Start with any 3-digit number which is not a palindrome.
Reverse the digits and find the positive difference between the two numbers.
Using this result, continue this process until the difference is a number with fewer than three digits.

1) What are the only possible results? Prove it. 2) What is the greatest number of steps any number could take to terminate (and which numbers are these?)

(In reply to re: Solution by Ady TZIDON)

Starting with 900, after the first step you get 891, one of the possibilities e.g. accounted for.

Posted by Charlie on 2013-03-29 11:42:21