From 7d107c1071c1926fd77fe32f92ea744f6f6f754b Mon Sep 17 00:00:00 2001
From: Mattrixwv <m_ellison@ymail.com>
Date: Fri, 19 Jun 2020 19:58:36 -0400
Subject: [PATCH] Updated problems to be more in line with conventions

---
 Problem1.lua  | 10 ++++----
 Problem10.lua |  6 ++---
 Problem11.lua |  8 +++----
 Problem12.lua |  6 ++---
 Problem13.lua |  8 +++----
 Problem14.lua |  8 +++----
 Problem15.lua | 12 +++++-----
 Problem16.lua |  4 ++--
 Problem17.lua | 10 ++++----
 Problem18.lua | 32 ++++++++++++-------------
 Problem19.lua | 65 ++++++++++++++++++++++++++-------------------------
 Problem2.lua  | 12 +++++-----
 Problem20.lua |  8 +++----
 Problem21.lua | 14 +++++------
 Problem22.lua | 10 ++++----
 Problem23.lua |  6 ++---
 Problem24.lua | 10 ++++----
 Problem25.lua |  6 ++---
 Problem26.lua |  4 ++--
 Problem27.lua |  4 ++--
 Problem28.lua |  4 ++--
 Problem29.lua |  4 ++--
 Problem3.lua  |  8 +++----
 Problem30.lua | 10 ++++----
 Problem4.lua  | 10 ++++----
 Problem5.lua  | 10 ++++----
 Problem6.lua  | 10 ++++----
 Problem67.lua | 37 +++++++++++------------------
 Problem7.lua  |  8 +++----
 Problem8.lua  |  6 ++---
 Problem9.lua  |  6 ++---
 31 files changed, 174 insertions(+), 182 deletions(-)

diff --git a/Problem1.lua b/Problem1.lua
index aa8b6f0..47db185 100644
--- a/Problem1.lua
+++ b/Problem1.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem1.lua
 --Matthew Ellison
 -- Created: 02-01-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --What is the sum of all the multiples of 3 or 5 that are less than 1000
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -25,11 +25,11 @@
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
-TOP_NUMBER = 999;	--This is the largest number that you are going to check
-sumOfMultiples = 0;
+local TOP_NUMBER = 999;	--This is the largest number that you are going to check
+local sumOfMultiples = 0;
 for num = 1, TOP_NUMBER do
 	if((num % 3) == 0) then
 		sumOfMultiples = sumOfMultiples + num;
diff --git a/Problem10.lua b/Problem10.lua
index 15aebcb..7946641 100644
--- a/Problem10.lua
+++ b/Problem10.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem10.lua
 --Matthew Ellison
 -- Created: 02-06-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --Find the sum of all the primes below two million
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -26,7 +26,7 @@ require "Stopwatch"
 require "Algorithms"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 LARGEST_PRIME = 2000000;	--Sum all prime numbers smaller than this
diff --git a/Problem11.lua b/Problem11.lua
index f05c920..dd6c624 100644
--- a/Problem11.lua
+++ b/Problem11.lua
@@ -1,7 +1,7 @@
 --ProjectEuler/lua/Problem11.lua
 --Matthew Ellison
 -- Created: 02-06-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --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
@@ -27,7 +27,7 @@
 ]]
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -47,7 +47,7 @@
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 --Setup the grid of numbers
@@ -74,7 +74,7 @@ GRID[19] = {20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 5
 GRID[20] = {1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48};
 
