN","BERNITA","ALTAGRACIA","ALETA","ADRIANNA","ZORAIDA","RONNIE","NICOLA","LYNDSEY","KENDALL",
"JANINA","CHRISSY","AMI","STARLA","PHYLIS","PHUONG","KYRA","CHARISSE","BLANCH","SANJUANITA","RONA","NANCI","MARILEE","MARANDA",
"CORY","BRIGETTE","SANJUANA","MARITA","KASSANDRA","JOYCELYN","IRA","FELIPA","CHELSIE","BONNY","MIREYA","LORENZA","KYONG","ILEANA",
"CANDELARIA","TONY","TOBY","SHERIE","OK","MARK","LUCIE","LEATRICE","LAKESHIA","GERDA","EDIE","BAMBI","MARYLIN","LAVON","HORTENSE",
"GARNET","EVIE","TRESSA","SHAYNA","LAVINA","KYUNG","JEANETTA","SHERRILL","SHARA","PHYLISS","MITTIE","ANABEL","ALESIA","THUY",
"TAWANDA","RICHARD","JOANIE","TIFFANIE","LASHANDA","KARISSA","ENRIQUETA","DARIA","DANIELLA","CORINNA","ALANNA","ABBEY","ROXANE",
"ROSEANNA","MAGNOLIA","LIDA","KYLE","JOELLEN","ERA","CORAL","CARLEEN","TRESA","PEGGIE","NOVELLA","NILA","MAYBELLE","JENELLE",
"CARINA","NOVA","MELINA","MARQUERITE","MARGARETTE","JOSEPHINA","EVONNE","DEVIN","CINTHIA","ALBINA","TOYA","TAWNYA","SHERITA",
"SANTOS","MYRIAM","LIZABETH","LISE","KEELY","JENNI","GISELLE","CHERYLE","ARDITH","ARDIS","ALESHA","ADRIANE","SHAINA","LINNEA",
"KAROLYN","HONG","FLORIDA","FELISHA","DORI","DARCI","ARTIE","ARMIDA","ZOLA","XIOMARA","VERGIE","SHAMIKA","NENA","NANNETTE","MAXIE",
"LOVIE","JEANE","JAIMIE","INGE","FARRAH","ELAINA","CAITLYN","STARR","FELICITAS","CHERLY","CARYL","YOLONDA","YASMIN","TEENA",
"PRUDENCE","PENNIE","NYDIA","MACKENZIE","ORPHA","MARVEL","LIZBETH","LAURETTE","JERRIE","HERMELINDA","CAROLEE","TIERRA","MIRIAN",
"META","MELONY","KORI","JENNETTE","JAMILA","ENA","ANH","YOSHIKO","SUSANNAH","SALINA","RHIANNON","JOLEEN","CRISTINE","ASHTON",
"ARACELY","TOMEKA","SHALONDA","MARTI","LACIE","KALA","JADA","ILSE","HAILEY","BRITTANI","ZONA","SYBLE","SHERRYL","RANDY","NIDIA",
"MARLO","KANDICE","KANDI","DEB","DEAN","AMERICA","ALYCIA","TOMMY","RONNA","NORENE","MERCY","JOSE","INGEBORG","GIOVANNA","GEMMA",
"CHRISTEL","AUDRY","ZORA","VITA","VAN","TRISH","STEPHAINE","SHIRLEE","SHANIKA","MELONIE","MAZIE","JAZMIN","INGA","HOA","HETTIE",
"GERALYN","FONDA","ESTRELLA","ADELLA","SU","SARITA","RINA","MILISSA","MARIBETH","GOLDA","EVON","ETHELYN","ENEDINA","CHERISE",
"CHANA","VELVA","TAWANNA","SADE","MIRTA","LI","KARIE","JACINTA","ELNA","DAVINA","CIERRA","ASHLIE","ALBERTHA","TANESHA","STEPHANI",
"NELLE","MINDI","LU","LORINDA","LARUE","FLORENE","DEMETRA","DEDRA","CIARA","CHANTELLE","ASHLY","SUZY","ROSALVA","NOELIA","LYDA",
"LEATHA","KRYSTYNA","KRISTAN","KARRI","DARLINE","DARCIE","CINDA","CHEYENNE","CHERRIE","AWILDA","ALMEDA","ROLANDA","LANETTE",
"JERILYN","GISELE","EVALYN","CYNDI","CLETA","CARIN","ZINA","ZENA","VELIA","TANIKA","PAUL","CHARISSA","THOMAS","TALIA","MARGARETE",
"LAVONDA","KAYLEE","KATHLENE","JONNA","IRENA","ILONA","IDALIA","CANDIS","CANDANCE","BRANDEE","ANITRA","ALIDA","SIGRID","NICOLETTE",
"MARYJO","LINETTE","HEDWIG","CHRISTIANA","CASSIDY","ALEXIA","TRESSIE","MODESTA","LUPITA","LITA","GLADIS","EVELIA","DAVIDA",
"CHERRI","CECILY","ASHELY","ANNABEL","AGUSTINA","WANITA","SHIRLY","ROSAURA","HULDA","EUN","BAILEY","YETTA","VERONA","THOMASINA",
"SIBYL","SHANNAN","MECHELLE","LUE","LEANDRA","LANI","KYLEE","KANDY","JOLYNN","FERNE","EBONI","CORENE","ALYSIA","ZULA","NADA",
"MOIRA","LYNDSAY","LORRETTA","JUAN","JAMMIE","HORTENSIA","GAYNELL","CAMERON","ADRIA","VINA","VICENTA","TANGELA","STEPHINE",
"NORINE","NELLA","LIANA","LESLEE","KIMBERELY","ILIANA","GLORY","FELICA","EMOGENE","ELFRIEDE","EDEN","EARTHA","CARMA","BEA","OCIE",
"MARRY","LENNIE","KIARA","JACALYN","CARLOTA","ARIELLE","YU","STAR","OTILIA","KIRSTIN","KACEY","JOHNETTA","JOEY","JOETTA",
"JERALDINE","JAUNITA","ELANA","DORTHEA","CAMI","AMADA","ADELIA","VERNITA","TAMAR","SIOBHAN","RENEA","RASHIDA","OUIDA","ODELL",
"NILSA","MERYL","KRISTYN","JULIETA","DANICA","BREANNE","AUREA","ANGLEA","SHERRON","ODETTE","MALIA","LORELEI","LIN","LEESA",
"KENNA","KATHLYN","FIONA","CHARLETTE","SUZIE","SHANTELL","SABRA","RACQUEL","MYONG","MIRA","MARTINE","LUCIENNE","LAVADA","JULIANN",
"JOHNIE","ELVERA","DELPHIA","CLAIR","CHRISTIANE","CHAROLETTE","CARRI","AUGUSTINE","ASHA","ANGELLA","PAOLA","NINFA","LEDA","LAI",
"EDA","SUNSHINE","STEFANI","SHANELL","PALMA","MACHELLE","LISSA","KECIA","KATHRYNE","KARLENE","JULISSA","JETTIE","JENNIFFER","HUI",
"CORRINA","CHRISTOPHER","CAROLANN","ALENA","TESS","ROSARIA","MYRTICE","MARYLEE","LIANE","KENYATTA","JUDIE","JANEY","IN","ELMIRA",
"ELDORA","DENNA","CRISTI","CATHI","ZAIDA","VONNIE","VIVA","VERNIE","ROSALINE","MARIELA","LUCIANA","LESLI","KARAN","FELICE",
"DENEEN","ADINA","WYNONA","TARSHA","SHERON","SHASTA","SHANITA","SHANI","SHANDRA","RANDA","PINKIE","PARIS","NELIDA","MARILOU",
"LYLA","LAURENE","LACI","JOI","JANENE","DOROTHA","DANIELE","DANI","CAROLYNN","CARLYN","BERENICE","AYESHA","ANNELIESE","ALETHEA",
"THERSA","TAMIKO","RUFINA","OLIVA","MOZELL","MARYLYN","MADISON","KRISTIAN","KATHYRN","KASANDRA","KANDACE","JANAE","GABRIEL",
"DOMENICA","DEBBRA","DANNIELLE","CHUN","BUFFY","BARBIE","ARCELIA","AJA","ZENOBIA","SHAREN","SHAREE","PATRICK","PAGE","MY",
"LAVINIA","KUM","KACIE","JACKELINE","HUONG","FELISA","EMELIA","ELEANORA","CYTHIA","CRISTIN","CLYDE","CLARIBEL","CARON",
"ANASTACIA","ZULMA","ZANDRA","YOKO","TENISHA","SUSANN","SHERILYN","SHAY","SHAWANDA","SABINE","ROMANA","MATHILDA","LINSEY",
"KEIKO","JOANA","ISELA","GRETTA","GEORGETTA","EUGENIE","DUSTY","DESIRAE","DELORA","CORAZON","ANTONINA","ANIKA","WILLENE","TRACEE",
"TAMATHA","REGAN","NICHELLE","MICKIE","MAEGAN","LUANA","LANITA","KELSIE","EDELMIRA","BREE","AFTON","TEODORA","TAMIE","SHENA",
"MEG","LINH","KELI","KACI","DANYELLE","BRITT","ARLETTE","ALBERTINE","ADELLE","TIFFINY","STORMY","SIMONA","NUMBERS","NICOLASA",
"NICHOL","NIA","NAKISHA","MEE","MAIRA","LOREEN","KIZZY","JOHNNY","JAY","FALLON","CHRISTENE","BOBBYE","ANTHONY","YING","VINCENZA",
"TANJA","RUBIE","RONI","QUEENIE","MARGARETT","KIMBERLI","IRMGARD","IDELL","HILMA","EVELINA","ESTA","EMILEE","DENNISE","DANIA",
"CARL","CARIE","ANTONIO","WAI","SANG","RISA","RIKKI","PARTICIA","MUI","MASAKO","MARIO","LUVENIA","LOREE","LONI","LIEN","KEVIN",
"GIGI","FLORENCIA","DORIAN","DENITA","DALLAS","CHI","BILLYE","ALEXANDER","TOMIKA","SHARITA","RANA","NIKOLE","NEOMA","MARGARITE",
"MADALYN","LUCINA","LAILA","KALI","JENETTE","GABRIELE","EVELYNE","ELENORA","CLEMENTINA","ALEJANDRINA","ZULEMA","VIOLETTE",
"VANNESSA","THRESA","RETTA","PIA","PATIENCE","NOELLA","NICKIE","JONELL","DELTA","CHUNG","CHAYA","CAMELIA","BETHEL","ANYA",
"ANDREW","THANH","SUZANN","SPRING","SHU","MILA","LILLA","LAVERNA","KEESHA","KATTIE","GIA","GEORGENE","EVELINE","ESTELL","ELIZBETH",
"VIVIENNE","VALLIE","TRUDIE","STEPHANE","MICHEL","MAGALY","MADIE","KENYETTA","KARREN","JANETTA","HERMINE","HARMONY","DRUCILLA",
"DEBBI","CELESTINA","CANDIE","BRITNI","BECKIE","AMINA","ZITA","YUN","YOLANDE","VIVIEN","VERNETTA","TRUDI","SOMMER","PEARLE",
"PATRINA","OSSIE","NICOLLE","LOYCE","LETTY","LARISA","KATHARINA","JOSELYN","JONELLE","JENELL","IESHA","HEIDE","FLORINDA",
"FLORENTINA","FLO","ELODIA","DORINE","BRUNILDA","BRIGID","ASHLI","ARDELLA","TWANA","THU","TARAH","SUNG","SHEA","SHAVON","SHANE",
"SERINA","RAYNA","RAMONITA","NGA","MARGURITE","LUCRECIA","KOURTNEY","KATI","JESUS","JESENIA","DIAMOND","CRISTA","AYANA","ALICA",
"ALIA","VINNIE","SUELLEN","ROMELIA","RACHELL","PIPER","OLYMPIA","MICHIKO","KATHALEEN","JOLIE","JESSI","JANESSA","HANA","HA",
"ELEASE","CARLETTA","BRITANY","SHONA","SALOME","ROSAMOND","REGENA","RAINA","NGOC","NELIA","LOUVENIA","LESIA","LATRINA","LATICIA",
"LARHONDA","JINA","JACKI","HOLLIS","HOLLEY","EMMY","DEEANN","CORETTA","ARNETTA","VELVET","THALIA","SHANICE","NETA","MIKKI","MICKI",
"LONNA","LEANA","LASHUNDA","KILEY","JOYE","JACQULYN","IGNACIA","HYUN","HIROKO","HENRY","HENRIETTE","ELAYNE","DELINDA","DARNELL",
"DAHLIA","COREEN","CONSUELA","CONCHITA","CELINE","BABETTE","AYANNA","ANETTE","ALBERTINA","SKYE","SHAWNEE","SHANEKA","QUIANA",
"PAMELIA","MIN","MERRI","MERLENE","MARGIT","KIESHA","KIERA","KAYLENE","JODEE","JENISE","ERLENE","EMMIE","ELSE","DARYL","DALILA",
"DAISEY","CODY","CASIE","BELIA","BABARA","VERSIE","VANESA","SHELBA","SHAWNDA","SAM","NORMAN","NIKIA","NAOMA","MARNA","MARGERET",
"MADALINE","LAWANA","KINDRA","JUTTA","JAZMINE","JANETT","HANNELORE","GLENDORA","GERTRUD","GARNETT","FREEDA","FREDERICA","FLORANCE",
"FLAVIA","DENNIS","CARLINE","BEVERLEE","ANJANETTE","VALDA","TRINITY","TAMALA","STEVIE","SHONNA","SHA","SARINA","ONEIDA","MICAH",
"MERILYN","MARLEEN","LURLINE","LENNA","KATHERIN","JIN","JENI","HAE","GRACIA","GLADY","FARAH","ERIC","ENOLA","EMA","DOMINQUE",
"DEVONA","DELANA","CECILA","CAPRICE","ALYSHA","ALI","ALETHIA","VENA","THERESIA","TAWNY","SONG","SHAKIRA","SAMARA","SACHIKO",
"RACHELE","PAMELLA","NICKY","MARNI","MARIEL","MAREN","MALISA","LIGIA","LERA","LATORIA","LARAE","KIMBER","KATHERN","KAREY",
"JENNEFER","JANETH","HALINA","FREDIA","DELISA","DEBROAH","CIERA","CHIN","ANGELIKA","ANDREE","ALTHA","YEN","VIVAN","TERRESA",
"TANNA","SUK","SUDIE","SOO","SIGNE","SALENA","RONNI","REBBECCA","MYRTIE","MCKENZIE","MALIKA","MAIDA","LOAN","LEONARDA","KAYLEIGH",
"FRANCE","ETHYL","ELLYN","DAYLE","CAMMIE","BRITTNI","BIRGIT","AVELINA","ASUNCION","ARIANNA","AKIKO","VENICE","TYESHA","TONIE",
"TIESHA","TAKISHA","STEFFANIE","SINDY","SANTANA","MEGHANN","MANDA","MACIE","LADY","KELLYE","KELLEE","JOSLYN","JASON","INGER",
"INDIRA","GLINDA","GLENNIS","FERNANDA","FAUSTINA","ENEIDA","ELICIA","DOT","DIGNA","DELL","ARLETTA","ANDRE","WILLIA","TAMMARA",
"TABETHA","SHERRELL","SARI","REFUGIO","REBBECA","PAULETTA","NIEVES","NATOSHA","NAKITA","MAMMIE","KENISHA","KAZUKO","KASSIE",
"GARY","EARLEAN","DAPHINE","CORLISS","CLOTILDE","CAROLYNE","BERNETTA","AUGUSTINA","AUDREA","ANNIS","ANNABELL","YAN","TENNILLE",
"TAMICA","SELENE","SEAN","ROSANA","REGENIA","QIANA","MARKITA","MACY","LEEANNE","LAURINE","KYM","JESSENIA","JANITA","GEORGINE",
"GENIE","EMIKO","ELVIE","DEANDRA","DAGMAR","CORIE","COLLEN","CHERISH","ROMAINE","PORSHA","PEARLENE","MICHELINE","MERNA","MARGORIE",
"MARGARETTA","LORE","KENNETH","JENINE","HERMINA","FREDERICKA","ELKE","DRUSILLA","DORATHY","DIONE","DESIRE","CELENA","BRIGIDA",
"ANGELES","ALLEGRA","THEO","TAMEKIA","SYNTHIA","STEPHEN","SOOK","SLYVIA","ROSANN","REATHA","RAYE","MARQUETTA","MARGART","LING",
"LAYLA","KYMBERLY","KIANA","KAYLEEN","KATLYN","KARMEN","JOELLA","IRINA","EMELDA","ELENI","DETRA","CLEMMIE","CHERYLL","CHANTELL",
"CATHEY","ARNITA","ARLA","ANGLE","ANGELIC","ALYSE","ZOFIA","THOMASINE","TENNIE","SON","SHERLY","SHERLEY","SHARYL","REMEDIOS",
"PETRINA","NICKOLE","MYUNG","MYRLE","MOZELLA","LOUANNE","LISHA","LATIA","LANE","KRYSTA","JULIENNE","JOEL","JEANENE","JACQUALINE",
"ISAURA","GWENDA","EARLEEN","DONALD","CLEOPATRA","CARLIE","AUDIE","ANTONIETTA","ALISE","ALEX","VERDELL","VAL","TYLER","TOMOKO",
"THAO","TALISHA","STEVEN","SO","SHEMIKA","SHAUN","SCARLET","SAVANNA","SANTINA","ROSIA","RAEANN","ODILIA","NANA","MINNA","MAGAN",
"LYNELLE","LE","KARMA","JOEANN","IVANA","INELL","ILANA","HYE","HONEY","HEE","GUDRUN","FRANK","DREAMA","CRISSY","CHANTE",
"CARMELINA","ARVILLA","ARTHUR","ANNAMAE","ALVERA","ALEIDA","AARON","YEE","YANIRA","VANDA","TIANNA","TAM","STEFANIA","SHIRA",
"PERRY","NICOL","NANCIE","MONSERRATE","MINH","MELYNDA","MELANY","MATTHEW","LOVELLA","LAURE","KIRBY","KACY","JACQUELYNN","HYON",
"GERTHA","FRANCISCO","ELIANA","CHRISTENA","CHRISTEEN","CHARISE","CATERINA","CARLEY","CANDYCE","ARLENA","AMMIE","YANG","WILLETTE",
"VANITA","TUYET","TINY","SYREETA","SILVA","SCOTT","RONALD","PENNEY","NYLA","MICHAL","MAURICE","MARYAM","MARYA","MAGEN","LUDIE",
"LOMA","LIVIA","LANELL","KIMBERLIE","JULEE","DONETTA","DIEDRA","DENISHA","DEANE","DAWNE","CLARINE","CHERRYL","BRONWYN","BRANDON",
"ALLA","VALERY","TONDA","SUEANN","SORAYA","SHOSHANA","SHELA","SHARLEEN","SHANELLE","NERISSA","MICHEAL","MERIDITH","MELLIE","MAYE",
"MAPLE","MAGARET","LUIS","LILI","LEONILA","LEONIE","LEEANNA","LAVONIA","LAVERA","KRISTEL","KATHEY","KATHE","JUSTIN","JULIAN",
"JIMMY","JANN","ILDA","HILDRED","HILDEGARDE","GENIA","FUMIKO","EVELIN","ERMELINDA","ELLY","DUNG","DOLORIS","DIONNA","DANAE",
"BERNEICE","ANNICE","ALIX","VERENA","VERDIE","TRISTAN","SHAWNNA","SHAWANA","SHAUNNA","ROZELLA","RANDEE","RANAE","MILAGRO",
"LYNELL","LUISE","LOUIE","LOIDA","LISBETH","KARLEEN","JUNITA","JONA","ISIS","HYACINTH","HEDY","GWENN","ETHELENE","ERLINE",
"EDWARD","DONYA","DOMONIQUE","DELICIA","DANNETTE","CICELY","BRANDA","BLYTHE","BETHANN","ASHLYN","ANNALEE","ALLINE","YUKO","VELLA",
"TRANG","TOWANDA","TESHA","SHERLYN","NARCISA","MIGUELINA","MERI","MAYBELL","MARLANA","MARGUERITA","MADLYN","LUNA","LORY",
"LORIANN","LIBERTY","LEONORE","LEIGHANN","LAURICE","LATESHA","LARONDA","KATRICE","KASIE","KARL","KALEY","JADWIGA","GLENNIE",
"GEARLDINE","FRANCINA","EPIFANIA","DYAN","DORIE","DIEDRE","DENESE","DEMETRICE","DELENA","DARBY","CRISTIE","CLEORA","CATARINA",
"CARISA","BERNIE","BARBERA","ALMETA","TRULA","TEREASA","SOLANGE","SHEILAH","SHAVONNE","SANORA","ROCHELL","MATHILDE","MARGARETA",
"MAIA","LYNSEY","LAWANNA","LAUNA","KENA","KEENA","KATIA","JAMEY","GLYNDA","GAYLENE","ELVINA","ELANOR","DANUTA","DANIKA","CRISTEN",
"CORDIE","COLETTA","CLARITA","CARMON","BRYNN","AZUCENA","AUNDREA","ANGELE","YI","WALTER","VERLIE","VERLENE","TAMESHA","SILVANA",
"SEBRINA","SAMIRA","REDA","RAYLENE","PENNI","PANDORA","NORAH","NOMA","MIREILLE","MELISSIA","MARYALICE","LARAINE","KIMBERY",
"KARYL","KARINE","KAM","JOLANDA","JOHANA","JESUSA","JALEESA","JAE","JACQUELYNE","IRISH","ILUMINADA","HILARIA","HANH","GENNIE",
"FRANCIE","FLORETTA","EXIE","EDDA","DREMA","DELPHA","BEV","BARBAR","ASSUNTA","ARDELL","ANNALISA","ALISIA","YUKIKO","YOLANDO",
"WONDA","WEI","WALTRAUD","VETA","TEQUILA","TEMEKA","TAMEIKA","SHIRLEEN","SHENITA","PIEDAD","OZELLA","MIRTHA","MARILU","KIMIKO",
"JULIANE","JENICE","JEN","JANAY","JACQUILINE","HILDE","FE","FAE","EVAN","EUGENE","ELOIS","ECHO","DEVORAH","CHAU","BRINDA",
"BETSEY","ARMINDA","ARACELIS","APRYL","ANNETT","ALISHIA","VEOLA","USHA","TOSHIKO","THEOLA","TASHIA","TALITHA","SHERY","RUDY",
"RENETTA","REIKO","RASHEEDA","OMEGA","OBDULIA","MIKA","MELAINE","MEGGAN","MARTIN","MARLEN","MARGET","MARCELINE","MANA","MAGDALEN",
"LIBRADA","LEZLIE","LEXIE","LATASHIA","LASANDRA","KELLE","ISIDRA","ISA","INOCENCIA","GWYN","FRANCOISE","ERMINIA","ERINN","DIMPLE",
"DEVORA","CRISELDA","ARMANDA","ARIE","ARIANE","ANGELO","ANGELENA","ALLEN","ALIZA","ADRIENE","ADALINE","XOCHITL","TWANNA","TRAN",
"TOMIKO","TAMISHA","TAISHA","SUSY","SIU","RUTHA","ROXY","RHONA","RAYMOND","OTHA","NORIKO","NATASHIA","MERRIE","MELVIN","MARINDA",
"MARIKO","MARGERT","LORIS","LIZZETTE","LEISHA","KAILA","KA","JOANNIE","JERRICA","JENE","JANNET","JANEE","JACINDA","HERTA",
"ELENORE","DORETTA","DELAINE","DANIELL","CLAUDIE","CHINA","BRITTA","APOLONIA","AMBERLY","ALEASE","YURI","YUK","WEN","WANETA",
"UTE","TOMI","SHARRI","SANDIE","ROSELLE","REYNALDA","RAGUEL","PHYLICIA","PATRIA","OLIMPIA","ODELIA","MITZIE","MITCHELL","MISS",
"MINDA","MIGNON","MICA","MENDY","MARIVEL","MAILE","LYNETTA","LAVETTE","LAURYN","LATRISHA","LAKIESHA","KIERSTEN","KARY","JOSPHINE",
"JOLYN","JETTA","JANISE","JACQUIE","IVELISSE","GLYNIS","GIANNA","GAYNELLE","EMERALD","DEMETRIUS","DANYELL","DANILLE","DACIA",
"CORALEE","CHER","CEOLA","BRETT","BELL","ARIANNE","ALESHIA","YUNG","WILLIEMAE","TROY","TRINH","THORA","TAI","SVETLANA","SHERIKA",
"SHEMEKA","SHAUNDA","ROSELINE","RICKI","MELDA","MALLIE","LAVONNA","LATINA","LARRY","LAQUANDA","LALA","LACHELLE","KLARA","KANDIS",
"JOHNA","JEANMARIE","JAYE","HANG","GRAYCE","GERTUDE","EMERITA","EBONIE","CLORINDA","CHING","CHERY","CAROLA","BREANN","BLOSSOM",
"BERNARDINE","BECKI","ARLETHA","ARGELIA","ARA","ALITA","YULANDA","YON","YESSENIA","TOBI","TASIA","SYLVIE","SHIRL","SHIRELY",
"SHERIDAN","SHELLA","SHANTELLE","SACHA","ROYCE","REBECKA","REAGAN","PROVIDENCIA","PAULENE","MISHA","MIKI","MARLINE","MARICA",
"LORITA","LATOYIA","LASONYA","KERSTIN","KENDA","KEITHA","KATHRIN","JAYMIE","JACK","GRICELDA","GINETTE","ERYN","ELINA","ELFRIEDA",
"DANYEL","CHEREE","CHANELLE","BARRIE","AVERY","AURORE","ANNAMARIA","ALLEEN","AILENE","AIDE","YASMINE","VASHTI","VALENTINE",
"TREASA","TORY","TIFFANEY","SHERYLL","SHARIE","SHANAE","SAU","RAISA","PA","NEDA","MITSUKO","MIRELLA","MILDA","MARYANNA","MARAGRET",
"MABELLE","LUETTA","LORINA","LETISHA","LATARSHA","LANELLE","LAJUANA","KRISSY","KARLY","KARENA","JON","JESSIKA","JERICA","JEANELLE",
"JANUARY","JALISA","JACELYN","IZOLA","IVEY","GREGORY","EUNA","ETHA","DREW","DOMITILA","DOMINICA","DAINA","CREOLA","CARLI","CAMIE",
"BUNNY","BRITTNY","ASHANTI","ANISHA","ALEEN","ADAH","YASUKO","WINTER","VIKI","VALRIE","TONA","TINISHA","THI","TERISA","TATUM",
"TANEKA","SIMONNE","SHALANDA","SERITA","RESSIE","REFUGIA","PAZ","OLENE","NA","MERRILL","MARGHERITA","MANDIE","MAN","MAIRE",
"LYNDIA","LUCI","LORRIANE","LORETA","LEONIA","LAVONA","LASHAWNDA","LAKIA","KYOKO","KRYSTINA","KRYSTEN","KENIA","KELSI","JUDE",
"JEANICE","ISOBEL","GEORGIANN","GENNY","FELICIDAD","EILENE","DEON","DELOISE","DEEDEE","DANNIE","CONCEPTION","CLORA","CHERILYN",
"CHANG","CALANDRA","BERRY","ARMANDINA","ANISA","ULA","TIMOTHY","TIERA","THERESSA","STEPHANIA","SIMA","SHYLA","SHONTA","SHERA",
"SHAQUITA","SHALA","SAMMY","ROSSANA","NOHEMI","NERY","MORIAH","MELITA","MELIDA","MELANI","MARYLYNN","MARISHA","MARIETTE","MALORIE",
"MADELENE","LUDIVINA","LORIA","LORETTE","LORALEE","LIANNE","LEON","LAVENIA","LAURINDA","LASHON","KIT","KIMI","KEILA","KATELYNN",
"KAI","JONE","JOANE","JI","JAYNA","JANELLA","JA","HUE","HERTHA","FRANCENE","ELINORE","DESPINA","DELSIE","DEEDRA","CLEMENCIA",
