All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
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.)
Hints/Tips other suggestions | Comment 10 of 11 |
Think about this problem this way. The smallest 21 step number is 924. This means that the smallest 22 step number, must be at least 924 after the first step. That is, the digits of its distinct factors must add to at least 924. Furthermore, the smallest 23 step number, must have factors whose digits add up to at least that number. That's why the values begin to increase so rapidly.
  Posted by Justin on 2006-01-13 11:15:24
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information