 --This function returns the product of all elements in a table
-function getTableProduct(numbers)
+local function getTableProduct(numbers)
 	local product = 1;	--Start with 1 because you are working with multiplication
 	--Loop through ever element in a table and multiply them all together
 	for location=1,#numbers do
diff --git a/Problem12.lua b/Problem12.lua
index 0ce6644..b7d0b24 100644
--- a/Problem12.lua
+++ b/Problem12.lua
@@ -1,11 +1,11 @@
 --ProjectEUler/lua/Problem12.lua
 --Matthew Ellison
 -- Created: 02-07-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --What is the value of the first triangle number to have over five hundred divisors?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -26,7 +26,7 @@ require "Stopwatch"
 require "Algorithms"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 GOAL_DIVISORS = 500;
diff --git a/Problem13.lua b/Problem13.lua
index 927479c..83a44b2 100644
--- a/Problem13.lua
+++ b/Problem13.lua
@@ -1,7 +1,7 @@
 --ProjectEuler/lua/Problem13.lua
 --Matthew Ellison
 -- Created: 02-07-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --Work out the first ten digits of the sum of the following one-hundred 50-digit numbers
 --[[
 37107287533902102798797998220837590246510135740250
@@ -108,7 +108,7 @@
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --I used the bigint library from https://github.com/empyreuma/bigint.lua
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -129,10 +129,10 @@ require "Stopwatch"
 local bigint = require "bigint"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
-NUMBERS = {};
+local NUMBERS = {};
 NUMBERS[#NUMBERS+1] = bigint.new("37107287533902102798797998220837590246510135740250")
 NUMBERS[#NUMBERS+1] = bigint.new("46376937677490009712648124896970078050417018260538")
 NUMBERS[#NUMBERS+1] = bigint.new("74324986199524741059474233309513058123726617309629")
diff --git a/Problem14.lua b/Problem14.lua
index 34e05ff..99023d6 100644
--- a/Problem14.lua
+++ b/Problem14.lua
@@ -1,7 +1,7 @@
 --ProjectEuler/lua/Problem14.lua
 --Matthew Ellison
 -- Created: 02-07-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --[[
 The following iterative sequence is defined for the set of positive integers:
 n → n/2 (n is even)
@@ -10,7 +10,7 @@ Which starting number, under one million, produces the longest chain?
 ]]
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -30,13 +30,13 @@ Which starting number, under one million, produces the longest chain?
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 TOP_NUM = 1000000	--The largest number that you will check against the chain
 
 --This function returns a table of numbers created by the chain
-function getChain(startNum)
+local function getChain(startNum)
 	--Put the starting number in the list
 	local chain = {};
 	chain[#chain+1] = startNum;
diff --git a/Problem15.lua b/Problem15.lua
index fd3e341..cd313cf 100644
--- a/Problem15.lua
+++ b/Problem15.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem15.lua
 --Matthew Ellison
 -- Created: 02-07-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --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?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -25,13 +25,13 @@
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 GRID_WIDTH = 20;
 GRID_HEIGHT = 20;
-lowestXReached = 20;
-function movement(currentX, currentY)
+local lowestXReached = 20;
+local function movement(currentX, currentY)
 	--Return 1 if you are at the finish location
 	if((currentX == GRID_WIDTH) and (currentY == GRID_HEIGHT)) then
 		return 1;
@@ -59,7 +59,7 @@ function movement(currentX, currentY)
 end
 
 --Start the recursion at the correct location and catch what is returned
-numberMoves = movement(0, 0);
+local numberMoves = movement(0, 0);
 
 timer:stop();
 
diff --git a/Problem16.lua b/Problem16.lua
index 1729ab0..a1d239f 100644
--- a/Problem16.lua
+++ b/Problem16.lua
@@ -1,12 +1,12 @@
 --ProjectEuler/lua/Problem16.lua
 --Matthew Ellison
 -- Created: 02-07-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --What is the sum of the digits of the number 2^1000?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --I used the bigint library from https://github.com/empyreuma/bigint.lua
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
diff --git a/Problem17.lua b/Problem17.lua
index b940914..705b16a 100644
--- a/Problem17.lua
+++ b/Problem17.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem17.lua
 --Matthew Ellison
 -- Created: 02-07-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -25,12 +25,12 @@
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 --This function takes a number and returns it as a string in english
 --This function only works for numbers -1,000,000 < num < 1,000,000
-function getStringFromNum(number)
+local function getStringFromNum(number)
 	local numberString = "";
 	--Starting with the largest digit create a string based on the number passed in
 	--Check for negative
@@ -144,7 +144,7 @@ function getStringFromNum(number)
 end
 