"CARRY","CAROLIN","CARLOS","BULAH","BRITTANIE","BOK","BLONDELL","BIBI","BEAULAH","BEATA","ANNITA","AGRIPINA","VIRGEN","VALENE",
"UN","TWANDA","TOMMYE","TOI","TARRA","TARI","TAMMERA","SHAKIA","SADYE","RUTHANNE","ROCHEL","RIVKA","PURA","NENITA","NATISHA",
"MING","MERRILEE","MELODEE","MARVIS","LUCILLA","LEENA","LAVETA","LARITA","LANIE","KEREN","ILEEN","GEORGEANN","GENNA","GENESIS",
"FRIDA","EWA","EUFEMIA","EMELY","ELA","EDYTH","DEONNA","DEADRA","DARLENA","CHANELL","CHAN","CATHERN","CASSONDRA","CASSAUNDRA",
"BERNARDA","BERNA","ARLINDA","ANAMARIA","ALBERT","WESLEY","VERTIE","VALERI","TORRI","TATYANA","STASIA","SHERISE","SHERILL",
"SEASON","SCOTTIE","SANDA","RUTHE","ROSY","ROBERTO","ROBBI","RANEE","QUYEN","PEARLY","PALMIRA","ONITA","NISHA","NIESHA","NIDA",
"NEVADA","NAM","MERLYN","MAYOLA","MARYLOUISE","MARYLAND","MARX","MARTH","MARGENE","MADELAINE","LONDA","LEONTINE","LEOMA","LEIA",
"LAWRENCE","LAURALEE","LANORA","LAKITA","KIYOKO","KETURAH","KATELIN","KAREEN","JONIE","JOHNETTE","JENEE","JEANETT","IZETTA",
"HIEDI","HEIKE","HASSIE","HAROLD","GIUSEPPINA","GEORGANN","FIDELA","FERNANDE","ELWANDA","ELLAMAE","ELIZ","DUSTI","DOTTY","CYNDY",
"CORALIE","CELESTA","ARGENTINA","ALVERTA","XENIA","WAVA","VANETTA","TORRIE","TASHINA","TANDY","TAMBRA","TAMA","STEPANIE","SHILA",
"SHAUNTA","SHARAN","SHANIQUA","SHAE","SETSUKO","SERAFINA","SANDEE","ROSAMARIA","PRISCILA","OLINDA","NADENE","MUOI","MICHELINA",
"MERCEDEZ","MARYROSE","MARIN","MARCENE","MAO","MAGALI","MAFALDA","LOGAN","LINN","LANNIE","KAYCE","KAROLINE","KAMILAH","KAMALA",
"JUSTA","JOLINE","JENNINE","JACQUETTA","IRAIDA","GERALD","GEORGEANNA","FRANCHESCA","FAIRY","EMELINE","ELANE","EHTEL","EARLIE",
"DULCIE","DALENE","CRIS","CLASSIE","CHERE","CHARIS","CAROYLN","CARMINA","CARITA","BRIAN","BETHANIE","AYAKO","ARICA","AN","ALYSA",
"ALESSANDRA","AKILAH","ADRIEN","ZETTA","YOULANDA","YELENA","YAHAIRA","XUAN","WENDOLYN","VICTOR","TIJUANA","TERRELL","TERINA",
"TERESIA","SUZI","SUNDAY","SHERELL","SHAVONDA","SHAUNTE","SHARDA","SHAKITA","SENA","RYANN","RUBI","RIVA","REGINIA","REA","RACHAL",
"PARTHENIA","PAMULA","MONNIE","MONET","MICHAELE","MELIA","MARINE","MALKA","MAISHA","LISANDRA","LEO","LEKISHA","LEAN","LAURENCE",
"LAKENDRA","KRYSTIN","KORTNEY","KIZZIE","KITTIE","KERA","KENDAL","KEMBERLY","KANISHA","JULENE","JULE","JOSHUA","JOHANNE","JEFFREY",
"JAMEE","HAN","HALLEY","GIDGET","GALINA","FREDRICKA","FLETA","FATIMAH","EUSEBIA","ELZA","ELEONORE","DORTHEY","DORIA","DONELLA",
"DINORAH","DELORSE","CLARETHA","CHRISTINIA","CHARLYN","BONG","BELKIS","AZZIE","ANDERA","AIKO","ADENA","YER","YAJAIRA","WAN",
"VANIA","ULRIKE","TOSHIA","TIFANY","STEFANY","SHIZUE","SHENIKA","SHAWANNA","SHAROLYN","SHARILYN","SHAQUANA","SHANTAY","SEE",
"ROZANNE","ROSELEE","RICKIE","REMONA","REANNA","RAELENE","QUINN","PHUNG","PETRONILA","NATACHA","NANCEY","MYRL","MIYOKO","MIESHA",
"MERIDETH","MARVELLA","MARQUITTA","MARHTA","MARCHELLE","LIZETH","LIBBIE","LAHOMA","LADAWN","KINA","KATHELEEN","KATHARYN","KARISA",
"KALEIGH","JUNIE","JULIEANN","JOHNSIE","JANEAN","JAIMEE","JACKQUELINE","HISAKO","HERMA","HELAINE","GWYNETH","GLENN","GITA",
"EUSTOLIA","EMELINA","ELIN","EDRIS","DONNETTE","DONNETTA","DIERDRE","DENAE","DARCEL","CLAUDE","CLARISA","CINDERELLA","CHIA",
"CHARLESETTA","CHARITA","CELSA","CASSY","CASSI","CARLEE","BRUNA","BRITTANEY","BRANDE","BILLI","BAO","ANTONETTA","ANGLA","ANGELYN",
"ANALISA","ALANE","WENONA","WENDIE","VERONIQUE","VANNESA","TOBIE","TEMPIE","SUMIKO","SULEMA","SPARKLE","SOMER","SHEBA","SHAYNE",
"SHARICE","SHANEL","SHALON","SAGE","ROY","ROSIO","ROSELIA","RENAY","REMA","REENA","PORSCHE","PING","PEG","OZIE","ORETHA","ORALEE",
"ODA","NU","NGAN","NAKESHA","MILLY","MARYBELLE","MARLIN","MARIS","MARGRETT","MARAGARET","MANIE","LURLENE","LILLIA","LIESELOTTE",
"LAVELLE","LASHAUNDA","LAKEESHA","KEITH","KAYCEE","KALYN","JOYA","JOETTE","JENAE","JANIECE","ILLA","GRISEL","GLAYDS","GENEVIE",
"GALA","FREDDA","FRED","ELMER","ELEONOR","DEBERA","DEANDREA","DAN","CORRINNE","CORDIA","CONTESSA","COLENE","CLEOTILDE","CHARLOTT",
"CHANTAY","CECILLE","BEATRIS","AZALEE","ARLEAN","ARDATH","ANJELICA","ANJA","ALFREDIA","ALEISHA","ADAM","ZADA","YUONNE","XIAO",
"WILLODEAN","WHITLEY","VENNIE","VANNA","TYISHA","TOVA","TORIE","TONISHA","TILDA","TIEN","TEMPLE","SIRENA","SHERRIL","SHANTI",
"SHAN","SENAIDA","SAMELLA","ROBBYN","RENDA","REITA","PHEBE","PAULITA","NOBUKO","NGUYET","NEOMI","MOON","MIKAELA","MELANIA",
"MAXIMINA","MARG","MAISIE","LYNNA","LILLI","LAYNE","LASHAUN","LAKENYA","LAEL","KIRSTIE","KATHLINE","KASHA","KARLYN","KARIMA",
"JOVAN","JOSEFINE","JENNELL","JACQUI","JACKELYN","HYO","HIEN","GRAZYNA","FLORRIE","FLORIA","ELEONORA","DWANA","DORLA","DONG",
"DELMY","DEJA","DEDE","DANN","CRYSTA","CLELIA","CLARIS","CLARENCE","CHIEKO","CHERLYN","CHERELLE","CHARMAIN","CHARA","CAMMY","BEE",
"ARNETTE","ARDELLE","ANNIKA","AMIEE","AMEE","ALLENA","YVONE","YUKI","YOSHIE","YEVETTE","YAEL","WILLETTA","VONCILE","VENETTA",
"TULA","TONETTE","TIMIKA","TEMIKA","TELMA","TEISHA","TAREN","TA","STACEE","SHIN","SHAWNTA","SATURNINA","RICARDA","POK","PASTY",
"ONIE","NUBIA","MORA","MIKE","MARIELLE","MARIELLA","MARIANELA","MARDELL","MANY","LUANNA","LOISE","LISABETH","LINDSY","LILLIANA",
"LILLIAM","LELAH","LEIGHA","LEANORA","LANG","KRISTEEN","KHALILAH","KEELEY","KANDRA","JUNKO","JOAQUINA","JERLENE","JANI","JAMIKA",
"JAME","HSIU","HERMILA","GOLDEN","GENEVIVE","EVIA","EUGENA","EMMALINE","ELFREDA","ELENE","DONETTE","DELCIE","DEEANNA","DARCEY",
"CUC","CLARINDA","CIRA","CHAE","CELINDA","CATHERYN","CATHERIN","CASIMIRA","CARMELIA","CAMELLIA","BREANA","BOBETTE","BERNARDINA",
"BEBE","BASILIA","ARLYNE","AMAL","ALAYNA","ZONIA","ZENIA","YURIKO","YAEKO","WYNELL","WILLOW","WILLENA","VERNIA","TU","TRAVIS",
"TORA","TERRILYN","TERICA","TENESHA","TAWNA","TAJUANA","TAINA","STEPHNIE","SONA","SOL","SINA","SHONDRA","SHIZUKO","SHERLENE",
"SHERICE","SHARIKA","ROSSIE","ROSENA","RORY","RIMA","RIA","RHEBA","RENNA","PETER","NATALYA","NANCEE","MELODI","MEDA","MAXIMA",
"MATHA","MARKETTA","MARICRUZ","MARCELENE","MALVINA","LUBA","LOUETTA","LEIDA","LECIA","LAURAN","LASHAWNA","LAINE","KHADIJAH",
"KATERINE","KASI","KALLIE","JULIETTA","JESUSITA","JESTINE","JESSIA","JEREMY","JEFFIE","JANYCE","ISADORA","GEORGIANNE","FIDELIA",
"EVITA","EURA","EULAH","ESTEFANA","ELSY","ELIZABET","ELADIA","DODIE","DION","DIA","DENISSE","DELORAS","DELILA","DAYSI","DAKOTA",
"CURTIS","CRYSTLE","CONCHA","COLBY","CLARETTA","CHU","CHRISTIA","CHARLSIE","CHARLENA","CARYLON","BETTYANN","ASLEY","ASHLEA",
"AMIRA","AI","AGUEDA","AGNUS","YUETTE","VINITA","VICTORINA","TYNISHA","TREENA","TOCCARA","TISH","THOMASENA","TEGAN","SOILA",
"SHILOH","SHENNA","SHARMAINE","SHANTAE","SHANDI","SEPTEMBER","SARAN","SARAI","SANA","SAMUEL","SALLEY","ROSETTE","ROLANDE","REGINE",
"OTELIA","OSCAR","OLEVIA","NICHOLLE","NECOLE","NAIDA","MYRTA","MYESHA","MITSUE","MINTA","MERTIE","MARGY","MAHALIA","MADALENE",
"LOVE","LOURA","LOREAN","LEWIS","LESHA","LEONIDA","LENITA","LAVONE","LASHELL","LASHANDRA","LAMONICA","KIMBRA","KATHERINA","KARRY",
"KANESHA","JULIO","JONG","JENEVA","JAQUELYN","HWA","GILMA","GHISLAINE","GERTRUDIS","FRANSISCA","FERMINA","ETTIE","ETSUKO","ELLIS",
"ELLAN","ELIDIA","EDRA","DORETHEA","DOREATHA","DENYSE","DENNY","DEETTA","DAINE","CYRSTAL","CORRIN","CAYLA","CARLITA","CAMILA",
"BURMA","BULA","BUENA","BLAKE","BARABARA","AVRIL","AUSTIN","ALAINE","ZANA","WILHEMINA","WANETTA","VIRGIL","VI","VERONIKA","VERNON",
"VERLINE","VASILIKI","TONITA","TISA","TEOFILA","TAYNA","TAUNYA","TANDRA","TAKAKO","SUNNI","SUANNE","SIXTA","SHARELL","SEEMA",
"RUSSELL","ROSENDA","ROBENA","RAYMONDE","PEI","PAMILA","OZELL","NEIDA","NEELY","MISTIE","MICHA","MERISSA","MAURITA","MARYLN",
"MARYETTA","MARSHALL","MARCELL","MALENA","MAKEDA","MADDIE","LOVETTA","LOURIE","LORRINE","LORILEE","LESTER","LAURENA","LASHAY",
"LARRAINE","LAREE","LACRESHA","KRISTLE","KRISHNA","KEVA","KEIRA","KAROLE","JOIE","JINNY","JEANNETTA","JAMA","HEIDY","GILBERTE",
"GEMA","FAVIOLA","EVELYNN","ENDA","ELLI","ELLENA","DIVINA","DAGNY","COLLENE","CODI","CINDIE","CHASSIDY","CHASIDY","CATRICE",
"CATHERINA","CASSEY","CAROLL","CARLENA","CANDRA","CALISTA","BRYANNA","BRITTENY","BEULA","BARI","AUDRIE","AUDRIA","ARDELIA",
"ANNELLE","ANGILA","ALONA","ALLYN","DOUGLAS","ROGER","JONATHAN","RALPH","NICHOLAS","BENJAMIN","BRUCE","HARRY","WAYNE","STEVE",
"HOWARD","ERNEST","PHILLIP","TODD","CRAIG","ALAN","PHILIP","EARL","DANNY","BRYAN","STANLEY","LEONARD","NATHAN","MANUEL","RODNEY",
"MARVIN","VINCENT","JEFFERY","JEFF","CHAD","JACOB","ALFRED","BRADLEY","HERBERT","FREDERICK","EDWIN","DON","RICKY","RANDALL",
"BARRY","BERNARD","LEROY","MARCUS","THEODORE","CLIFFORD","MIGUEL","JIM","TOM","CALVIN","BILL","LLOYD","DEREK","WARREN","DARRELL",
"JEROME","FLOYD","ALVIN","TIM","GORDON","GREG","JORGE","DUSTIN","PEDRO","DERRICK","ZACHARY","HERMAN","GLEN","HECTOR","RICARDO",
"RICK","BRENT","RAMON","GILBERT","MARC","REGINALD","RUBEN","NATHANIEL","RAFAEL","EDGAR","MILTON","RAUL","BEN","CHESTER","DUANE",
"FRANKLIN","BRAD","RON","ROLAND","ARNOLD","HARVEY","JARED","ERIK","DARRYL","NEIL","JAVIER","FERNANDO","CLINTON","TED","MATHEW",
"TYRONE","DARREN","LANCE","KURT","ALLAN","NELSON","GUY","CLAYTON","HUGH","MAX","DWAYNE","DWIGHT","ARMANDO","FELIX","EVERETT",
"IAN","WALLACE","KEN","BOB","ALFREDO","ALBERTO","DAVE","IVAN","BYRON","ISAAC","MORRIS","CLIFTON","WILLARD","ROSS","ANDY",
"SALVADOR","KIRK","SERGIO","SETH","KENT","TERRANCE","EDUARDO","TERRENCE","ENRIQUE","WADE","STUART","FREDRICK","ARTURO","ALEJANDRO",
"NICK","LUTHER","WENDELL","JEREMIAH","JULIUS","OTIS","TREVOR","OLIVER","LUKE","HOMER","GERARD","DOUG","KENNY","HUBERT","LYLE",
"MATT","ALFONSO","ORLANDO","REX","CARLTON","ERNESTO","NEAL","PABLO","LORENZO","OMAR","WILBUR","GRANT","HORACE","RODERICK",
"ABRAHAM","WILLIS","RICKEY","ANDRES","CESAR","JOHNATHAN","MALCOLM","RUDOLPH","DAMON","KELVIN","PRESTON","ALTON","ARCHIE","MARCO",
"WM","PETE","RANDOLPH","GARRY","GEOFFREY","JONATHON","FELIPE","GERARDO","ED","DOMINIC","DELBERT","COLIN","GUILLERMO","EARNEST",
"LUCAS","BENNY","SPENCER","RODOLFO","MYRON","EDMUND","GARRETT","SALVATORE","CEDRIC","LOWELL","GREGG","SHERMAN","WILSON",
"SYLVESTER","ROOSEVELT","ISRAEL","JERMAINE","FORREST","WILBERT","LELAND","SIMON","CLARK","IRVING","BRYANT","OWEN","RUFUS",
"WOODROW","KRISTOPHER","MACK","LEVI","MARCOS","GUSTAVO","JAKE","LIONEL","GILBERTO","CLINT","NICOLAS","ISMAEL","ORVILLE","ERVIN",
"DEWEY","AL","WILFRED","JOSH","HUGO","IGNACIO","CALEB","TOMAS","SHELDON","ERICK","STEWART","DOYLE","DARREL","ROGELIO","TERENCE",
"SANTIAGO","ALONZO","ELIAS","BERT","ELBERT","RAMIRO","CONRAD","NOAH","GRADY","PHIL","CORNELIUS","LAMAR","ROLANDO","CLAY","PERCY",
"DEXTER","BRADFORD","DARIN","AMOS","MOSES","IRVIN","SAUL","ROMAN","RANDAL","TIMMY","DARRIN","WINSTON","BRENDAN","ABEL","DOMINICK",
"BOYD","EMILIO","ELIJAH","DOMINGO","EMMETT","MARLON","EMANUEL","JERALD","EDMOND","EMIL","DEWAYNE","WILL","OTTO","TEDDY",
"REYNALDO","BRET","JESS","TRENT","HUMBERTO","EMMANUEL","STEPHAN","VICENTE","LAMONT","GARLAND","MILES","EFRAIN","HEATH","RODGER",
"HARLEY","ETHAN","ELDON","ROCKY","PIERRE","JUNIOR","FREDDY","ELI","BRYCE","ANTOINE","STERLING","CHASE","GROVER","ELTON",
"CLEVELAND","DYLAN","CHUCK","DAMIAN","REUBEN","STAN","AUGUST","LEONARDO","JASPER","RUSSEL","ERWIN","BENITO","HANS","MONTE",
"BLAINE","ERNIE","CURT","QUENTIN","AGUSTIN","MURRAY","JAMAL","ADOLFO","HARRISON","TYSON","BURTON","BRADY","ELLIOTT","WILFREDO",
"BART","JARROD","VANCE","DENIS","DAMIEN","JOAQUIN","HARLAN","DESMOND","ELLIOT","DARWIN","GREGORIO","BUDDY","XAVIER","KERMIT",
"ROSCOE","ESTEBAN","ANTON","SOLOMON","SCOTTY","NORBERT","ELVIN","WILLIAMS","NOLAN","ROD","QUINTON","HAL","BRAIN","ROB","ELWOOD",
"KENDRICK","DARIUS","MOISES","FIDEL","THADDEUS","CLIFF","MARCEL","JACKSON","RAPHAEL","BRYON","ARMAND","ALVARO","JEFFRY","DANE",
"JOESPH","THURMAN","NED","RUSTY","MONTY","FABIAN","REGGIE","MASON","GRAHAM","ISAIAH","VAUGHN","GUS","LOYD","DIEGO","ADOLPH",
"NORRIS","MILLARD","ROCCO","GONZALO","DERICK","RODRIGO","WILEY","RIGOBERTO","ALPHONSO","TY","NOE","VERN","REED","JEFFERSON",
"ELVIS","BERNARDO","MAURICIO","HIRAM","DONOVAN","BASIL","RILEY","NICKOLAS","MAYNARD","SCOT","VINCE","QUINCY","EDDY","SEBASTIAN",
"FEDERICO","ULYSSES","HERIBERTO","DONNELL","COLE","DAVIS","GAVIN","EMERY","WARD","ROMEO","JAYSON","DANTE","CLEMENT","COY",
"MAXWELL","JARVIS","BRUNO","ISSAC","DUDLEY","BROCK","SANFORD","CARMELO","BARNEY","NESTOR","STEFAN","DONNY","ART","LINWOOD","BEAU",
"WELDON","GALEN","ISIDRO","TRUMAN","DELMAR","JOHNATHON","SILAS","FREDERIC","DICK","IRWIN","MERLIN","CHARLEY","MARCELINO","HARRIS",
"CARLO","TRENTON","KURTIS","HUNTER","AURELIO","WINFRED","VITO","COLLIN","DENVER","CARTER","LEONEL","EMORY","PASQUALE","MOHAMMAD",
"MARIANO","DANIAL","LANDON","DIRK","BRANDEN","ADAN","BUFORD","GERMAN","WILMER","EMERSON","ZACHERY","FLETCHER","JACQUES","ERROL",
"DALTON","MONROE","JOSUE","EDWARDO","BOOKER","WILFORD","SONNY","SHELTON","CARSON","THERON","RAYMUNDO","DAREN","HOUSTON","ROBBY",
"LINCOLN","GENARO","BENNETT","OCTAVIO","CORNELL","HUNG","ARRON","ANTONY","HERSCHEL","GIOVANNI","GARTH","CYRUS","CYRIL","RONNY",
"LON","FREEMAN","DUNCAN","KENNITH","CARMINE","ERICH","CHADWICK","WILBURN","RUSS","REID","MYLES","ANDERSON","MORTON","JONAS",
"FOREST","MITCHEL","MERVIN","ZANE","RICH","JAMEL","LAZARO","ALPHONSE","RANDELL","MAJOR","JARRETT","BROOKS","ABDUL","LUCIANO",
"SEYMOUR","EUGENIO","MOHAMMED","VALENTIN","CHANCE","ARNULFO","LUCIEN","FERDINAND","THAD","EZRA","ALDO","RUBIN","ROYAL","MITCH",
"EARLE","ABE","WYATT","MARQUIS","LANNY","KAREEM","JAMAR","BORIS","ISIAH","EMILE","ELMO","ARON","LEOPOLDO","EVERETTE","JOSEF",
"ELOY","RODRICK","REINALDO","LUCIO","JERROD","WESTON","HERSHEL","BARTON","PARKER","LEMUEL","BURT","JULES","GIL","ELISEO","AHMAD",
"NIGEL","EFREN","ANTWAN","ALDEN","MARGARITO","COLEMAN","DINO","OSVALDO","LES","DEANDRE","NORMAND","KIETH","TREY","NORBERTO",
"NAPOLEON","JEROLD","FRITZ","ROSENDO","MILFORD","CHRISTOPER","ALFONZO","LYMAN","JOSIAH","BRANT","WILTON","RICO","JAMAAL","DEWITT",
"BRENTON","OLIN","FOSTER","FAUSTINO","CLAUDIO","JUDSON","GINO","EDGARDO","ALEC","TANNER","JARRED","DONN","TAD","PRINCE","PORFIRIO",
"ODIS","LENARD","CHAUNCEY","TOD","MEL","MARCELO","KORY","AUGUSTUS","KEVEN","HILARIO","BUD","SAL","ORVAL","MAURO","ZACHARIAH",
"OLEN","ANIBAL","MILO","JED","DILLON","AMADO","NEWTON","LENNY","RICHIE","HORACIO","BRICE","MOHAMED","DELMER","DARIO","REYES","MAC",
"JONAH","JERROLD","ROBT","HANK","RUPERT","ROLLAND","KENTON","DAMION","ANTONE","WALDO","FREDRIC","BRADLY","KIP","BURL","WALKER",
"TYREE","JEFFEREY","AHMED","WILLY","STANFORD","OREN","NOBLE","MOSHE","MIKEL","ENOCH","BRENDON","QUINTIN","JAMISON","FLORENCIO",
"DARRICK","TOBIAS","HASSAN","GIUSEPPE","DEMARCUS","CLETUS","TYRELL","LYNDON","KEENAN","WERNER","GERALDO","COLUMBUS","CHET",
"BERTRAM","MARKUS","HUEY","HILTON","DWAIN","DONTE","TYRON","OMER","ISAIAS","HIPOLITO","FERMIN","ADALBERTO","BO","BARRETT",
"TEODORO","MCKINLEY","MAXIMO","GARFIELD","RALEIGH","LAWERENCE","ABRAM","RASHAD","KING","EMMITT","DARON","SAMUAL","MIQUEL",
"EUSEBIO","DOMENIC","DARRON","BUSTER","WILBER","RENATO","JC","HOYT","HAYWOOD","EZEKIEL","CHAS","FLORENTINO","ELROY","CLEMENTE",
"ARDEN","NEVILLE","EDISON","DESHAWN","NATHANIAL","JORDON","DANILO","CLAUD","SHERWOOD","RAYMON","RAYFORD","CRISTOBAL","AMBROSE",
"TITUS","HYMAN","FELTON","EZEQUIEL","ERASMO","STANTON","LONNY","LEN","IKE","MILAN","LINO","JAROD","HERB","ANDREAS","WALTON",
"RHETT","PALMER","DOUGLASS","CORDELL","OSWALDO","ELLSWORTH","VIRGILIO","TONEY","NATHANAEL","DEL","BENEDICT","MOSE","JOHNSON",
"ISREAL","GARRET","FAUSTO","ASA","ARLEN","ZACK","WARNER","MODESTO","FRANCESCO","MANUAL","GAYLORD","GASTON","FILIBERTO","DEANGELO",
"MICHALE","GRANVILLE","WES","MALIK","ZACKARY","TUAN","ELDRIDGE","CRISTOPHER","CORTEZ","ANTIONE","MALCOM","LONG","KOREY","JOSPEH",
"COLTON","WAYLON","VON","HOSEA","SHAD","SANTO","RUDOLF","ROLF","REY","RENALDO","MARCELLUS","LUCIUS","KRISTOFER","BOYCE","BENTON",
"HAYDEN","HARLAND","ARNOLDO","RUEBEN","LEANDRO","KRAIG","JERRELL","JEROMY","HOBERT","CEDRICK","ARLIE","WINFORD","WALLY","LUIGI",
"KENETH","JACINTO","GRAIG","FRANKLYN","EDMUNDO","SID","PORTER","LEIF","JERAMY","BUCK","WILLIAN","VINCENZO","SHON","LYNWOOD","JERE",
"HAI","ELDEN","DORSEY","DARELL","BRODERICK","ALONSO"]
def Problem22():
#Setup the variables
sums = [] #Holds the score based on the sum of the characters in the name
prod = [] #Holds the score based on the sum of the characters and the location in alphabetical order
#Sort all the names
__NAMES.sort()
#Step through every name adding up the values of the characters
for nameCnt in range(0, len(__NAMES)):
#Step through every character in the current name adding up the value of the characters
sums.append(0)
for charCnt in range(0, len(__NAMES[nameCnt])):
#A = 65 so subtracting 64 means A - 1. This will only work correctly if all letters are capitalized
sums[nameCnt] += (ord(__NAMES[nameCnt][charCnt]) - 64)
#Get the product for all numbers
for cnt in range(0, len(sums)):
prod.append(sums[cnt] * (cnt + 1))
#Print the results
print("The answer to the question is " + str(sum(prod)))
#This ensures the correct function is called if this is called as a stand along script
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem22()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The answer to the question is 871198282
It took 9.206 milliseconds to run this algorithm
"""

