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?)

2) The required greatest number of steps is 5. Any number whose first and last digits differ by either 2 or 10 will take the full 5 steps. (there are 150 such numbers.)

Edited on September 14, 2023, 12:51 am

Posted by K Sengupta on 2023-01-09 02:28:37