 --This function returns the number of letters in a string, ignoring punctuation, whitespace, and numbers
-function getNumberChars(number)
+local function getNumberChars(number)
 	local sumOfLetters = 0;
 	--Start at location 1 and count the number of letters, ignoring punctuation and whitespace
 	for location=1,string.len(number) do
diff --git a/Problem18.lua b/Problem18.lua
index c5a90a6..2b26986 100644
--- a/Problem18.lua
+++ b/Problem18.lua
@@ -1,7 +1,7 @@
 --ProjectEuler/lua/Problem18.lua
 --Matthew Ellison
 -- Created: 03-12-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --Find the maximum total from top to bottom
 --[[
 75
@@ -23,7 +23,7 @@
 --This is done using a breadth first search
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -51,7 +51,7 @@ location = {
 };
 ]]
 
-function invert(list)
+local function invert(list)
 	for rowCnt=1,NUM_ROWS do
 		for colCnt=1,#list[rowCnt] do
 			list[rowCnt][colCnt] = 100 - list[rowCnt][colCnt];
@@ -59,7 +59,7 @@ function invert(list)
 	end
 end
 
-function foundInList(list, loc)
+local function foundInList(list, loc)
 	for location=1,#list do
 		if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then
 			return true;
@@ -68,8 +68,8 @@ function foundInList(list, loc)
 	return false;
 end
 
-function remove_if(list, loc)
-	location = 1;
+local function remove_if(list, loc)
+	local location = 1;
 	while(location <= #list) do
 		if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then
 			table.remove(list, location);
@@ -80,13 +80,13 @@ function remove_if(list, loc)
 end
 
 --Create a timer and time the algorithm
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
-NUM_ROWS = 15;
+local NUM_ROWS = 15;
 
 
-list = {};
+local list = {};
 list[1]  = {75};
 list[2]  = {95, 64};
 list[3]  = {17, 47, 82};
@@ -106,18 +106,18 @@ list[15] = {04, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 04, 23};
 --Invert the list so all elements are 100 - element
 invert(list);
 
-foundPoints = {};	--This is a table of locations
+local foundPoints = {};	--This is a table of locations
 foundPoints[1] = {xLocation = 1, yLocation = 1, total = list[1][1], fromRight = false};
-possiblePoints = {};	--This is a table of locations
+local possiblePoints = {};	--This is a table of locations
 --Add the second row as possible points
 possiblePoints[1] = {xLocation = 1, yLocation = 2, total = (list[1][1] + list[2][1]), fromRight = true};
 possiblePoints[2] = {xLocation = 2, yLocation = 2, total = (list[1][1] + list[2][2]), fromRight = false};
-foundBottom = false;	--Used when you find a point at the bottom
+local foundBottom = false;	--Used when you find a point at the bottom
 
 --Loop until you find the bottom
 while(not foundBottom) do
 	--Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one
-	minLoc = possiblePoints[1];
+	local minLoc = possiblePoints[1];
 	for loc=1,#possiblePoints do
 		if(possiblePoints[loc].total < minLoc.total) then
 			minLoc = possiblePoints[loc];
@@ -137,8 +137,8 @@ while(not foundBottom) do
 
 	--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;	--Add one because you will always be moving to the next row
+	local xLoc = minLoc.xLocation;
+	local yLoc = minLoc.yLocation + 1;	--Add one because you will always be moving to the next row
 	if(yLoc > NUM_ROWS) then
 		foundBottom = true;
 	else
@@ -150,7 +150,7 @@ while(not foundBottom) do
 	end
 end
 
-actualTotal = ((100 * (NUM_ROWS)) - foundPoints[#foundPoints].total);
+local actualTotal = ((100 * (NUM_ROWS)) - foundPoints[#foundPoints].total);
 
