Project Euler “is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.”

I've been working through some of the projects on the website to help teach myself Ruby in my space time.

Problem 4 of Project Euler states the following:

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 99.

Find the largest palindrome made from the product of two 3-digit numbers.

Just doing some simple calculations, the smallest number that can be generated by two 3 digits numbers multiplied together is:

100 * 100 = 10,000 which is a five digit number.  
An example of a five digit palindrome is 10101

The largest number is:

999 x 999 = 998,001 which is a six digit numbers.
An example of a six digit palindrome is 101101.

With this information in mind, the solution I came up with in Ruby is below.

class Palendromes
 
  def initialize
    @Solutions = []
  end
 
def FindPalendromes
 
  for x in 100..999
    for y in 100..999
 
      a = x * y
      a = a.to_s
      next if(a.length % 2 != 0)  
 
      b = []
      a.scan(/[0-9]/) do |z|
        b << z
      end
 
     @Solutions << a if(isPalendome?(b)) 
 
    end
  end
 
  @Solutions.sort
 
end
 
def isPalendome?(array)
 
  reversearray = array.reverse
  for x in 0..array.length
    return false if array[x] != reversearray[x]
  end
 
  return true
 
end
 
end
 
a = Palendromes.new
solutions = a.FindPalendromes
puts solutions

Starting at the bottom, a is set equal to a new instance of class Palindromes which is initialized with a call to the new method which in turn calls the initialize method which declares a new array called 'Solutions' where all the possible palindromes will be stored.  To find the palindromes, the 'FindPalindromes' method is deployed.  

FindPalindromes creates two loops from 100 to 999 so that every product of two three digit combination of numbers will be checked.  Entering the double for loop, x and y are multiplied together and stored in 'a'.  'a' is converted to a string so it can be more easily manipulated and it's length is checked.  If a is a five digit number and not a six digit number, a is discarded because it is obviously not the 'largest palindrome.'  

Next, using Regular Expressions,  each individual number is extracted from a (which is one long string) and put in individual elements in an newly created array b.  

For example the following conversion is made if a is equal to the string  '123456.'

b = {1, 2, 3, 4, 5, 6} 

This is done so that array functions can be used to check if the number is actually a palindrome.  

Next, b is sent to the method isPalindrome() which checks if the numbers contained in b are of a palindromic nature.  The isPalindrome() method is simple.  The method reverses b and stores the results in 'reversearray,' then, it loops through the length of the array comparing each element.  If an element doesn't match up, it returns false and nothing happens.  If however, every element matches, the isPalindrome method returns true and a is pushed into the Solutions array.

When the double for loop has exhausted every possible triple digit product combination, the solution array is sorted and returned to be printed to the screen.  

The answer is: 906609

My solution, while yielding the correct answer, is not the most elegant solution I discovered (not to my surprise as I am still learning the intricacies of the Ruby Programming language).  On the Project Euler forum, Olathe posted the following code:

max = 0
100.upto(999) { |a|
  a.upto(999) { |b|
    prod = a * b
    max = [max, prod].max if prod.to_s == prod.to_s.reverse
  }
}
puts "Maximum palindrome is #{ max }."

This code is sick (in a good way). He creates two for loops, finds the product of two three digit numbers, and converts the answer to a string — which is what I did in my code, but this is where the similarities end. Instead of extracting single digits into an array, he simply compares the product string to a reversed product string. If they match (if the number is a palindrome), he compares the number to the previous maximum number stored in the 'max' variable. If bigger then the previous max, he stores the number in match. If less, he discards it. Yes. Very Nice.