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#ProjectEuler/Python/Problem23.py
#Matthew Ellison
# Created: 03-22-19
#Modified: 03-28-19
#Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers
#All of my imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
import Algorithms
__maxNum = 28123
#A function that returns true if num can be created by adding two elements from abund and false if it cannot
def isSum(abund: list, num: int) -> bool:
sumOfNums = 0
#Pick a number for the first part of the sum
for firstNum in range(0, len(abund)):
#Pick a number for the second part of the sum
for secondNum in range(0, len(abund)):
sumOfNums = abund[firstNum] + abund[secondNum]
if(sumOfNums == num):
return True
elif(sumOfNums > num):
break
#If you have run through the entire list and did not find a sum then it is false
return False
def Problem23():
#Setup the variables
divisorSums = []
#Make sure every element has a 0 in it's location
for cnt in range(0, __maxNum):
divisorSums.append(0)
#Get the sum of the divisors of all numbers < __maxNum
for cnt in range(1, __maxNum):
div = Algorithms.getDivisors(cnt)
if(len(div) > 1):
div.remove(div[len(div) - 1])
divisorSums[cnt] = sum(div)
#Get the abundant numbers
abund = []
for cnt in range(0, len(divisorSums)):
if(divisorSums[cnt] > cnt):
abund.append(cnt)
#Check if each number can be the sum of 2 abundant numbers and add to the sum if no
sumOfNums = 0
for cnt in range(1, __maxNum):
if(not isSum(abund, cnt)):
sumOfNums += cnt
#Print the results
print("The answer is " + str(sumOfNums))
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem23()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The answer is 4179871
It took 27.738 minutes to run this algorithm
"""