 --Stop the timer
 timer:stop();
diff --git a/Problem19.lua b/Problem19.lua
index a4c1bf7..80c8345 100644
--- a/Problem19.lua
+++ b/Problem19.lua
@@ -1,7 +1,7 @@
 --ProjectEuler/lua/Problem19.lua
 --Matthew Ellison
 -- Created: 03-13-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --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.
@@ -16,7 +16,7 @@ A leap year occurs on any year evenly divisible by 4, but not on a century unles
 ]]
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -48,20 +48,41 @@ DAYS = {
 	ERROR = 8;
 }
 
-START_YEAR = 1901;
-END_YEAR = 2000;
+local START_YEAR = 1901;
+local END_YEAR = 2000;
+
+local function isLeapYear(year)
+	local answer;
+	if(year < 1) then
+		answer = false;
+	elseif((year % 100) == 0) then
+		--This rule only applies at and after 1800
+		if(year <= 1700) then
+			answer = true;
+		elseif((year % 400) == 0) then
+			answer = true;
+		else
+			answer = false;
+		end
+	elseif((year % 4) == 0) then
+		answer = true;
+	else
+		answer = false;
+	end
+	return answer;
+end
 
 --Return the day of the week that the date you pass into it is on
-function getDay(month, day, year)
+local function getDay(month, day, year)
 	--Make sure the numbers are within propper bounds
 	if((month < 1) or (month > 12) or (day < 1) or (day > 31) or (year < 1)) then
 		return DAYS.ERROR;
 	end
 
-	numDays = 0;
-	currentYear = 1;
-	currentMonth = 1;
-	currentDay = DAYS.SATURDAY;
+	local numDays = 0;
+	local currentYear = 1;
+	local currentMonth = 1;
+	local currentDay = DAYS.SATURDAY;
 	day = day - 1;
 
 	--Add the correct number of days for every year
@@ -132,29 +153,9 @@ function getDay(month, day, year)
 	return day;
 end
 
-function isLeapYear(year)
-	if(year < 1) then
-		answer = false;
-	elseif((year % 100) == 0) then
-		--This rule only applies at and after 1800
-		if(year <= 1700) then
-			answer = true;
-		elseif((year % 400) == 0) then
-			answer = true;
-		else
-			answer = false;
-		end
-	elseif((year % 4) == 0) then
-		answer = true;
-	else
-		answer = false;
-	end
-	return answer;
-end
-
 --Setup the variables
-timer = Stopwatch:create();
-totalSundays = 0;
+local timer = Stopwatch:create();
+local totalSundays = 0;
 
 --Start the timer
 timer:start();
@@ -163,7 +164,7 @@ timer:start();
 for year=START_YEAR,END_YEAR do
 	--Run for all months in the year
 	for month=1,12 do
-		day = getDay(month, 1, year);
+		local day = getDay(month, 1, year);
 		if(day == DAYS.ERROR) then
 			io.output("There was an error with the day\n");
 			os.exit();
diff --git a/Problem2.lua b/Problem2.lua
index 93081bb..5152a66 100644
--- a/Problem2.lua
+++ b/Problem2.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem1.lua
 --Matthew Ellison
 -- Created: 02-01-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --The sum of the even Fibonacci numbers less than 4,000,000
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -25,16 +25,16 @@
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 --Setup the variables
 TOP_NUM = 4000000;	--The highest looked for Fibonacci numbers
-fibSum = 0;		--Holds the sum of the Fibonacci numbers
-fibNums = {1, 1, 2};	--An array to keep track of the Fibonacci numbers
+local fibSum = 0;		--Holds the sum of the Fibonacci numbers
+local fibNums = {1, 1, 2};	--An array to keep track of the Fibonacci numbers
 
