Detects whether a number is palindromic without converting the number to a String.

palindrome.rb

module Palindrome
  def self.palindrome?(n)
    n == reverse(n)
  end
  
  def self.reverse(n)
    rs = 0
    while n > 0
      n, r  = n.divmod 10
      rs    = rs * 10 + r
    end
    rs
  end
end