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#ProjectEuler/Python/Problem24.py
#Matthew Ellison
# Created: 03-24-19
#Modified: 03-28-19
#What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
import Algorithms
__neededPerm = 1000000 #The number of the permutation that you need
def Problem24():
#Setup the variables
nums = "0123456789"
#Get all permutations of the string
permutations = Algorithms.getPermutations(nums)
#Print the results
print("The 1 millionth permutation is " + str(permutations[__neededPerm - 1]))
#This calls the appropriate functions if the script is called stand alone
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem24()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The 1 millionth permutation is 2783915460
It took 7.363 seconds to run this algorithm
"""

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#ProjectEuler/Python/Problem25.py
#Matthew Ellison
# Created: 03-25-19
#Modified: 03-28-19
#What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
import Algorithms
__numDigits = 1000 #The number of digits to calculate up to
def Problem25():
#Setup the variables
number = 0 #The current Fibonacci number
index = 2 #The index of the just calculated Fibonacci number
#Move through all Fibonacci numbers until you reach the one with at least __numDigits digits
while(len(str(number)) < __numDigits):
index += 1 #Increase the index number. Doing this at the beginning keeps the index correct at the end of the loop
number = Algorithms.getFib(index) #Calculate the number
#Print the results
print("The first Fibonacci number with " + str(__numDigits) + " digits is " + str(number))
print("Its index is " + str(index))
#This runs the appropriate functions if the script is called by itself
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem25()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The first Fibonacci number with 1000 digits is 1070066266382758936764980584457396885083683896632151665013235203375314520604694040621889147582489792657804694888177591957484336466672569959512996030461262748092482186144069433051234774442750273781753087579391666192149259186759553966422837148943113074699503439547001985432609723067290192870526447243726117715821825548491120525013201478612965931381792235559657452039506137551467837543229119602129934048260706175397706847068202895486902666185435124521900369480641357447470911707619766945691070098024393439617474103736912503231365532164773697023167755051595173518460579954919410967778373229665796581646513903488154256310184224190259846088000110186255550245493937113651657039447629584714548523425950428582425306083544435428212611008992863795048006894330309773217834864543113205765659868456288616808718693835297350643986297640660000723562917905207051164077614812491885830945940566688339109350944456576357666151619317753792891661581327159616877487983821820492520348473874384736771934512787029218636250627816
Its index is 4782
It took 4.216 seconds to run this algorithm
"""

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#ProjectEuler/Python/Problem26.py
#Matthew Ellison
# Created: 07-29-19
#Modified: 08-02-19
#Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
import Algorithms
__topNumber = 999 #The largest denominator to be checked
def Problem26():
longestCycle = 0
longestNumber = 1
#Start with 1/2 and find out how long the longest cycle is by checking the remainders
#Loop through every number from 2-999 and use it for the denominator
for denominator in range(2, __topNumber):
remainderList = [] #Holds the list of remainders
endFound = False #Holds whether we have found an end to the number (either a cycle or a 0 for remainder)
cycleFound = False #Holds whether a cycle was detected
numerator = 1 #The numerator that will be divided
while(not endFound):
#Get the remainder after the division
remainder = numerator % denominator
#Check if the remainder is 0
#If it is set the flag
if(remainder == 0):
endFound = True
#Check if the remainder is in the list
#If it is in the list, set the appropriate flags
elif remainder in remainderList:
endFound = True
cycleFound = True
#Else add it to the list
else:
remainderList.append(remainder)
#Multiply the remainder by 10 to continue finding the next remainder
numerator = remainder * 10
#If a cycle was found check the size of the list against the largest cycle
if(cycleFound):
#If it is larger than the largest, set it as the new largest
if(len(remainderList) > longestCycle):
longestCycle = len(remainderList)
longestNumber = denominator
#Print the results
print("The longest cycle is " + str(longestCycle) + " digits long")
print("It is started with the number " + str(longestNumber))
#This calls the appropriate functions if the script is called stand along
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem26()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The longest cycle is 982 digits long
It is started with the number 983
It took 182.704 milliseconds to run this algorithm
"""

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#ProjectEuler/Python/Problem27.py
#Matthew Ellison
# Created: 09-15-19
#Modified: 09-15-19
#Find the product of the coefficients, |a| < 1000 and |b| <= 1000, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n=0.
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
import Algorithms
def Problem27():
#Setup the variables
topA = 0 #The A for the most n's generated
topB = 0 #The B for the most n's generated
topN = 0 #The most n's generated
primes = Algorithms.getPrimes(12000) #A list of all primes that could possibly be generated with this formula
#Start with the lowest possible A and check all possibilities after that
for a in range(-999, 999):
#Start with the lowest possible B and check all possibilities after that
for b in range(-1000, 1000):
#Start with n=0 and check the formula to see how many primes you can get get with concecutive n's
n = 0
quadratic = (n * n) + (a * n) + b
while(quadratic in primes):
n += 1
quadratic = (n * n) + (a * n) + b
n -= 1 #Negate an n because the last formula failed
#Set all the largest numbers if this created more primes than any other
if(n > topN):
topN = n
topB = b
topA = a
print("The greatest number of primes found is " + str(topN))
print("It was found with A = " + str(topA) + ", B = " + str(topB))
print("The product of A and B is " + str(topA * topB))
#This calls the appropriate functions if the script is called stand alone
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem27()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The greatest number of primes found is 70
It was found with A = -61, B = 971
The product of A and B is -59231
It took 35.775 seconds to run this algorithm
"""

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#ProjectEuler/Python/Problem28.py
#Matthew Ellison
# Created: 09-22-19
#Modified: 09-22-19
#What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed by starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
def setupGrid() -> list:
#Setup the grid to be the right size and fill it with 0's
grid = [[0 for x in range(1001)] for y in range(1001)]
finalLocation = False #A flag to indicate if the final location to be filled has been reached
currentNum = 1 #Set the number that is going to be put at each location
#Start with the middle location and set it correctly and advance the tracker to the next number
xLocation = 500
yLocation = 500
grid[yLocation][xLocation] = currentNum
currentNum += 1
#Move right the first time
xLocation += 1
#Move in a circular pattern until you reach the final location
while(not finalLocation):
#Move down until you reach a blank location on the left
while(grid[yLocation][xLocation - 1] != 0):
grid[yLocation][xLocation] = currentNum
currentNum += 1
yLocation += 1
#Move left until you reach a blank location above
while(grid[yLocation - 1][xLocation] != 0):
grid[yLocation][xLocation] = currentNum
currentNum += 1
xLocation -= 1
#Move up until you reach a blank location to the right
while(grid[yLocation][xLocation + 1] != 0):
grid[yLocation][xLocation] = currentNum
currentNum += 1
yLocation -= 1
#Move right until you reach a blank location below
while(grid[yLocation + 1][xLocation] != 0):
grid[yLocation][xLocation] = currentNum
currentNum += 1
xLocation += 1
#Check if you are at the final location and break the loop if you are
if(xLocation == len(grid)):
finalLocation = True
break
return grid
def findSum(grid: list) -> int:
sumOfDiagonals = 0
leftSide = 0
rightSide = len(grid) - 1
row = 0
while(row < len(grid)):
#This ensure the middle location is only counted once
if(leftSide == rightSide):
sumOfDiagonals += grid[row][leftSide]
else:
sumOfDiagonals += grid[row][leftSide]
sumOfDiagonals += grid[row][rightSide]
row += 1
leftSide += 1
rightSide -= 1
return sumOfDiagonals
def Problem28():
#Setup the grid
grid = setupGrid()
#Find the sum of the diagonals in the grid
diagSum = findSum(grid)
#Print the results
print("The sum of the diagonals in the given grid is " + str(diagSum))
#This calls the appropriate functions if the script is called stand alone
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem28()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The sum of the diagonals in the given grid is 669171001
It took 197.764 milliseconds to run this algorithm
"""

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Problem29.py Normal file
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#ProjectEuler/Python/Problem29.py
#Matthew Ellison
# Created: 10-10-19
#Modified: 10-10-19
#How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
#Setup the variables
__BOTTOM_A = 2 #The lowest possible value for A
__TOP_A = 100 #The highest possible value for A
__BOTTOM_B = 2 #The lowest possible value for B
__TOP_B = 100 #The highest possible value for B
def Problem29():
unique = [] #This will hold all of the unique answers
#Start with the first A and move towards the top
for currentA in range(__BOTTOM_A, __TOP_A + 1):
#Start with the first B and move towards the top
for currentB in range(__BOTTOM_B, __TOP_B + 1):
#Get the new number
currentNum = currentA ** currentB
#If the new number isn't in the list add it
if currentNum not in unique:
unique.append(currentNum)
#Print the results
print("The number of unique values generated by a^b for " + str(__BOTTOM_A) + " <= a < = " + str(__TOP_A) + " and " + str(__BOTTOM_B) + " <= b <= " + str(__TOP_B) + " is " + str(len(unique)))
#This calls the appropriate functions if the script is called stand alone
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem29()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The number of unique values generated by a^b for 2 <= a < = 100 and 2 <= b <= 100 is 9183
It took 304.630 milliseconds to run this algorithm
"""

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#ProjectEuler/Python/Problem3.py
#Matthew Ellison
# Created: 01-27-19
#Modified: 03-28-19
#The largest prime factor of 600851475143
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
from Algorithms import getFactors
__targetNumber = 600851475143
def Problem3():
#Get the factors of the number
factors = getFactors(__targetNumber)
#The largest number will be the answer
#Print the results
print("The largest prime factor of " + str(__targetNumber) + " is " + str(factors[(len(factors) - 1)]))
#If you are running this file, automatically start the correct function
if __name__ == '__main__':
timer = Stopwatch() #Used to determine the algorithm's run time
timer.start() #Start the timer
Problem3() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The largest prime factor of 600851475143 is 6857
It took 1.685 seconds to run this algorithm
"""

76
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#ProjectEuler/Python/Problem30.py
#Matthew Ellison
# Created: 10-28-19
#Modified: 10-28-19
#Find the sum of all the numbers that can be written as the sum of the fifth powers of their digits.
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
#Setup the variables
__TOP_NUM = 1000000 #This is the largest number that will be checked
__BOTTOM_NUM = 2 #Starts with 2 because 0 and 1 don't count
__POWER_RAISED = 5 #This is the power that the digits are raised to
#Returns a list with the individual digits of the number passed to it
def getDigits(num: int) -> list:
listOfDigits = [] #This list holds the individual digits of num
#The easiest way to get the individual digits of a number is by converting it to a string
digits = str(num)
#Start with the first digit, convert it to an integer, store it in the list, and move to the next digit
for cnt in range(0, len(digits)):
listOfDigits.append(int(digits[cnt]))
#Return the list of digits
return listOfDigits
def Problem30():
sumOfFifthNumbers = [] #This is a list of the numbers that are the sum of the fifth power of their digits
#Start with the lowest number and increment until you reach the largest number
for currentNum in range(__BOTTOM_NUM, __TOP_NUM):
#Get the digits of the number
digits = getDigits(currentNum)
#Get the sum of the powers
sumOfPowers = 0
for cnt in range(0, len(digits)):
sumOfPowers += digits[cnt]**__POWER_RAISED
#Check if the sum of the powers is the same as the number
#If it is add it to the list, otherwise continue to the next number
if(sumOfPowers == currentNum):
sumOfFifthNumbers.append(currentNum)
#Print the results
print("The sum of all the numbers that can be written as the sum of the fifth powers of their digits is " + str(sum(sumOfFifthNumbers)))
#This calls the appropriate functions if the script is called stand alone
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem30()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The sum of all the numbers that can be written as the sum of the fifth powers of their digits is 443839
It took 3.284 seconds to run this algorithm
"""

63
Problem4.py Normal file
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#ProjectEuler/Python/Problem4.py
#Matthew Ellison
# Created: 01-28-19
#Modified: 03-28-19
#Find the largest palindrome made from the product of two 3-digit numbers
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
__lowestNum = 100
__highestNum = 1000
def Problem4():
#Setup the variables
palindromes = [] #Holds all of the palindromes
currentNum = 0 #Holds the product of the two numbers I am currently working on
#Loop through every number from __lowestNum to __highestNum twice and multiply every number together
for num1 in range(__lowestNum, __highestNum + 1):
for num2 in range(num1, __highestNum + 1): #You can start at num1 because 100 * 101 == 101 * 100
currentNum = num1 * num2
#If the number is a palindrome add it to the list of palindromes, otherwise ignore it
#Using strings makes it easier to determine a palindrome
if(str(currentNum) == str(currentNum)[::-1]):
palindromes.append(currentNum)
#Sort the palindromes so that the last element is the largest
palindromes.sort()
#Print the results
print("The largest palindrome made from the product of two 3-digit numbers is " + str(palindromes[len(palindromes) - 1]))
#If you are running this file, automatically start the correct function
if __name__ == '__main__':
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem4() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The largest palindrome made from the product of two 3-digit numbers is 906609
It took 177.314 milliseconds to run this algorithm
"""