 --Loop to generate the Fibonacci numbers
-cnt = 2;	--A counter to hold the location in the array of the currently working Fibonacci number
+local cnt = 2;	--A counter to hold the location in the array of the currently working Fibonacci number
 fibNums[(cnt % 3) + 1] = fibNums[((cnt - 1) % 3) + 1] + fibNums[((cnt - 2) % 3) + 1];
 while(fibNums[(cnt % 3) + 1] < TOP_NUM) do
 	--If the number is even add it to the sum, otherwise ignore it
diff --git a/Problem20.lua b/Problem20.lua
index 197e4dc..10ee275 100644
--- a/Problem20.lua
+++ b/Problem20.lua
@@ -1,12 +1,12 @@
 --ProjectEuler/lua/Problem20.lua
 --Matthew Ellison
 -- Created: 03-14-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --What is the sum of the digits of 100!
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --I used the bigint library from https://github.com/empyreuma/bigint.lua
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -30,7 +30,7 @@ TOP_NUM = 100;
 
 
 --Start the timer
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 local num = bigint.new(1);	--The number to be generated
@@ -41,7 +41,7 @@ for cnt = 1, TOP_NUM do
 end
 
 --Get a string of the number because it is easier to pull appart the individual characters to get the sum
-numString = bigint.unserialize(num, 's');
+local numString = bigint.unserialize(num, 's');
 --Run through every character in the string, convert it back to an integer and add it to the running sum
 for cnt = 1, string.len(numString) do
 	sum = sum + tonumber(string.sub(numString, cnt, cnt));
diff --git a/Problem21.lua b/Problem21.lua
index 98bef74..4824ec0 100644
--- a/Problem21.lua
+++ b/Problem21.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem21.lua
 --Matthew Ellison
 -- Created: 03-19-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --Evaluate the sum of all the amicable numbers under 10000
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -29,26 +29,26 @@ LIMIT = 10000;	--The top number that will be evaluated
 
 
 --Setup the timer
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 
 --Setup the variables
-divisorSum = {};	--Holds the sum of the factors of the subscript number
+local divisorSum = {};	--Holds the sum of the factors of the subscript number
 
 --Start the timer
 timer:start();
 
 --Generate the factors of all the numbers < 10000, get their sum, and add it to the list
 for cnt = 1, LIMIT do
-	divisors = getDivisors(cnt);	--Get all the divisors of a number
+	local divisors = getDivisors(cnt);	--Get all the divisors of a number
 	if(#divisors > 1) then
 		table.remove(divisors);	--Remove the last entry because it will be the number itself
 	end
 	divisorSum[#divisorSum + 1] = getSum(divisors);	--Add the sum of the divisors to the vector
 end
 --Check every sum of divisors in the list for a matching sum
-amicable = {};
+local amicable = {};
 for cnt = 1, #divisorSum do
-	sum = divisorSum[cnt];
+	local sum = 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(sum >= #divisorSum) then
 	--We know that divisorSum[cnt] == sum, do if divisorSum[sum] == cnt we have found an amicable number
diff --git a/Problem22.lua b/Problem22.lua
index dc247b8..8ab27a6 100644
--- a/Problem22.lua
+++ b/Problem22.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem22.lua
 --Matthew Ellison
 -- Created: 03-20-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --What is the total of all the name scores in the file?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -397,9 +397,9 @@ NAMES = {"MARY","PATRICIA","LINDA","BARBARA","ELIZABETH","JENNIFER","MARIA","SUS
 
 
 --Setup the variables
-timer = Stopwatch:create();
-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
+local timer = Stopwatch:create();
+local sums = {}	--Holds the score based on the sum of the characters in the name
+local prod = {}	--Holds the score based on the sum of the characters and the location in alphabetical order
 
 --Start the timer
 timer:start();
diff --git a/Problem23.lua b/Problem23.lua
index 5030b78..1640c38 100644
--- a/Problem23.lua
+++ b/Problem23.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem23.lua
 --Matthew Ellison
 -- Created: 03-22-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -29,7 +29,7 @@ require "Algorithms"
 MAX_NUM = 28123;	--The highest number that will be evaluated
 
