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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.)
Fractals & a hard extension | Comment 5 of 11 |

I did make a graph showing the chains for 1 through 100.  It kind of looks fractal.  I wouldn't know how to begin proving it or anything like that.

Now that you know which number<1000 takes the most steps, try to find the smallest numbers that take more steps.

  Posted by Jer on 2006-01-11 14:26:40
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