69
Problem5.py Normal file
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#ProjectEulter/Python/Project5.py
#Matthew Ellison
# Created: 01-28-19
#Modified: 03-28-19
#What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
__startNum = 1
__stopNum = 20
def Problem5():
#Setup the variables
numFound = False #Holds whether we have found the divisible number yet
#Start at 20 and loop through all numbers until you find one that works
#It must be at least 20 to be divisible by 20
num = 20 #Holds the number that you are currently checking against
while((not numFound) and (num > 0)): #Set an escape, just in case there is no answer and you overflow
#Set that you found the number to true, because you set this flag when you don't find it
numFound = True
#See if the current number is divisible by all numbers from 1 to 20
for divisor in range(__startNum, __stopNum + 1):
#If it is not set a flag to move to the next possible number
if((num % divisor) != 0):
numFound = False
break
#Increment the number by 2 to check the next one if you didn't find the number
if not numFound:
num += 2
#Print the results
if(num < 0):
print("There was an error: Could not find a number that fit the criteria")
else:
print("The smallest positive number that is evenly divisible by all numbers 1-20 is " + str(num))
#If you are running this file, automatically start the correct function
if __name__ == '__main__':
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem5() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The smallest positive number that is evenly divisible by all numbers 1-20 is 232792560
It took 50.236 seconds to run this algorithm
"""

56
Problem6.py Normal file
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#ProjectEuler/Python/Problem6.py
#Matthew Ellison
# Created: 01-28-19
#Modified: 03-28-19
#Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch #To time the algorithm
def Problem6():
#Setup the variables
sumOfSquares = 0 #Holds the sum of the square of the numbers
squareOfSum = 0 #Holds the square of the sum of the numbers
#Run through all numbers from 1-100 and add them to the approriate sums
for num in range(1, 101):
sumOfSquares += num * num #Get the sum of the squares of the first 100 natural numbers
squareOfSum += num #Get the sum of the first 100 natural numbers so you can square it later
#Square the normal sum
squareOfSum *= squareOfSum
#Print the result
print("The difference between the sum of the squares and the square of the sum of the numbers 1-100 is " + str(abs(sumOfSquares - squareOfSum)))
#If you are running this file, automatically start the correct function
if __name__ == '__main__':
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem6() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The difference between the sum of the squares and the square of the sum of the numbers 1-100 is 25164150
It took 24.384 microseconds to run this algorithm
"""