 
-function isSum(abund, num)
+local function isSum(abund, num)
 	local sumOfNums = 0;
 	--Pick a number for the first part of the sum
 	for firstNum = 1, #abund do
diff --git a/Problem24.lua b/Problem24.lua
index 7a68020..80ca20a 100644
--- a/Problem24.lua
+++ b/Problem24.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem24.lua
 --Matthew Ellison
 -- Created: 03-24-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -29,14 +29,14 @@ NEEDED_PERM = 1000000;	--The number of the permutation that you need
 
 
 --Setup the variables
-timer = Stopwatch:create();
-nums = "0123456789";
+local timer = Stopwatch:create();
+local nums = "0123456789";
 
 --Start the timer
 timer:start();
 
 --Get all permutations of the string
-permutations = getPermutations(nums);
+local permutations = getPermutations(nums);
 
 --Stop the timer
 timer:stop();
diff --git a/Problem25.lua b/Problem25.lua
index db52598..d23e21c 100644
--- a/Problem25.lua
+++ b/Problem25.lua
@@ -1,12 +1,12 @@
 --ProjectEuler/lua/Problem25.lua
 --Matthew Ellison
 -- Created: 03-26-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --I used the bigint library from https://github.com/empyreuma/bigint.lua
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -28,7 +28,7 @@ require "Algorithms";
 local bigint = require "bigint";
 
 
-NUM_DIGITS = 1000;	--The number of digits to calculate up to
+local NUM_DIGITS = 1000;	--The number of digits to calculate up to
 
 
 --Setup the variables
diff --git a/Problem26.lua b/Problem26.lua
index 04bafe3..a1baec7 100644
--- a/Problem26.lua
+++ b/Problem26.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem26.lua
 --Matthew Ellison
 -- Created: 08-02-19
---Modified: 08-02-19
+--Modified: 06-19-20
 --Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
diff --git a/Problem27.lua b/Problem27.lua
index 879c76e..c32134e 100644
--- a/Problem27.lua
+++ b/Problem27.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem27.lua
 --Matthew Ellison
 -- Created: 09-15-19
---Modified: 09-15-19
+--Modified: 06-19-20
 --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.
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
diff --git a/Problem28.lua b/Problem28.lua
index 4b7fd4f..42ba82f 100644
--- a/Problem28.lua
+++ b/Problem28.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem28.lua
 --Matthew Ellison
 -- Created: 09-15-19
---Modified: 10-06-19
+--Modified: 06-19-20
 --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.
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
diff --git a/Problem29.lua b/Problem29.lua
index d43ef41..b485e50 100644
--- a/Problem29.lua
+++ b/Problem29.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem29.lua
 -- Created: 10-10-19
---Modified: 10-10-19
+--Modified: 06-19-20
 --How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --I used the bigint library from https://github.com/empyreuma/bigint.lua
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
diff --git a/Problem3.lua b/Problem3.lua
index 978eaa3..2e0fcf0 100644
--- a/Problem3.lua
+++ b/Problem3.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem3.lua
 --Matthew Ellison
 -- Created: 02-04-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --The largest prime factor of 600851475143
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -26,13 +26,13 @@ require "Stopwatch"
 require "Algorithms"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 
 TARGET_NUMBER = 600851475143;
 --Get the factors of the number
-factors = getFactors(TARGET_NUMBER);
+local factors = getFactors(TARGET_NUMBER);
 timer:stop();
 
 --The largest number will be the answer
diff --git a/Problem30.lua b/Problem30.lua
index a933b27..0fb2f23 100644
--- a/Problem30.lua
+++ b/Problem30.lua
@@ -1,10 +1,10 @@
---ProjectEuler/lua/Problem29.lua
+--ProjectEuler/lua/Problem30.lua
 -- Created: 10-28-19
---Modified: 10-28-19
+--Modified: 06-19-20
 --Find the sum of all the numbers that can be written as the sum of the fifth powers of their digits.
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -25,7 +25,7 @@ require "Stopwatch"
 
