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Reverse and Differ (Posted on 2005-02-01) Difficulty: 2 of 5
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?)

See The Solution Submitted by Jer    
Rating: 2.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some thoughts | Comment 2 of 5 |

It seems that the greatest number of steps is 5 and the numbers that take 5 steps are...

(All palindromes < 200) + 2
(All palindromes > 200 & < 800) 2
(All palindromes > 800 & < 890) - 2
898  2 (i.e. 896 & 900)
(All palindromes > 900 & < 999) + 1 or - 2
999 - 2 (i.e. 997)


  Posted by Sing4TheDay on 2005-02-02 15:21:53
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