309
Problem67.py Normal file
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#ProjectEuler/Python/Problem67.py
#Matthew Ellison
# Created: 03-26-19
#Modified: 03-28-19
#Find the maximum total from top to bottom
"""
59
73 41
52 40 09
26 53 06 34
10 51 87 86 81
61 95 66 57 25 68
90 81 80 38 92 67 73
30 28 51 76 81 18 75 44
84 14 95 87 62 81 17 78 58
21 46 71 58 02 79 62 39 31 09
56 34 35 53 78 31 81 18 90 93 15
78 53 04 21 84 93 32 13 97 11 37 51
45 03 81 79 05 18 78 86 13 30 63 99 95
39 87 96 28 03 38 42 17 82 87 58 07 22 57
06 17 51 17 07 93 09 07 75 97 95 78 87 08 53
67 66 59 60 88 99 94 65 55 77 55 34 27 53 78 28
76 40 41 04 87 16 09 42 75 69 23 97 30 60 10 79 87
12 10 44 26 21 36 32 84 98 60 13 12 36 16 63 31 91 35
70 39 06 05 55 27 38 48 28 22 34 35 62 62 15 14 94 89 86
66 56 68 84 96 21 34 34 34 81 62 40 65 54 62 05 98 03 02 60
38 89 46 37 99 54 34 53 36 14 70 26 02 90 45 13 31 61 83 73 47
36 10 63 96 60 49 41 05 37 42 14 58 84 93 96 17 09 43 05 43 06 59
66 57 87 57 61 28 37 51 84 73 79 15 39 95 88 87 43 39 11 86 77 74 18
54 42 05 79 30 49 99 73 46 37 50 02 45 09 54 52 27 95 27 65 19 45 26 45
71 39 17 78 76 29 52 90 18 99 78 19 35 62 71 19 23 65 93 85 49 33 75 09 02
33 24 47 61 60 55 32 88 57 55 91 54 46 57 07 77 98 52 80 99 24 25 46 78 79 05
92 09 13 55 10 67 26 78 76 82 63 49 51 31 24 68 05 57 07 54 69 21 67 43 17 63 12
24 59 06 08 98 74 66 26 61 60 13 03 09 09 24 30 71 08 88 70 72 70 29 90 11 82 41 34
66 82 67 04 36 60 92 77 91 85 62 49 59 61 30 90 29 94 26 41 89 04 53 22 83 41 09 74 90
48 28 26 37 28 52 77 26 51 32 18 98 79 36 62 13 17 08 19 54 89 29 73 68 42 14 08 16 70 37
37 60 69 70 72 71 09 59 13 60 38 13 57 36 09 30 43 89 30 39 15 02 44 73 05 73 26 63 56 86 12
55 55 85 50 62 99 84 77 28 85 03 21 27 22 19 26 82 69 54 04 13 07 85 14 01 15 70 59 89 95 10 19
04 09 31 92 91 38 92 86 98 75 21 05 64 42 62 84 36 20 73 42 21 23 22 51 51 79 25 45 85 53 03 43 22
75 63 02 49 14 12 89 14 60 78 92 16 44 82 38 30 72 11 46 52 90 27 08 65 78 03 85 41 57 79 39 52 33 48
78 27 56 56 39 13 19 43 86 72 58 95 39 07 04 34 21 98 39 15 39 84 89 69 84 46 37 57 59 35 59 50 26 15 93
42 89 36 27 78 91 24 11 17 41 05 94 07 69 51 96 03 96 47 90 90 45 91 20 50 56 10 32 36 49 04 53 85 92 25 65
52 09 61 30 61 97 66 21 96 92 98 90 06 34 96 60 32 69 68 33 75 84 18 31 71 50 84 63 03 03 19 11 28 42 75 45 45
61 31 61 68 96 34 49 39 05 71 76 59 62 67 06 47 96 99 34 21 32 47 52 07 71 60 42 72 94 56 82 83 84 40 94 87 82 46
01 20 60 14 17 38 26 78 66 81 45 95 18 51 98 81 48 16 53 88 37 52 69 95 72 93 22 34 98 20 54 27 73 61 56 63 60 34 63
93 42 94 83 47 61 27 51 79 79 45 01 44 73 31 70 83 42 88 25 53 51 30 15 65 94 80 44 61 84 12 77 02 62 02 65 94 42 14 94
32 73 09 67 68 29 74 98 10 19 85 48 38 31 85 67 53 93 93 77 47 67 39 72 94 53 18 43 77 40 78 32 29 59 24 06 02 83 50 60 66
32 01 44 30 16 51 15 81 98 15 10 62 86 79 50 62 45 60 70 38 31 85 65 61 64 06 69 84 14 22 56 43 09 48 66 69 83 91 60 40 36 61
92 48 22 99 15 95 64 43 01 16 94 02 99 19 17 69 11 58 97 56 89 31 77 45 67 96 12 73 08 20 36 47 81 44 50 64 68 85 40 81 85 52 09
91 35 92 45 32 84 62 15 19 64 21 66 06 01 52 80 62 59 12 25 88 28 91 50 40 16 22 99 92 79 87 51 21 77 74 77 07 42 38 42 74 83 02 05
46 19 77 66 24 18 05 32 02 84 31 99 92 58 96 72 91 36 62 99 55 29 53 42 12 37 26 58 89 50 66 19 82 75 12 48 24 87 91 85 02 07 03 76 86
99 98 84 93 07 17 33 61 92 20 66 60 24 66 40 30 67 05 37 29 24 96 03 27 70 62 13 04 45 47 59 88 43 20 66 15 46 92 30 04 71 66 78 70 53 99
67 60 38 06 88 04 17 72 10 99 71 07 42 25 54 05 26 64 91 50 45 71 06 30 67 48 69 82 08 56 80 67 18 46 66 63 01 20 08 80 47 07 91 16 03 79 87
18 54 78 49 80 48 77 40 68 23 60 88 58 80 33 57 11 69 55 53 64 02 94 49 60 92 16 35 81 21 82 96 25 24 96 18 02 05 49 03 50 77 06 32 84 27 18 38
68 01 50 04 03 21 42 94 53 24 89 05 92 26 52 36 68 11 85 01 04 42 02 45 15 06 50 04 53 73 25 74 81 88 98 21 67 84 79 97 99 20 95 04 40 46 02 58 87
94 10 02 78 88 52 21 03 88 60 06 53 49 71 20 91 12 65 07 49 21 22 11 41 58 99 36 16 09 48 17 24 52 36 23 15 72 16 84 56 02 99 43 76 81 71 29 39 49 17
64 39 59 84 86 16 17 66 03 09 43 06 64 18 63 29 68 06 23 07 87 14 26 35 17 12 98 41 53 64 78 18 98 27 28 84 80 67 75 62 10 11 76 90 54 10 05 54 41 39 66
43 83 18 37 32 31 52 29 95 47 08 76 35 11 04 53 35 43 34 10 52 57 12 36 20 39 40 55 78 44 07 31 38 26 08 15 56 88 86 01 52 62 10 24 32 05 60 65 53 28 57 99
03 50 03 52 07 73 49 92 66 80 01 46 08 67 25 36 73 93 07 42 25 53 13 96 76 83 87 90 54 89 78 22 78 91 73 51 69 09 79 94 83 53 09 40 69 62 10 79 49 47 03 81 30
71 54 73 33 51 76 59 54 79 37 56 45 84 17 62 21 98 69 41 95 65 24 39 37 62 03 24 48 54 64 46 82 71 78 33 67 09 16 96 68 52 74 79 68 32 21 13 78 96 60 09 69 20 36
73 26 21 44 46 38 17 83 65 98 07 23 52 46 61 97 33 13 60 31 70 15 36 77 31 58 56 93 75 68 21 36 69 53 90 75 25 82 39 50 65 94 29 30 11 33 11 13 96 02 56 47 07 49 02
76 46 73 30 10 20 60 70 14 56 34 26 37 39 48 24 55 76 84 91 39 86 95 61 50 14 53 93 64 67 37 31 10 84 42 70 48 20 10 72 60 61 84 79 69 65 99 73 89 25 85 48 92 56 97 16
03 14 80 27 22 30 44 27 67 75 79 32 51 54 81 29 65 14 19 04 13 82 04 91 43 40 12 52 29 99 07 76 60 25 01 07 61 71 37 92 40 47 99 66 57 01 43 44 22 40 53 53 09 69 26 81 07
49 80 56 90 93 87 47 13 75 28 87 23 72 79 32 18 27 20 28 10 37 59 21 18 70 04 79 96 03 31 45 71 81 06 14 18 17 05 31 50 92 79 23 47 09 39 47 91 43 54 69 47 42 95 62 46 32 85
37 18 62 85 87 28 64 05 77 51 47 26 30 65 05 70 65 75 59 80 42 52 25 20 44 10 92 17 71 95 52 14 77 13 24 55 11 65 26 91 01 30 63 15 49 48 41 17 67 47 03 68 20 90 98 32 04 40 68
90 51 58 60 06 55 23 68 05 19 76 94 82 36 96 43 38 90 87 28 33 83 05 17 70 83 96 93 06 04 78 47 80 06 23 84 75 23 87 72 99 14 50 98 92 38 90 64 61 58 76 94 36 66 87 80 51 35 61 38
57 95 64 06 53 36 82 51 40 33 47 14 07 98 78 65 39 58 53 06 50 53 04 69 40 68 36 69 75 78 75 60 03 32 39 24 74 47 26 90 13 40 44 71 90 76 51 24 36 50 25 45 70 80 61 80 61 43 90 64 11
18 29 86 56 68 42 79 10 42 44 30 12 96 18 23 18 52 59 02 99 67 46 60 86 43 38 55 17 44 93 42 21 55 14 47 34 55 16 49 24 23 29 96 51 55 10 46 53 27 92 27 46 63 57 30 65 43 27 21 20 24 83
81 72 93 19 69 52 48 01 13 83 92 69 20 48 69 59 20 62 05 42 28 89 90 99 32 72 84 17 08 87 36 03 60 31 36 36 81 26 97 36 48 54 56 56 27 16 91 08 23 11 87 99 33 47 02 14 44 73 70 99 43 35 33
90 56 61 86 56 12 70 59 63 32 01 15 81 47 71 76 95 32 65 80 54 70 34 51 40 45 33 04 64 55 78 68 88 47 31 47 68 87 03 84 23 44 89 72 35 08 31 76 63 26 90 85 96 67 65 91 19 14 17 86 04 71 32 95
37 13 04 22 64 37 37 28 56 62 86 33 07 37 10 44 52 82 52 06 19 52 57 75 90 26 91 24 06 21 14 67 76 30 46 14 35 89 89 41 03 64 56 97 87 63 22 34 03 79 17 45 11 53 25 56 96 61 23 18 63 31 37 37 47
77 23 26 70 72 76 77 04 28 64 71 69 14 85 96 54 95 48 06 62 99 83 86 77 97 75 71 66 30 19 57 90 33 01 60 61 14 12 90 99 32 77 56 41 18 14 87 49 10 14 90 64 18 50 21 74 14 16 88 05 45 73 82 47 74 44
22 97 41 13 34 31 54 61 56 94 03 24 59 27 98 77 04 09 37 40 12 26 87 09 71 70 07 18 64 57 80 21 12 71 83 94 60 39 73 79 73 19 97 32 64 29 41 07 48 84 85 67 12 74 95 20 24 52 41 67 56 61 29 93 35 72 69
72 23 63 66 01 11 07 30 52 56 95 16 65 26 83 90 50 74 60 18 16 48 43 77 37 11 99 98 30 94 91 26 62 73 45 12 87 73 47 27 01 88 66 99 21 41 95 80 02 53 23 32 61 48 32 43 43 83 14 66 95 91 19 81 80 67 25 88
08 62 32 18 92 14 83 71 37 96 11 83 39 99 05 16 23 27 10 67 02 25 44 11 55 31 46 64 41 56 44 74 26 81 51 31 45 85 87 09 81 95 22 28 76 69 46 48 64 87 67 76 27 89 31 11 74 16 62 03 60 94 42 47 09 34 94 93 72
56 18 90 18 42 17 42 32 14 86 06 53 33 95 99 35 29 15 44 20 49 59 25 54 34 59 84 21 23 54 35 90 78 16 93 13 37 88 54 19 86 67 68 55 66 84 65 42 98 37 87 56 33 28 58 38 28 38 66 27 52 21 81 15 08 22 97 32 85 27
91 53 40 28 13 34 91 25 01 63 50 37 22 49 71 58 32 28 30 18 68 94 23 83 63 62 94 76 80 41 90 22 82 52 29 12 18 56 10 08 35 14 37 57 23 65 67 40 72 39 93 39 70 89 40 34 07 46 94 22 20 05 53 64 56 30 05 56 61 88 27
23 95 11 12 37 69 68 24 66 10 87 70 43 50 75 07 62 41 83 58 95 93 89 79 45 39 02 22 05 22 95 43 62 11 68 29 17 40 26 44 25 71 87 16 70 85 19 25 59 94 90 41 41 80 61 70 55 60 84 33 95 76 42 63 15 09 03 40 38 12 03 32
09 84 56 80 61 55 85 97 16 94 82 94 98 57 84 30 84 48 93 90 71 05 95 90 73 17 30 98 40 64 65 89 07 79 09 19 56 36 42 30 23 69 73 72 07 05 27 61 24 31 43 48 71 84 21 28 26 65 65 59 65 74 77 20 10 81 61 84 95 08 52 23 70
47 81 28 09 98 51 67 64 35 51 59 36 92 82 77 65 80 24 72 53 22 07 27 10 21 28 30 22 48 82 80 48 56 20 14 43 18 25 50 95 90 31 77 08 09 48 44 80 90 22 93 45 82 17 13 96 25 26 08 73 34 99 06 49 24 06 83 51 40 14 15 10 25 01
54 25 10 81 30 64 24 74 75 80 36 75 82 60 22 69 72 91 45 67 03 62 79 54 89 74 44 83 64 96 66 73 44 30 74 50 37 05 09 97 70 01 60 46 37 91 39 75 75 18 58 52 72 78 51 81 86 52 08 97 01 46 43 66 98 62 81 18 70 93 73 08 32 46 34
96 80 82 07 59 71 92 53 19 20 88 66 03 26 26 10 24 27 50 82 94 73 63 08 51 33 22 45 19 13 58 33 90 15 22 50 36 13 55 06 35 47 82 52 33 61 36 27 28 46 98 14 73 20 73 32 16 26 80 53 47 66 76 38 94 45 02 01 22 52 47 96 64 58 52 39
88 46 23 39 74 63 81 64 20 90 33 33 76 55 58 26 10 46 42 26 74 74 12 83 32 43 09 02 73 55 86 54 85 34 28 23 29 79 91 62 47 41 82 87 99 22 48 90 20 05 96 75 95 04 43 28 81 39 81 01 28 42 78 25 39 77 90 57 58 98 17 36 73 22 63 74 51
29 39 74 94 95 78 64 24 38 86 63 87 93 06 70 92 22 16 80 64 29 52 20 27 23 50 14 13 87 15 72 96 81 22 08 49 72 30 70 24 79 31 16 64 59 21 89 34 96 91 48 76 43 53 88 01 57 80 23 81 90 79 58 01 80 87 17 99 86 90 72 63 32 69 14 28 88 69
37 17 71 95 56 93 71 35 43 45 04 98 92 94 84 96 11 30 31 27 31 60 92 03 48 05 98 91 86 94 35 90 90 08 48 19 33 28 68 37 59 26 65 96 50 68 22 07 09 49 34 31 77 49 43 06 75 17 81 87 61 79 52 26 27 72 29 50 07 98 86 01 17 10 46 64 24 18 56
51 30 25 94 88 85 79 91 40 33 63 84 49 67 98 92 15 26 75 19 82 05 18 78 65 93 61 48 91 43 59 41 70 51 22 15 92 81 67 91 46 98 11 11 65 31 66 10 98 65 83 21 05 56 05 98 73 67 46 74 69 34 08 30 05 52 07 98 32 95 30 94 65 50 24 63 28 81 99 57
19 23 61 36 09 89 71 98 65 17 30 29 89 26 79 74 94 11 44 48 97 54 81 55 39 66 69 45 28 47 13 86 15 76 74 70 84 32 36 33 79 20 78 14 41 47 89 28 81 05 99 66 81 86 38 26 06 25 13 60 54 55 23 53 27 05 89 25 23 11 13 54 59 54 56 34 16 24 53 44 06
13 40 57 72 21 15 60 08 04 19 11 98 34 45 09 97 86 71 03 15 56 19 15 44 97 31 90 04 87 87 76 08 12 30 24 62 84 28 12 85 82 53 99 52 13 94 06 65 97 86 09 50 94 68 69 74 30 67 87 94 63 07 78 27 80 36 69 41 06 92 32 78 37 82 30 05 18 87 99 72 19 99
44 20 55 77 69 91 27 31 28 81 80 27 02 07 97 23 95 98 12 25 75 29 47 71 07 47 78 39 41 59 27 76 13 15 66 61 68 35 69 86 16 53 67 63 99 85 41 56 08 28 33 40 94 76 90 85 31 70 24 65 84 65 99 82 19 25 54 37 21 46 33 02 52 99 51 33 26 04 87 02 08 18 96
54 42 61 45 91 06 64 79 80 82 32 16 83 63 42 49 19 78 65 97 40 42 14 61 49 34 04 18 25 98 59 30 82 72 26 88 54 36 21 75 03 88 99 53 46 51 55 78 22 94 34 40 68 87 84 25 30 76 25 08 92 84 42 61 40 38 09 99 40 23 29 39 46 55 10 90 35 84 56 70 63 23 91 39
52 92 03 71 89 07 09 37 68 66 58 20 44 92 51 56 13 71 79 99 26 37 02 06 16 67 36 52 58 16 79 73 56 60 59 27 44 77 94 82 20 50 98 33 09 87 94 37 40 83 64 83 58 85 17 76 53 02 83 52 22 27 39 20 48 92 45 21 09 42 24 23 12 37 52 28 50 78 79 20 86 62 73 20 59
54 96 80 15 91 90 99 70 10 09 58 90 93 50 81 99 54 38 36 10 30 11 35 84 16 45 82 18 11 97 36 43 96 79 97 65 40 48 23 19 17 31 64 52 65 65 37 32 65 76 99 79 34 65 79 27 55 33 03 01 33 27 61 28 66 08 04 70 49 46 48 83 01 45 19 96 13 81 14 21 31 79 93 85 50 05
92 92 48 84 59 98 31 53 23 27 15 22 79 95 24 76 05 79 16 93 97 89 38 89 42 83 02 88 94 95 82 21 01 97 48 39 31 78 09 65 50 56 97 61 01 07 65 27 21 23 14 15 80 97 44 78 49 35 33 45 81 74 34 05 31 57 09 38 94 07 69 54 69 32 65 68 46 68 78 90 24 28 49 51 45 86 35
41 63 89 76 87 31 86 09 46 14 87 82 22 29 47 16 13 10 70 72 82 95 48 64 58 43 13 75 42 69 21 12 67 13 64 85 58 23 98 09 37 76 05 22 31 12 66 50 29 99 86 72 45 25 10 28 19 06 90 43 29 31 67 79 46 25 74 14 97 35 76 37 65 46 23 82 06 22 30 76 93 66 94 17 96 13 20 72
63 40 78 08 52 09 90 41 70 28 36 14 46 44 85 96 24 52 58 15 87 37 05 98 99 39 13 61 76 38 44 99 83 74 90 22 53 80 56 98 30 51 63 39 44 30 91 91 04 22 27 73 17 35 53 18 35 45 54 56 27 78 48 13 69 36 44 38 71 25 30 56 15 22 73 43 32 69 59 25 93 83 45 11 34 94 44 39 92
12 36 56 88 13 96 16 12 55 54 11 47 19 78 17 17 68 81 77 51 42 55 99 85 66 27 81 79 93 42 65 61 69 74 14 01 18 56 12 01 58 37 91 22 42 66 83 25 19 04 96 41 25 45 18 69 96 88 36 93 10 12 98 32 44 83 83 04 72 91 04 27 73 07 34 37 71 60 59 31 01 54 54 44 96 93 83 36 04 45
30 18 22 20 42 96 65 79 17 41 55 69 94 81 29 80 91 31 85 25 47 26 43 49 02 99 34 67 99 76 16 14 15 93 08 32 99 44 61 77 67 50 43 55 87 55 53 72 17 46 62 25 50 99 73 05 93 48 17 31 70 80 59 09 44 59 45 13 74 66 58 94 87 73 16 14 85 38 74 99 64 23 79 28 71 42 20 37 82 31 23
51 96 39 65 46 71 56 13 29 68 53 86 45 33 51 49 12 91 21 21 76 85 02 17 98 15 46 12 60 21 88 30 92 83 44 59 42 50 27 88 46 86 94 73 45 54 23 24 14 10 94 21 20 34 23 51 04 83 99 75 90 63 60 16 22 33 83 70 11 32 10 50 29 30 83 46 11 05 31 17 86 42 49 01 44 63 28 60 07 78 95 40
44 61 89 59 04 49 51 27 69 71 46 76 44 04 09 34 56 39 15 06 94 91 75 90 65 27 56 23 74 06 23 33 36 69 14 39 05 34 35 57 33 22 76 46 56 10 61 65 98 09 16 69 04 62 65 18 99 76 49 18 72 66 73 83 82 40 76 31 89 91 27 88 17 35 41 35 32 51 32 67 52 68 74 85 80 57 07 11 62 66 47 22 67
65 37 19 97 26 17 16 24 24 17 50 37 64 82 24 36 32 11 68 34 69 31 32 89 79 93 96 68 49 90 14 23 04 04 67 99 81 74 70 74 36 96 68 09 64 39 88 35 54 89 96 58 66 27 88 97 32 14 06 35 78 20 71 06 85 66 57 02 58 91 72 05 29 56 73 48 86 52 09 93 22 57 79 42 12 01 31 68 17 59 63 76 07 77
73 81 14 13 17 20 11 09 01 83 08 85 91 70 84 63 62 77 37 07 47 01 59 95 39 69 39 21 99 09 87 02 97 16 92 36 74 71 90 66 33 73 73 75 52 91 11 12 26 53 05 26 26 48 61 50 90 65 01 87 42 47 74 35 22 73 24 26 56 70 52 05 48 41 31 18 83 27 21 39 80 85 26 08 44 02 71 07 63 22 05 52 19 08 20
17 25 21 11 72 93 33 49 64 23 53 82 03 13 91 65 85 02 40 05 42 31 77 42 05 36 06 54 04 58 07 76 87 83 25 57 66 12 74 33 85 37 74 32 20 69 03 97 91 68 82 44 19 14 89 28 85 85 80 53 34 87 58 98 88 78 48 65 98 40 11 57 10 67 70 81 60 79 74 72 97 59 79 47 30 20 54 80 89 91 14 05 33 36 79 39
60 85 59 39 60 07 57 76 77 92 06 35 15 72 23 41 45 52 95 18 64 79 86 53 56 31 69 11 91 31 84 50 44 82 22 81 41 40 30 42 30 91 48 94 74 76 64 58 74 25 96 57 14 19 03 99 28 83 15 75 99 01 89 85 79 50 03 95 32 67 44 08 07 41 62 64 29 20 14 76 26 55 48 71 69 66 19 72 44 25 14 01 48 74 12 98 07
64 66 84 24 18 16 27 48 20 14 47 69 30 86 48 40 23 16 61 21 51 50 26 47 35 33 91 28 78 64 43 68 04 79 51 08 19 60 52 95 06 68 46 86 35 97 27 58 04 65 30 58 99 12 12 75 91 39 50 31 42 64 70 04 46 07 98 73 98 93 37 89 77 91 64 71 64 65 66 21 78 62 81 74 42 20 83 70 73 95 78 45 92 27 34 53 71 15
30 11 85 31 34 71 13 48 05 14 44 03 19 67 23 73 19 57 06 90 94 72 57 69 81 62 59 68 88 57 55 69 49 13 07 87 97 80 89 05 71 05 05 26 38 40 16 62 45 99 18 38 98 24 21 26 62 74 69 04 85 57 77 35 58 67 91 79 79 57 86 28 66 34 72 51 76 78 36 95 63 90 08 78 47 63 45 31 22 70 52 48 79 94 15 77 61 67 68
23 33 44 81 80 92 93 75 94 88 23 61 39 76 22 03 28 94 32 06 49 65 41 34 18 23 08 47 62 60 03 63 33 13 80 52 31 54 73 43 70 26 16 69 57 87 83 31 03 93 70 81 47 95 77 44 29 68 39 51 56 59 63 07 25 70 07 77 43 53 64 03 94 42 95 39 18 01 66 21 16 97 20 50 90 16 70 10 95 69 29 06 25 61 41 26 15 59 63 35
"""
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
from collections import namedtuple
location = namedtuple("location", "xLocation yLocation total fromRight")
NUM_ROWS = 100
def invert(listNum):
for rowCnt in range(0, NUM_ROWS):
for colCnt in range(0, len(listNum[rowCnt])):
listNum[rowCnt][colCnt] = 100 - listNum[rowCnt][colCnt]
def removeIf(listNum: list, loc):
location = 0
while(location < len(listNum)):
if((listNum[location].xLocation == loc.xLocation) and (listNum[location].yLocation == loc.yLocation)):
del listNum[location]
else:
location += 1
def Problem67():
listNum = [[59],
[73, 41],
[52, 40, 9],
[26, 53, 6, 34],
[10, 51, 87, 86, 81],
[61, 95, 66, 57, 25, 68],
[90, 81, 80, 38, 92, 67, 73],
[30, 28, 51, 76, 81, 18, 75, 44],
[84, 14, 95, 87, 62, 81, 17, 78, 58],
[21, 46, 71, 58, 2, 79, 62, 39, 31, 9],
[56, 34, 35, 53, 78, 31, 81, 18, 90, 93, 15],
[78, 53, 4, 21, 84, 93, 32, 13, 97, 11, 37, 51],
[45, 3, 81, 79, 5, 18, 78, 86, 13, 30, 63, 99, 95],
[39, 87, 96, 28, 3, 38, 42, 17, 82, 87, 58, 7, 22, 57],
[ 6, 17, 51, 17, 7, 93, 9, 7, 75, 97, 95, 78, 87, 8, 53],
[67, 66, 59, 60, 88, 99, 94, 65, 55, 77, 55, 34, 27, 53, 78, 28],
[76, 40, 41, 4, 87, 16, 9, 42, 75, 69, 23, 97, 30, 60, 10, 79, 87],
[12, 10, 44, 26, 21, 36, 32, 84, 98, 60, 13, 12, 36, 16, 63, 31, 91, 35],
[70, 39, 6, 5, 55, 27, 38, 48, 28, 22, 34, 35, 62, 62, 15, 14, 94, 89, 86],
[66, 56, 68, 84, 96, 21, 34, 34, 34, 81, 62, 40, 65, 54, 62, 5, 98, 3, 2, 60],
[38, 89, 46, 37, 99, 54, 34, 53, 36, 14, 70, 26, 2, 90, 45, 13, 31, 61, 83, 73, 47],
[36, 10, 63, 96, 60, 49, 41, 5, 37, 42, 14, 58, 84, 93, 96, 17, 9, 43, 5, 43, 6, 59],
[66, 57, 87, 57, 61, 28, 37, 51, 84, 73, 79, 15, 39, 95, 88, 87, 43, 39, 11, 86, 77, 74, 18],
[54, 42, 5, 79, 30, 49, 99, 73, 46, 37, 50, 2, 45, 9, 54, 52, 27, 95, 27, 65, 19, 45, 26, 45],
[71, 39, 17, 78, 76, 29, 52, 90, 18, 99, 78, 19, 35, 62, 71, 19, 23, 65, 93, 85, 49, 33, 75, 9, 2],
[33, 24, 47, 61, 60, 55, 32, 88, 57, 55, 91, 54, 46, 57, 7, 77, 98, 52, 80, 99, 24, 25, 46, 78, 79, 5],
[92, 9, 13, 55, 10, 67, 26, 78, 76, 82, 63, 49, 51, 31, 24, 68, 5, 57, 7, 54, 69, 21, 67, 43, 17, 63, 12],
[24, 59, 6, 8, 98, 74, 66, 26, 61, 60, 13, 3, 9, 9, 24, 30, 71, 8, 88, 70, 72, 70, 29, 90, 11, 82, 41, 34],
[66, 82, 67, 4, 36, 60, 92, 77, 91, 85, 62, 49, 59, 61, 30, 90, 29, 94, 26, 41, 89, 4, 53, 22, 83, 41, 9, 74, 90],
[48, 28, 26, 37, 28, 52, 77, 26, 51, 32, 18, 98, 79, 36, 62, 13, 17, 8, 19, 54, 89, 29, 73, 68, 42, 14, 8, 16, 70, 37],
[37, 60, 69, 70, 72, 71, 9, 59, 13, 60, 38, 13, 57, 36, 9, 30, 43, 89, 30, 39, 15, 2, 44, 73, 5, 73, 26, 63, 56, 86, 12],
[55, 55, 85, 50, 62, 99, 84, 77, 28, 85, 3, 21, 27, 22, 19, 26, 82, 69, 54, 4, 13, 7, 85, 14, 1, 15, 70, 59, 89, 95, 10, 19],
[ 4, 9, 31, 92, 91, 38, 92, 86, 98, 75, 21, 5, 64, 42, 62, 84, 36, 20, 73, 42, 21, 23, 22, 51, 51, 79, 25, 45, 85, 53, 3, 43, 22],
[75, 63, 2, 49, 14, 12, 89, 14, 60, 78, 92, 16, 44, 82, 38, 30, 72, 11, 46, 52, 90, 27, 8, 65, 78, 3, 85, 41, 57, 79, 39, 52, 33, 48],
[78, 27, 56, 56, 39, 13, 19, 43, 86, 72, 58, 95, 39, 7, 4, 34, 21, 98, 39, 15, 39, 84, 89, 69, 84, 46, 37, 57, 59, 35, 59, 50, 26, 15, 93],
[42, 89, 36, 27, 78, 91, 24, 11, 17, 41, 5, 94, 7, 69, 51, 96, 3, 96, 47, 90, 90, 45, 91, 20, 50, 56, 10, 32, 36, 49, 4, 53, 85, 92, 25, 65],
[52, 9, 61, 30, 61, 97, 66, 21, 96, 92, 98, 90, 6, 34, 96, 60, 32, 69, 68, 33, 75, 84, 18, 31, 71, 50, 84, 63, 3, 3, 19, 11, 28, 42, 75, 45, 45],
[61, 31, 61, 68, 96, 34, 49, 39, 5, 71, 76, 59, 62, 67, 6, 47, 96, 99, 34, 21, 32, 47, 52, 7, 71, 60, 42, 72, 94, 56, 82, 83, 84, 40, 94, 87, 82, 46],