 
 --Returns a table with the individual digits of the number passed to it
-function getDigits(num)
+local function getDigits(num)
 	local listOfDigits = {};	--This table holds the individual digits of num
 	--The easiest way to get the individual digits of a number is by converting it to a string
 	local digits = tostring(num);
@@ -38,7 +38,7 @@ function getDigits(num)
 end
 
 --Gets the sum of a table of numbers
-function getSumOfTable(ary)
+local function getSumOfTable(ary)
 	local sum = 0;	--Start the sum at 0 so you can add to it
 	--Add every number in the table to the sum
 	for cnt = 1, #ary do
diff --git a/Problem4.lua b/Problem4.lua
index b14e0df..fd9c2b0 100644
--- a/Problem4.lua
+++ b/Problem4.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem4.lua
 --Matthew Ellison
 -- Created: 02-05-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --Find the largest palindrome made from the product of two 3-digit numbers
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -25,14 +25,14 @@
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
-palindromes = {};	--Holds all palindromes the program finds
+local palindromes = {};	--Holds all palindromes the program finds
 --Loop through every number 100-999 twice, nested, so you can multiply every number by every other number in the array
 for num1=100,999 do
 	for num2=num1,999 do
-		currentNum = num1 * num2;
+		local 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(tostring(currentNum) == string.reverse(tostring(currentNum))) then
diff --git a/Problem5.lua b/Problem5.lua
index d419a37..b467a58 100644
--- a/Problem5.lua
+++ b/Problem5.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem5.lua
 --Matthew Ellison
 -- Created: 02-05-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -25,12 +25,12 @@
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 --Setup the variables you need
-numFound = false;
-currentNum = 22;	--Start looking at 22 becuase it must be divisible by 2 and greater than 20
+local numFound = false;
+local currentNum = 22;	--Start looking at 22 becuase it must be divisible by 2 and greater than 20
 --Start a loop looking for the correct number
 while((not numFound) and (currentNum > 0)) do
 	--Set that you found the number to true because you set this flag when you don't find it
diff --git a/Problem6.lua b/Problem6.lua
index a4697c1..039242e 100644
--- a/Problem6.lua
+++ b/Problem6.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem6.lua
 --Matthew Ellison
 -- Created: 02-06-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -25,12 +25,12 @@
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 --Create the variables you need
-sumOfSquares = 0;
-squareOfSum = 0;
+local sumOfSquares = 0;
+local squareOfSum = 0;
 --Loop through all numbers 1-100 to do the appropriate math with them
 for num=1,100 do
 	sumOfSquares = sumOfSquares + num^2;	--Get the sum of the squares of the first 100 natural number
diff --git a/Problem67.lua b/Problem67.lua
index 66a2edd..8bc39b2 100644
--- a/Problem67.lua
+++ b/Problem67.lua
@@ -1,7 +1,7 @@
 --ProjectEuler/lua/Problem67.lua
 --Matthew Ellison
 -- Created: 03-26-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --Find the maximum total from top to bottom
 --[[
 59
@@ -108,7 +108,7 @@
 --This is done using a breadth first search
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -136,7 +136,7 @@ location = {
 };
 ]]
 
-function invert(list)
+local function invert(list)
 	for rowCnt=1,NUM_ROWS do
 		for colCnt=1,#list[rowCnt] do
 			list[rowCnt][colCnt] = 100 - list[rowCnt][colCnt];
@@ -144,17 +144,8 @@ function invert(list)
 	end
 end
 
-function foundInList(list, loc)
-	for location=1,#list do
-		if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then
-			return true;
-		end
-	end
-	return false;
-end
-
-function remove_if(list, loc)
-	location = 1;
+local function remove_if(list, loc)
+	local location = 1;
 	while(location <= #list) do
 		if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then
 			table.remove(list, location);
@@ -165,13 +156,13 @@ function remove_if(list, loc)
 end
 
 --Create a timer and time the algorithm
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 NUM_ROWS = 100;
 
