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Stupid number trick III (Posted on 2006-01-11) Difficulty: 3 of 5
Pick any whole number greater than 1.

1. Write down all of its proper divisors (including 1 and the number itself)
2. Add the digits of these divisors.
3. Use this sum to repeat steps 1 and 2 until your number does not change.

Must the process terminate?
At what number(s) can the process terminate at?
What numbers <1000 take the most steps to terminate?

See The Solution Submitted by Jer    
Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Fractals & a hard extension | Comment 8 of 11 |
(In reply to re: Fractals & a hard extension by Bob Smith)

>Are you suggesting there's a way other than just pointing the computer in the right direction and letting it run?

Not really, but you don't really have to check every number. 

>I ran numbers up to 10000, I think, and the longest chain was still 21.

Keep going... a chain of 22 is farther.  What's amazing is how high you have to go to get a chain of 23.


  Posted by Jer on 2006-01-12 07:41:19
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