[ 1, 20, 60, 14, 17, 38, 26, 78, 66, 81, 45, 95, 18, 51, 98, 81, 48, 16, 53, 88, 37, 52, 69, 95, 72, 93, 22, 34, 98, 20, 54, 27, 73, 61, 56, 63, 60, 34, 63],
[93, 42, 94, 83, 47, 61, 27, 51, 79, 79, 45, 1, 44, 73, 31, 70, 83, 42, 88, 25, 53, 51, 30, 15, 65, 94, 80, 44, 61, 84, 12, 77, 2, 62, 2, 65, 94, 42, 14, 94],
[32, 73, 9, 67, 68, 29, 74, 98, 10, 19, 85, 48, 38, 31, 85, 67, 53, 93, 93, 77, 47, 67, 39, 72, 94, 53, 18, 43, 77, 40, 78, 32, 29, 59, 24, 6, 2, 83, 50, 60, 66],
[32, 1, 44, 30, 16, 51, 15, 81, 98, 15, 10, 62, 86, 79, 50, 62, 45, 60, 70, 38, 31, 85, 65, 61, 64, 6, 69, 84, 14, 22, 56, 43, 9, 48, 66, 69, 83, 91, 60, 40, 36, 61],
[92, 48, 22, 99, 15, 95, 64, 43, 1, 16, 94, 2, 99, 19, 17, 69, 11, 58, 97, 56, 89, 31, 77, 45, 67, 96, 12, 73, 8, 20, 36, 47, 81, 44, 50, 64, 68, 85, 40, 81, 85, 52, 9],
[91, 35, 92, 45, 32, 84, 62, 15, 19, 64, 21, 66, 6, 1, 52, 80, 62, 59, 12, 25, 88, 28, 91, 50, 40, 16, 22, 99, 92, 79, 87, 51, 21, 77, 74, 77, 7, 42, 38, 42, 74, 83, 2, 5],
[46, 19, 77, 66, 24, 18, 5, 32, 2, 84, 31, 99, 92, 58, 96, 72, 91, 36, 62, 99, 55, 29, 53, 42, 12, 37, 26, 58, 89, 50, 66, 19, 82, 75, 12, 48, 24, 87, 91, 85, 2, 7, 3, 76, 86],
[99, 98, 84, 93, 7, 17, 33, 61, 92, 20, 66, 60, 24, 66, 40, 30, 67, 5, 37, 29, 24, 96, 3, 27, 70, 62, 13, 4, 45, 47, 59, 88, 43, 20, 66, 15, 46, 92, 30, 4, 71, 66, 78, 70, 53, 99],
[67, 60, 38, 6, 88, 4, 17, 72, 10, 99, 71, 7, 42, 25, 54, 5, 26, 64, 91, 50, 45, 71, 6, 30, 67, 48, 69, 82, 8, 56, 80, 67, 18, 46, 66, 63, 1, 20, 8, 80, 47, 7, 91, 16, 3, 79, 87],
[18, 54, 78, 49, 80, 48, 77, 40, 68, 23, 60, 88, 58, 80, 33, 57, 11, 69, 55, 53, 64, 2, 94, 49, 60, 92, 16, 35, 81, 21, 82, 96, 25, 24, 96, 18, 2, 5, 49, 3, 50, 77, 6, 32, 84, 27, 18, 38],
[68, 1, 50, 4, 3, 21, 42, 94, 53, 24, 89, 5, 92, 26, 52, 36, 68, 11, 85, 1, 4, 42, 2, 45, 15, 6, 50, 4, 53, 73, 25, 74, 81, 88, 98, 21, 67, 84, 79, 97, 99, 20, 95, 4, 40, 46, 2, 58, 87],
[94, 10, 2, 78, 88, 52, 21, 3, 88, 60, 6, 53, 49, 71, 20, 91, 12, 65, 7, 49, 21, 22, 11, 41, 58, 99, 36, 16, 9, 48, 17, 24, 52, 36, 23, 15, 72, 16, 84, 56, 2, 99, 43, 76, 81, 71, 29, 39, 49, 17],
[64, 39, 59, 84, 86, 16, 17, 66, 3, 9, 43, 6, 64, 18, 63, 29, 68, 6, 23, 7, 87, 14, 26, 35, 17, 12, 98, 41, 53, 64, 78, 18, 98, 27, 28, 84, 80, 67, 75, 62, 10, 11, 76, 90, 54, 10, 5, 54, 41, 39, 66],
[43, 83, 18, 37, 32, 31, 52, 29, 95, 47, 8, 76, 35, 11, 4, 53, 35, 43, 34, 10, 52, 57, 12, 36, 20, 39, 40, 55, 78, 44, 7, 31, 38, 26, 8, 15, 56, 88, 86, 1, 52, 62, 10, 24, 32, 5, 60, 65, 53, 28, 57, 99],
[ 3, 50, 3, 52, 7, 73, 49, 92, 66, 80, 1, 46, 8, 67, 25, 36, 73, 93, 7, 42, 25, 53, 13, 96, 76, 83, 87, 90, 54, 89, 78, 22, 78, 91, 73, 51, 69, 9, 79, 94, 83, 53, 9, 40, 69, 62, 10, 79, 49, 47, 3, 81, 30],
[71, 54, 73, 33, 51, 76, 59, 54, 79, 37, 56, 45, 84, 17, 62, 21, 98, 69, 41, 95, 65, 24, 39, 37, 62, 3, 24, 48, 54, 64, 46, 82, 71, 78, 33, 67, 9, 16, 96, 68, 52, 74, 79, 68, 32, 21, 13, 78, 96, 60, 9, 69, 20, 36],
[73, 26, 21, 44, 46, 38, 17, 83, 65, 98, 7, 23, 52, 46, 61, 97, 33, 13, 60, 31, 70, 15, 36, 77, 31, 58, 56, 93, 75, 68, 21, 36, 69, 53, 90, 75, 25, 82, 39, 50, 65, 94, 29, 30, 11, 33, 11, 13, 96, 2, 56, 47, 7, 49, 2],
[76, 46, 73, 30, 10, 20, 60, 70, 14, 56, 34, 26, 37, 39, 48, 24, 55, 76, 84, 91, 39, 86, 95, 61, 50, 14, 53, 93, 64, 67, 37, 31, 10, 84, 42, 70, 48, 20, 10, 72, 60, 61, 84, 79, 69, 65, 99, 73, 89, 25, 85, 48, 92, 56, 97, 16],
[ 3, 14, 80, 27, 22, 30, 44, 27, 67, 75, 79, 32, 51, 54, 81, 29, 65, 14, 19, 4, 13, 82, 4, 91, 43, 40, 12, 52, 29, 99, 7, 76, 60, 25, 1, 7, 61, 71, 37, 92, 40, 47, 99, 66, 57, 1, 43, 44, 22, 40, 53, 53, 9, 69, 26, 81, 7],
[49, 80, 56, 90, 93, 87, 47, 13, 75, 28, 87, 23, 72, 79, 32, 18, 27, 20, 28, 10, 37, 59, 21, 18, 70, 4, 79, 96, 3, 31, 45, 71, 81, 6, 14, 18, 17, 5, 31, 50, 92, 79, 23, 47, 9, 39, 47, 91, 43, 54, 69, 47, 42, 95, 62, 46, 32, 85],
[37, 18, 62, 85, 87, 28, 64, 5, 77, 51, 47, 26, 30, 65, 5, 70, 65, 75, 59, 80, 42, 52, 25, 20, 44, 10, 92, 17, 71, 95, 52, 14, 77, 13, 24, 55, 11, 65, 26, 91, 1, 30, 63, 15, 49, 48, 41, 17, 67, 47, 3, 68, 20, 90, 98, 32, 4, 40, 68],
[90, 51, 58, 60, 6, 55, 23, 68, 5, 19, 76, 94, 82, 36, 96, 43, 38, 90, 87, 28, 33, 83, 5, 17, 70, 83, 96, 93, 6, 4, 78, 47, 80, 6, 23, 84, 75, 23, 87, 72, 99, 14, 50, 98, 92, 38, 90, 64, 61, 58, 76, 94, 36, 66, 87, 80, 51, 35, 61, 38],
[57, 95, 64, 6, 53, 36, 82, 51, 40, 33, 47, 14, 7, 98, 78, 65, 39, 58, 53, 6, 50, 53, 4, 69, 40, 68, 36, 69, 75, 78, 75, 60, 3, 32, 39, 24, 74, 47, 26, 90, 13, 40, 44, 71, 90, 76, 51, 24, 36, 50, 25, 45, 70, 80, 61, 80, 61, 43, 90, 64, 11],
[18, 29, 86, 56, 68, 42, 79, 10, 42, 44, 30, 12, 96, 18, 23, 18, 52, 59, 2, 99, 67, 46, 60, 86, 43, 38, 55, 17, 44, 93, 42, 21, 55, 14, 47, 34, 55, 16, 49, 24, 23, 29, 96, 51, 55, 10, 46, 53, 27, 92, 27, 46, 63, 57, 30, 65, 43, 27, 21, 20, 24, 83],
[81, 72, 93, 19, 69, 52, 48, 1, 13, 83, 92, 69, 20, 48, 69, 59, 20, 62, 5, 42, 28, 89, 90, 99, 32, 72, 84, 17, 8, 87, 36, 3, 60, 31, 36, 36, 81, 26, 97, 36, 48, 54, 56, 56, 27, 16, 91, 8, 23, 11, 87, 99, 33, 47, 2, 14, 44, 73, 70, 99, 43, 35, 33],
[90, 56, 61, 86, 56, 12, 70, 59, 63, 32, 1, 15, 81, 47, 71, 76, 95, 32, 65, 80, 54, 70, 34, 51, 40, 45, 33, 4, 64, 55, 78, 68, 88, 47, 31, 47, 68, 87, 3, 84, 23, 44, 89, 72, 35, 8, 31, 76, 63, 26, 90, 85, 96, 67, 65, 91, 19, 14, 17, 86, 4, 71, 32, 95],
[37, 13, 4, 22, 64, 37, 37, 28, 56, 62, 86, 33, 7, 37, 10, 44, 52, 82, 52, 6, 19, 52, 57, 75, 90, 26, 91, 24, 6, 21, 14, 67, 76, 30, 46, 14, 35, 89, 89, 41, 3, 64, 56, 97, 87, 63, 22, 34, 3, 79, 17, 45, 11, 53, 25, 56, 96, 61, 23, 18, 63, 31, 37, 37, 47],
[77, 23, 26, 70, 72, 76, 77, 4, 28, 64, 71, 69, 14, 85, 96, 54, 95, 48, 6, 62, 99, 83, 86, 77, 97, 75, 71, 66, 30, 19, 57, 90, 33, 1, 60, 61, 14, 12, 90, 99, 32, 77, 56, 41, 18, 14, 87, 49, 10, 14, 90, 64, 18, 50, 21, 74, 14, 16, 88, 5, 45, 73, 82, 47, 74, 44],
[22, 97, 41, 13, 34, 31, 54, 61, 56, 94, 3, 24, 59, 27, 98, 77, 4, 9, 37, 40, 12, 26, 87, 9, 71, 70, 7, 18, 64, 57, 80, 21, 12, 71, 83, 94, 60, 39, 73, 79, 73, 19, 97, 32, 64, 29, 41, 7, 48, 84, 85, 67, 12, 74, 95, 20, 24, 52, 41, 67, 56, 61, 29, 93, 35, 72, 69],
[72, 23, 63, 66, 1, 11, 7, 30, 52, 56, 95, 16, 65, 26, 83, 90, 50, 74, 60, 18, 16, 48, 43, 77, 37, 11, 99, 98, 30, 94, 91, 26, 62, 73, 45, 12, 87, 73, 47, 27, 1, 88, 66, 99, 21, 41, 95, 80, 2, 53, 23, 32, 61, 48, 32, 43, 43, 83, 14, 66, 95, 91, 19, 81, 80, 67, 25, 88],
[ 8, 62, 32, 18, 92, 14, 83, 71, 37, 96, 11, 83, 39, 99, 5, 16, 23, 27, 10, 67, 2, 25, 44, 11, 55, 31, 46, 64, 41, 56, 44, 74, 26, 81, 51, 31, 45, 85, 87, 9, 81, 95, 22, 28, 76, 69, 46, 48, 64, 87, 67, 76, 27, 89, 31, 11, 74, 16, 62, 3, 60, 94, 42, 47, 9, 34, 94, 93, 72],
[56, 18, 90, 18, 42, 17, 42, 32, 14, 86, 6, 53, 33, 95, 99, 35, 29, 15, 44, 20, 49, 59, 25, 54, 34, 59, 84, 21, 23, 54, 35, 90, 78, 16, 93, 13, 37, 88, 54, 19, 86, 67, 68, 55, 66, 84, 65, 42, 98, 37, 87, 56, 33, 28, 58, 38, 28, 38, 66, 27, 52, 21, 81, 15, 8, 22, 97, 32, 85, 27],
[91, 53, 40, 28, 13, 34, 91, 25, 1, 63, 50, 37, 22, 49, 71, 58, 32, 28, 30, 18, 68, 94, 23, 83, 63, 62, 94, 76, 80, 41, 90, 22, 82, 52, 29, 12, 18, 56, 10, 8, 35, 14, 37, 57, 23, 65, 67, 40, 72, 39, 93, 39, 70, 89, 40, 34, 7, 46, 94, 22, 20, 5, 53, 64, 56, 30, 5, 56, 61, 88, 27],
[23, 95, 11, 12, 37, 69, 68, 24, 66, 10, 87, 70, 43, 50, 75, 7, 62, 41, 83, 58, 95, 93, 89, 79, 45, 39, 2, 22, 5, 22, 95, 43, 62, 11, 68, 29, 17, 40, 26, 44, 25, 71, 87, 16, 70, 85, 19, 25, 59, 94, 90, 41, 41, 80, 61, 70, 55, 60, 84, 33, 95, 76, 42, 63, 15, 9, 3, 40, 38, 12, 3, 32],
[ 9, 84, 56, 80, 61, 55, 85, 97, 16, 94, 82, 94, 98, 57, 84, 30, 84, 48, 93, 90, 71, 5, 95, 90, 73, 17, 30, 98, 40, 64, 65, 89, 7, 79, 9, 19, 56, 36, 42, 30, 23, 69, 73, 72, 7, 5, 27, 61, 24, 31, 43, 48, 71, 84, 21, 28, 26, 65, 65, 59, 65, 74, 77, 20, 10, 81, 61, 84, 95, 8, 52, 23, 70],
[47, 81, 28, 9, 98, 51, 67, 64, 35, 51, 59, 36, 92, 82, 77, 65, 80, 24, 72, 53, 22, 7, 27, 10, 21, 28, 30, 22, 48, 82, 80, 48, 56, 20, 14, 43, 18, 25, 50, 95, 90, 31, 77, 8, 9, 48, 44, 80, 90, 22, 93, 45, 82, 17, 13, 96, 25, 26, 8, 73, 34, 99, 6, 49, 24, 6, 83, 51, 40, 14, 15, 10, 25, 1],
[54, 25, 10, 81, 30, 64, 24, 74, 75, 80, 36, 75, 82, 60, 22, 69, 72, 91, 45, 67, 3, 62, 79, 54, 89, 74, 44, 83, 64, 96, 66, 73, 44, 30, 74, 50, 37, 5, 9, 97, 70, 1, 60, 46, 37, 91, 39, 75, 75, 18, 58, 52, 72, 78, 51, 81, 86, 52, 8, 97, 1, 46, 43, 66, 98, 62, 81, 18, 70, 93, 73, 8, 32, 46, 34],
[96, 80, 82, 7, 59, 71, 92, 53, 19, 20, 88, 66, 3, 26, 26, 10, 24, 27, 50, 82, 94, 73, 63, 8, 51, 33, 22, 45, 19, 13, 58, 33, 90, 15, 22, 50, 36, 13, 55, 6, 35, 47, 82, 52, 33, 61, 36, 27, 28, 46, 98, 14, 73, 20, 73, 32, 16, 26, 80, 53, 47, 66, 76, 38, 94, 45, 2, 1, 22, 52, 47, 96, 64, 58, 52, 39],
[88, 46, 23, 39, 74, 63, 81, 64, 20, 90, 33, 33, 76, 55, 58, 26, 10, 46, 42, 26, 74, 74, 12, 83, 32, 43, 9, 2, 73, 55, 86, 54, 85, 34, 28, 23, 29, 79, 91, 62, 47, 41, 82, 87, 99, 22, 48, 90, 20, 5, 96, 75, 95, 4, 43, 28, 81, 39, 81, 1, 28, 42, 78, 25, 39, 77, 90, 57, 58, 98, 17, 36, 73, 22, 63, 74, 51],
[29, 39, 74, 94, 95, 78, 64, 24, 38, 86, 63, 87, 93, 6, 70, 92, 22, 16, 80, 64, 29, 52, 20, 27, 23, 50, 14, 13, 87, 15, 72, 96, 81, 22, 8, 49, 72, 30, 70, 24, 79, 31, 16, 64, 59, 21, 89, 34, 96, 91, 48, 76, 43, 53, 88, 1, 57, 80, 23, 81, 90, 79, 58, 1, 80, 87, 17, 99, 86, 90, 72, 63, 32, 69, 14, 28, 88, 69],
[37, 17, 71, 95, 56, 93, 71, 35, 43, 45, 4, 98, 92, 94, 84, 96, 11, 30, 31, 27, 31, 60, 92, 3, 48, 5, 98, 91, 86, 94, 35, 90, 90, 8, 48, 19, 33, 28, 68, 37, 59, 26, 65, 96, 50, 68, 22, 7, 9, 49, 34, 31, 77, 49, 43, 6, 75, 17, 81, 87, 61, 79, 52, 26, 27, 72, 29, 50, 7, 98, 86, 1, 17, 10, 46, 64, 24, 18, 56],
[51, 30, 25, 94, 88, 85, 79, 91, 40, 33, 63, 84, 49, 67, 98, 92, 15, 26, 75, 19, 82, 5, 18, 78, 65, 93, 61, 48, 91, 43, 59, 41, 70, 51, 22, 15, 92, 81, 67, 91, 46, 98, 11, 11, 65, 31, 66, 10, 98, 65, 83, 21, 5, 56, 5, 98, 73, 67, 46, 74, 69, 34, 8, 30, 5, 52, 7, 98, 32, 95, 30, 94, 65, 50, 24, 63, 28, 81, 99, 57],
[19, 23, 61, 36, 9, 89, 71, 98, 65, 17, 30, 29, 89, 26, 79, 74, 94, 11, 44, 48, 97, 54, 81, 55, 39, 66, 69, 45, 28, 47, 13, 86, 15, 76, 74, 70, 84, 32, 36, 33, 79, 20, 78, 14, 41, 47, 89, 28, 81, 5, 99, 66, 81, 86, 38, 26, 6, 25, 13, 60, 54, 55, 23, 53, 27, 5, 89, 25, 23, 11, 13, 54, 59, 54, 56, 34, 16, 24, 53, 44, 6],
[13, 40, 57, 72, 21, 15, 60, 8, 4, 19, 11, 98, 34, 45, 9, 97, 86, 71, 3, 15, 56, 19, 15, 44, 97, 31, 90, 4, 87, 87, 76, 8, 12, 30, 24, 62, 84, 28, 12, 85, 82, 53, 99, 52, 13, 94, 6, 65, 97, 86, 9, 50, 94, 68, 69, 74, 30, 67, 87, 94, 63, 7, 78, 27, 80, 36, 69, 41, 6, 92, 32, 78, 37, 82, 30, 5, 18, 87, 99, 72, 19, 99],
[44, 20, 55, 77, 69, 91, 27, 31, 28, 81, 80, 27, 2, 7, 97, 23, 95, 98, 12, 25, 75, 29, 47, 71, 7, 47, 78, 39, 41, 59, 27, 76, 13, 15, 66, 61, 68, 35, 69, 86, 16, 53, 67, 63, 99, 85, 41, 56, 8, 28, 33, 40, 94, 76, 90, 85, 31, 70, 24, 65, 84, 65, 99, 82, 19, 25, 54, 37, 21, 46, 33, 2, 52, 99, 51, 33, 26, 4, 87, 2, 8, 18, 96],
[54, 42, 61, 45, 91, 6, 64, 79, 80, 82, 32, 16, 83, 63, 42, 49, 19, 78, 65, 97, 40, 42, 14, 61, 49, 34, 4, 18, 25, 98, 59, 30, 82, 72, 26, 88, 54, 36, 21, 75, 3, 88, 99, 53, 46, 51, 55, 78, 22, 94, 34, 40, 68, 87, 84, 25, 30, 76, 25, 8, 92, 84, 42, 61, 40, 38, 9, 99, 40, 23, 29, 39, 46, 55, 10, 90, 35, 84, 56, 70, 63, 23, 91, 39],
[52, 92, 3, 71, 89, 7, 9, 37, 68, 66, 58, 20, 44, 92, 51, 56, 13, 71, 79, 99, 26, 37, 2, 6, 16, 67, 36, 52, 58, 16, 79, 73, 56, 60, 59, 27, 44, 77, 94, 82, 20, 50, 98, 33, 9, 87, 94, 37, 40, 83, 64, 83, 58, 85, 17, 76, 53, 2, 83, 52, 22, 27, 39, 20, 48, 92, 45, 21, 9, 42, 24, 23, 12, 37, 52, 28, 50, 78, 79, 20, 86, 62, 73, 20, 59],
[54, 96, 80, 15, 91, 90, 99, 70, 10, 9, 58, 90, 93, 50, 81, 99, 54, 38, 36, 10, 30, 11, 35, 84, 16, 45, 82, 18, 11, 97, 36, 43, 96, 79, 97, 65, 40, 48, 23, 19, 17, 31, 64, 52, 65, 65, 37, 32, 65, 76, 99, 79, 34, 65, 79, 27, 55, 33, 3, 1, 33, 27, 61, 28, 66, 8, 4, 70, 49, 46, 48, 83, 1, 45, 19, 96, 13, 81, 14, 21, 31, 79, 93, 85, 50, 5],
[92, 92, 48, 84, 59, 98, 31, 53, 23, 27, 15, 22, 79, 95, 24, 76, 5, 79, 16, 93, 97, 89, 38, 89, 42, 83, 2, 88, 94, 95, 82, 21, 1, 97, 48, 39, 31, 78, 9, 65, 50, 56, 97, 61, 1, 7, 65, 27, 21, 23, 14, 15, 80, 97, 44, 78, 49, 35, 33, 45, 81, 74, 34, 5, 31, 57, 9, 38, 94, 7, 69, 54, 69, 32, 65, 68, 46, 68, 78, 90, 24, 28, 49, 51, 45, 86, 35],
[41, 63, 89, 76, 87, 31, 86, 9, 46, 14, 87, 82, 22, 29, 47, 16, 13, 10, 70, 72, 82, 95, 48, 64, 58, 43, 13, 75, 42, 69, 21, 12, 67, 13, 64, 85, 58, 23, 98, 9, 37, 76, 5, 22, 31, 12, 66, 50, 29, 99, 86, 72, 45, 25, 10, 28, 19, 6, 90, 43, 29, 31, 67, 79, 46, 25, 74, 14, 97, 35, 76, 37, 65, 46, 23, 82, 6, 22, 30, 76, 93, 66, 94, 17, 96, 13, 20, 72],
[63, 40, 78, 8, 52, 9, 90, 41, 70, 28, 36, 14, 46, 44, 85, 96, 24, 52, 58, 15, 87, 37, 5, 98, 99, 39, 13, 61, 76, 38, 44, 99, 83, 74, 90, 22, 53, 80, 56, 98, 30, 51, 63, 39, 44, 30, 91, 91, 4, 22, 27, 73, 17, 35, 53, 18, 35, 45, 54, 56, 27, 78, 48, 13, 69, 36, 44, 38, 71, 25, 30, 56, 15, 22, 73, 43, 32, 69, 59, 25, 93, 83, 45, 11, 34, 94, 44, 39, 92],
[12, 36, 56, 88, 13, 96, 16, 12, 55, 54, 11, 47, 19, 78, 17, 17, 68, 81, 77, 51, 42, 55, 99, 85, 66, 27, 81, 79, 93, 42, 65, 61, 69, 74, 14, 1, 18, 56, 12, 1, 58, 37, 91, 22, 42, 66, 83, 25, 19, 4, 96, 41, 25, 45, 18, 69, 96, 88, 36, 93, 10, 12, 98, 32, 44, 83, 83, 4, 72, 91, 4, 27, 73, 7, 34, 37, 71, 60, 59, 31, 1, 54, 54, 44, 96, 93, 83, 36, 4, 45],
[30, 18, 22, 20, 42, 96, 65, 79, 17, 41, 55, 69, 94, 81, 29, 80, 91, 31, 85, 25, 47, 26, 43, 49, 2, 99, 34, 67, 99, 76, 16, 14, 15, 93, 8, 32, 99, 44, 61, 77, 67, 50, 43, 55, 87, 55, 53, 72, 17, 46, 62, 25, 50, 99, 73, 5, 93, 48, 17, 31, 70, 80, 59, 9, 44, 59, 45, 13, 74, 66, 58, 94, 87, 73, 16, 14, 85, 38, 74, 99, 64, 23, 79, 28, 71, 42, 20, 37, 82, 31, 23],
[51, 96, 39, 65, 46, 71, 56, 13, 29, 68, 53, 86, 45, 33, 51, 49, 12, 91, 21, 21, 76, 85, 2, 17, 98, 15, 46, 12, 60, 21, 88, 30, 92, 83, 44, 59, 42, 50, 27, 88, 46, 86, 94, 73, 45, 54, 23, 24, 14, 10, 94, 21, 20, 34, 23, 51, 4, 83, 99, 75, 90, 63, 60, 16, 22, 33, 83, 70, 11, 32, 10, 50, 29, 30, 83, 46, 11, 5, 31, 17, 86, 42, 49, 1, 44, 63, 28, 60, 7, 78, 95, 40],
[44, 61, 89, 59, 4, 49, 51, 27, 69, 71, 46, 76, 44, 4, 9, 34, 56, 39, 15, 6, 94, 91, 75, 90, 65, 27, 56, 23, 74, 6, 23, 33, 36, 69, 14, 39, 5, 34, 35, 57, 33, 22, 76, 46, 56, 10, 61, 65, 98, 9, 16, 69, 4, 62, 65, 18, 99, 76, 49, 18, 72, 66, 73, 83, 82, 40, 76, 31, 89, 91, 27, 88, 17, 35, 41, 35, 32, 51, 32, 67, 52, 68, 74, 85, 80, 57, 7, 11, 62, 66, 47, 22, 67],
[65, 37, 19, 97, 26, 17, 16, 24, 24, 17, 50, 37, 64, 82, 24, 36, 32, 11, 68, 34, 69, 31, 32, 89, 79, 93, 96, 68, 49, 90, 14, 23, 4, 4, 67, 99, 81, 74, 70, 74, 36, 96, 68, 9, 64, 39, 88, 35, 54, 89, 96, 58, 66, 27, 88, 97, 32, 14, 6, 35, 78, 20, 71, 6, 85, 66, 57, 2, 58, 91, 72, 5, 29, 56, 73, 48, 86, 52, 9, 93, 22, 57, 79, 42, 12, 1, 31, 68, 17, 59, 63, 76, 7, 77],
[73, 81, 14, 13, 17, 20, 11, 9, 1, 83, 8, 85, 91, 70, 84, 63, 62, 77, 37, 7, 47, 1, 59, 95, 39, 69, 39, 21, 99, 9, 87, 2, 97, 16, 92, 36, 74, 71, 90, 66, 33, 73, 73, 75, 52, 91, 11, 12, 26, 53, 5, 26, 26, 48, 61, 50, 90, 65, 1, 87, 42, 47, 74, 35, 22, 73, 24, 26, 56, 70, 52, 5, 48, 41, 31, 18, 83, 27, 21, 39, 80, 85, 26, 8, 44, 2, 71, 7, 63, 22, 5, 52, 19, 8, 20],
[17, 25, 21, 11, 72, 93, 33, 49, 64, 23, 53, 82, 3, 13, 91, 65, 85, 2, 40, 5, 42, 31, 77, 42, 5, 36, 6, 54, 4, 58, 7, 76, 87, 83, 25, 57, 66, 12, 74, 33, 85, 37, 74, 32, 20, 69, 3, 97, 91, 68, 82, 44, 19, 14, 89, 28, 85, 85, 80, 53, 34, 87, 58, 98, 88, 78, 48, 65, 98, 40, 11, 57, 10, 67, 70, 81, 60, 79, 74, 72, 97, 59, 79, 47, 30, 20, 54, 80, 89, 91, 14, 5, 33, 36, 79, 39],
[60, 85, 59, 39, 60, 7, 57, 76, 77, 92, 6, 35, 15, 72, 23, 41, 45, 52, 95, 18, 64, 79, 86, 53, 56, 31, 69, 11, 91, 31, 84, 50, 44, 82, 22, 81, 41, 40, 30, 42, 30, 91, 48, 94, 74, 76, 64, 58, 74, 25, 96, 57, 14, 19, 3, 99, 28, 83, 15, 75, 99, 1, 89, 85, 79, 50, 3, 95, 32, 67, 44, 8, 7, 41, 62, 64, 29, 20, 14, 76, 26, 55, 48, 71, 69, 66, 19, 72, 44, 25, 14, 1, 48, 74, 12, 98, 7],
[64, 66, 84, 24, 18, 16, 27, 48, 20, 14, 47, 69, 30, 86, 48, 40, 23, 16, 61, 21, 51, 50, 26, 47, 35, 33, 91, 28, 78, 64, 43, 68, 4, 79, 51, 8, 19, 60, 52, 95, 6, 68, 46, 86, 35, 97, 27, 58, 4, 65, 30, 58, 99, 12, 12, 75, 91, 39, 50, 31, 42, 64, 70, 4, 46, 7, 98, 73, 98, 93, 37, 89, 77, 91, 64, 71, 64, 65, 66, 21, 78, 62, 81, 74, 42, 20, 83, 70, 73, 95, 78, 45, 92, 27, 34, 53, 71, 15],
[30, 11, 85, 31, 34, 71, 13, 48, 5, 14, 44, 3, 19, 67, 23, 73, 19, 57, 6, 90, 94, 72, 57, 69, 81, 62, 59, 68, 88, 57, 55, 69, 49, 13, 7, 87, 97, 80, 89, 5, 71, 5, 5, 26, 38, 40, 16, 62, 45, 99, 18, 38, 98, 24, 21, 26, 62, 74, 69, 4, 85, 57, 77, 35, 58, 67, 91, 79, 79, 57, 86, 28, 66, 34, 72, 51, 76, 78, 36, 95, 63, 90, 8, 78, 47, 63, 45, 31, 22, 70, 52, 48, 79, 94, 15, 77, 61, 67, 68],
[23, 33, 44, 81, 80, 92, 93, 75, 94, 88, 23, 61, 39, 76, 22, 3, 28, 94, 32, 6, 49, 65, 41, 34, 18, 23, 8, 47, 62, 60, 3, 63, 33, 13, 80, 52, 31, 54, 73, 43, 70, 26, 16, 69, 57, 87, 83, 31, 3, 93, 70, 81, 47, 95, 77, 44, 29, 68, 39, 51, 56, 59, 63, 7, 25, 70, 7, 77, 43, 53, 64, 3, 94, 42, 95, 39, 18, 1, 66, 21, 16, 97, 20, 50, 90, 16, 70, 10, 95, 69, 29, 6, 25, 61, 41, 26, 15, 59, 63, 35]]
#Invert the list so that each element = 100 - element
invert(listNum)
#Holds points we know are of the shortest route
foundPoints = []
#Add the tip of the pyramid because everything has to go through that
foundPoints.append(location(0, 0, listNum[0][0], True))
#Holds points that might be the shortest route
possiblePoints = []
#Add the second row as possible points because everything must pass through the second row
possiblePoints.append(location(0, 1, (listNum[0][0] + listNum[1][0]), True))
possiblePoints.append(location(1, 1, (listNum[0][0] + listNum[1][1]), False))
foundBottom = False
#Loop until you find the bottom
while(not foundBottom):
#Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one
minLoc = possiblePoints[0]
for loc in possiblePoints:
if(loc.total < minLoc.total):
minLoc = loc
#Remove it from the list of possible points
removeIf(possiblePoints, minLoc)
foundPoints.append(minLoc)
#Add to the list of possible points from the point we just found and
#If you are at the bottom raise the flag to end the program
xLoc = minLoc.xLocation
yLoc = minLoc.yLocation + 1
if(yLoc >= NUM_ROWS):
foundBottom = True
else:
possiblePoints.append(location(xLoc, yLoc, minLoc.total + listNum[yLoc][xLoc], True))
xLoc += 1
possiblePoints.append(location(xLoc, yLoc, minLoc.total + listNum[yLoc][xLoc], False))
#Get the real total of the journey
actualTotal = ((100 * NUM_ROWS) - foundPoints[len(foundPoints) - 1].total)
#Invert the list so it can be read again
invert(listNum)
#Print the results
print("The value of the longest path is " + str(actualTotal))
if __name__ == "__main__":
timer = Stopwatch()
timer.start()
Problem67()
timer.stop()
print("It took " + timer.getString() + " to run this algorithm")
""" Results:
The value of the longest path is 7273
It took 16.483 seconds to run this algorithm
"""

