=begin

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.

=end

n = 3

start = 10**n - 1
start.downto 10**(n-1) do |i|
  j = (i.to_s+i.to_s.reverse).to_i
  Math.sqrt(j).floor.downto 10**(n-1) do |k|
    qt = j / k.to_f
    if qt == qt.truncate && qt.truncate.to_s.length == n
      print(j.to_s+' = '+qt.to_s+' * '+k.to_s+"\n")
      exit
    end
  end
end