Added problems 4 and 5 and a helper function for 4 to Project Euler

ProjectEuler/Problem4.m

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+%ProjectEuler/Problem4.m
+%This is a script to answer Problem 4 for Project Euler
+%Find the largest palindrome made from the product of two 3-digit numbers
+
+%Make your variables
+answer = 0;	%For the product of the two numbers
+numbers = [100:999];	%Create an array with a list of all 3 digit numbers
+palindromes = [];	%Holds all the numbers that are palindromes
+%Create 2 counters for an inner loop and an outer loop
+%This allows you to multiply 2 numbers from the same array
+outerCounter = 1;
+innerCounter = 1;
+
+while(outerCounter < size(numbers)(2))
+	innerCounter = outerCounter;	%Once you have multiplied 2 numbers there is no need to multiply them again, so skip what has already been done
+	while(innerCounter < size(numbers)(2))
+		%Multiply the two numbers
+		answer = numbers(outerCounter) * numbers(innerCounter);
+
+		%See if the number is a palindromes
+		%%WARNING - Ocatave does not have a Reverse function. I had to create one that reversed strings
+		if(num2str(answer) == Reverse(num2str(answer)))
+			%Add it to the palindromes list
+			palindromes(end + 1) = answer;
+		end
+		++innerCounter;	%Increment
+	end
+	++outerCounter;	%Increment
+end
+
+clear outerCounter;
+clear innerCounter;
+clear answer;
+clear numbers;
+
+max(palindromes)
+
+%This way is slow. I would like to find a faster way
+%{
+The palindrome can be written as: abccba Which then simpifies to: 100000a + 10000b + 1000c + 100c + 10b + a And then: 100001a + 10010b + 1100c Factoring out 11, you get: 11(9091a + 910b + 100c) So the palindrome must be divisible by 11. Seeing as 11 is prime, at least one of the numbers must be divisible by 11
+%}

ProjectEuler/Problem5.m

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+%ProjectEuler/Problem5.m
+%This is a script to answer Problem 5 for Project Euler
+%What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
+
+%Create your variables
+value = 0;	%The value that is evenly divisible
+nums = [1:20];
+factors = [1];	%The factors that are already in the number
+list = [];	%For a temperary list of the factors of the current number
+counter = 1;
+
+%You need to find the factors of all the numbers from 1->20
+while(counter <= size(nums)(2))
+	list = factor(nums(counter));
+
+	%Search factors and try to match all elements in list
+	listCnt = 1;
+	factorCnt = 1;
+	while(listCnt <= size(list)(2))
+		if((factorCnt > size(factors)(2)) || (factors(factorCnt) > list(listCnt)))
+			%If it was not found add the factor to the list for the number and reset the counters
+			factors(end + 1) = list(listCnt);
+			factors = sort(factors);
+			factorCnt = 1;
+			listCnt = 1;
+		elseif(factors(factorCnt) == list(listCnt))
+			++listCnt;
+			++factorCnt;
+		else
+			++factorCnt;
+		end
+	end
+	++counter;
+end
+
+%Cleanup your variables
+clear counter;
+clear factorCnt;
+clear listCnt;
+clear list;
+clear nums;
+clear ans;	%Appears whenever you use increment
+
+value = prod(factors);
+value

ProjectEuler/Reverse.m

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+function [rString] = Reverse(str)
+%Reverse(string)
+%This function Reverse the order of the elements in an array
+%It was specifically designed for a string, but should work on other 1xX arrays
+%
+
+	if(nargin ~= 1)
+		error('That is not a valid number of arguments')
+		return;
+	end
+
+	counter = size(str)(2);	%Set the counter to the last element in string
+	%Loop until the counter reaches 0
+	while(counter > 0)
+		%Add the current element of string to rString
+		rString(end + 1) = str(counter);
+		--counter;
+	end
+end