50
Problem7.py Normal file
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@@ -0,0 +1,50 @@
#Project Eulter/Python/Problem7.py
#Matthew Ellison
# Created: 01-29-19
#Modified: 03-28-19
#What is the 10001th prime number?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
from Algorithms import getNumPrimes
__numPrimes = 10001 #The number of the prime number desired
def Problem7():
#Get the correct number of primes
primes = getNumPrimes(__numPrimes)
#Print the results
print("The " + str(__numPrimes) + "th prime number is " + str(primes[__numPrimes - 1]))
#If you are running this file, automatically start the correct function
if __name__ == '__main__':
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem7() #Call the function that answers the question
timer.stop() #Stop the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The 10001th prime number is 104743
It took 139.545 milliseconds to run this algorithm
"""

85
Problem8.py Normal file
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@@ -0,0 +1,85 @@
#Project Euler/Python/Problem8.py
#Matthew Ellison
# Created: 01-29-19
#Modified: 03-28-19
#Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?
"""
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
"""
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
#The number
__number = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"
def Problem8():
#Setup the variables
largestProduct = 0 #Holds the largest product of 13 adjacent digits
largestString = "" #Holds the 13 adjacent numbers that produce the largest product
#Start at the 13th entry and multiply all single digit numbers before and including that number together
numberLocation = 12 #The location in the number that you are working from
while(numberLocation < len(__number)):
currentProduct = int(__number[numberLocation]) * int(__number[numberLocation - 1]) * int(__number[numberLocation - 2]) * int(__number[numberLocation - 3]) * int(__number[numberLocation - 4]) * int(__number[numberLocation - 5]) * int(__number[numberLocation - 6]) * int(__number[numberLocation - 7]) * int(__number[numberLocation - 8]) * int(__number[numberLocation - 9]) * int(__number[numberLocation - 10]) * int(__number[numberLocation - 11]) * int(__number[numberLocation - 12])
#Save the largest product
if(currentProduct > largestProduct):
largestProduct = currentProduct
largestString = __number[numberLocation - 12:numberLocation + 1] #Have to add one because it stops before the second subscript
#Move to the next location
numberLocation += 1
#Print the results
print("The largest product of 13 adjacent digits in the number is " + str(largestProduct))
print("The numbers are: " + largestString)
#If you are running this file, automatically start the correct function
if __name__ == '__main__':
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem8() #Call the function that answers the question
timer.stop() #Stop the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The largest product of 13 adjacent digits in the number is 23514624000
The numbers are: 5576689664895
It took 2.593 milliseconds to run this algorithm
"""

73
Problem9.py Normal file
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@@ -0,0 +1,73 @@
#Project Euler/Python/Problem9.py
#Matthew Ellison
# Created: 01-29-19
#Modified: 03-28-19
#There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
Copyright (C) 2019 Matthew Ellison
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
"""
from Stopwatch import Stopwatch
import math
def Problem9():
#Setup the variables
foundTriplet = False
sideA = 1
#Start with the lowest possible a , 1, and search for the b and c to complete the triplet
while((sideA <= (1000 / 3)) and (not foundTriplet)):
#Setup b and c
sideB = sideA + 1 #b must be > a to be a triplet
sideC = math.hypot(sideA, sideB) #C is the hyp
#Loop through possible b's and calculate c's until you find the numbers or the sum gets too large
while((sideA + sideB + sideC) < 1000):
sideB += 1
sideC = math.hypot(sideA, sideB)
#If c is an integer make it one
if((sideC % 1) == 0):
sideC = int(round(sideC))
#Check if the correct sides were found
if((sideA + sideB + sideC) == 1000):
foundTriplet = True
#Otherwise increment a to the next possible number
else:
sideA += 1
#Print the results
if(foundTriplet):
print("The Pythagorean triplet where a + b + c = 1000 is " + str(sideA) + " " + str(sideB) + " " + str(int(sideC)))
print("The product of those numbers is " + str(int(sideA * sideB * sideC)))
else:
print("Could not find the triplet where a + b + c = 1000")
#If you are running this file, automatically start the correct function
if __name__ == "__main__":
timer = Stopwatch() #Determines the algorithm's run time
timer.start() #Start the timer
Problem9() #Call the function that answers the question
timer.stop() #Start the timer
#Print the results of the timer
print("It took " + timer.getString() + " to run this algorithm")
"""Results:
The Pythagorean triplet where a + b + c = 1000 is 200 375 425
The product of those numbers is 31875000
It took 22.106 milliseconds to run this algorithm
"""