 
-list = {};
+local list = {};
 list[1]  = {59};
 list[2]  = {73, 41};
 list[3]  = {52, 40,  9};
@@ -276,18 +267,18 @@ list[100] ={23, 33, 44, 81, 80, 92, 93, 75, 94, 88, 23, 61, 39, 76, 22, 03, 28,
 --Invert the list so all elements are 100 - element
 invert(list);
 
-foundPoints = {};	--This is a table of locations
+local foundPoints = {};	--This is a table of locations
 foundPoints[1] = {xLocation = 1, yLocation = 1, total = list[1][1], fromRight = false};
-possiblePoints = {};	--This is a table of locations
+local possiblePoints = {};	--This is a table of locations
 --Add the second row as possible points
 possiblePoints[1] = {xLocation = 1, yLocation = 2, total = (list[1][1] + list[2][1]), fromRight = true};
 possiblePoints[2] = {xLocation = 2, yLocation = 2, total = (list[1][1] + list[2][2]), fromRight = false};
-foundBottom = false;	--Used when you find a point at the bottom
+local foundBottom = false;	--Used when you find a point at the bottom
 
 --Loop until you find the bottom
 while(not foundBottom) do
 	--Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one
-	minLoc = possiblePoints[1];
+	local minLoc = possiblePoints[1];
 	for loc=1,#possiblePoints do
 		if(possiblePoints[loc].total < minLoc.total) then
 			minLoc = possiblePoints[loc];
@@ -301,8 +292,8 @@ while(not foundBottom) do
 
 	--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;	--Add one because you will always be moving to the next row
+	local xLoc = minLoc.xLocation;
+	local yLoc = minLoc.yLocation + 1;	--Add one because you will always be moving to the next row
 	if(yLoc > NUM_ROWS) then
 		foundBottom = true;
 	else
@@ -312,7 +303,7 @@ while(not foundBottom) do
 	end
 end
 
-actualTotal = ((100 * (NUM_ROWS)) - foundPoints[#foundPoints].total);
+local actualTotal = ((100 * (NUM_ROWS)) - foundPoints[#foundPoints].total);
 
 --Stop the timer
 timer:stop();
diff --git a/Problem7.lua b/Problem7.lua
index 5ff8c83..18c82c9 100644
--- a/Problem7.lua
+++ b/Problem7.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem7.lua
 --Matthew Ellison
 -- Created: 02-05-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --What is the 10001th prime number?
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -26,12 +26,12 @@ require "Stopwatch"
 require "Algorithms"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 NUM_PRIMES = 10001;	--The number of the prime number desired
 --Get the correct number of primes
-primes = getNumPrimes(NUM_PRIMES);
+local primes = getNumPrimes(NUM_PRIMES);
 
 timer:stop();
 
diff --git a/Problem8.lua b/Problem8.lua
index 13aadd2..ca8d7ab 100644
--- a/Problem8.lua
+++ b/Problem8.lua
@@ -1,7 +1,7 @@
 --ProjectEuler/lua/Problem8.lua
 --Matthew Ellison
 -- Created: 02-06-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?
 --[[
 73167176531330624919225119674426574742355349194934
@@ -27,7 +27,7 @@
 ]]
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -47,7 +47,7 @@
 require "Stopwatch"
 
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 --Put the number into a variable. A string will do for now
diff --git a/Problem9.lua b/Problem9.lua
index 4153b13..fa011b2 100644
--- a/Problem9.lua
+++ b/Problem9.lua
@@ -1,11 +1,11 @@
 --ProjectEuler/lua/Problem9.lua
 --Matthew Ellison
 -- Created: 02-06-19
---Modified: 03-28-19
+--Modified: 06-19-20
 --There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
 --All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
 --[[
-	Copyright (C) 2019  Matthew Ellison
+	Copyright (C) 2020  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
@@ -24,7 +24,7 @@
 
 require "Stopwatch"
 
-timer = Stopwatch:create();
+local timer = Stopwatch:create();
 timer:start();
 
 local foundTriplet = false;	--A simple flag to determine if we have found what we are looking for