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

Home > Just Math
Two happy ends (Posted on 2011-03-07) Difficulty: 3 of 5
Consider a series of numbers, defined as follows:
Starting with any natural number, each member is a sum of the squares of the previous member`s digits.

Prove : The series always reaches either a stuck-on-one sequence: 1,1,1 or a closed loop of the following 8 numbers: 145,42,20,4,16,37,58,89, ...

Ex1: 12345,55,50,25,29,85,89,145.. etc
Ex2: 66,72,53,34,25,29,85,89,145
Ex3: 91,10,1,1,1..

See The Solution Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re(4): solution NOT enough | Comment 6 of 11 |
(In reply to re(3): solution NOT enough by Jer)

I understand that -- but it seems like your solution is the same as Charlie's -- the only thing you left out is the program, which he provided for you. I suppose Ady was just noting that for the benefit of other readers.

  Posted by Gamer on 2011-03-09 04:46:40

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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information