Start with any integer, reverse its digits, then add the two numbers together. Repeat the process: a palindromic number should soon emerge.
Let’s try 87, for example:
87 + 78 = 165; 165 + 561 = 726; 726 + 627 = 1,353; 1,353 + 3,531 = 4,884, which is a palindrome. The integer 159 produces a palindrome in just two steps:
159 + 951 = 1,110; 1,110 + 0,111 = 1,221.
The number of steps is unpredictable: try 89 (twenty-four steps are needed to obtain 8,813,200,023,188).
The number 196 is the smallest integer that stubbornly refuses to produce a palindrome. Although billions of iterations have been performed, resulting in integers with more than a billion digits, no palindrome has yet been found… Fire up your computers!
