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

Home > Just Math
S.O.S. partition needed!! (Posted on 2011-04-23) Difficulty: 3 of 5
Make a list of all 120 five-digit numbers created by permuting the digits 1,2,3,4,5.
Consider it as a set of numbers in base-10 system, ranging from 12345 to 54321.

Show that it is possible to partition this set into 2 subsets possessing equal sums of squares of their respective members.

bonus question: Is the result dependent of the base we choose?

  Submitted by Ady TZIDON    
No Rating
Solution: (Hide)
DIVIDE THE SET OF 120 POSSIBLE COMBINATIONS INTO TWO SUBSETS OF 60.
In the 1st subset a appears before b , like abcde, dacbe.
In the 2nd b appears before a , like bacde, dbcae.
Clearly the sums will be equal,independent of base and of the power (squares,cubes or else)we chose.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
abcdeJer2011-04-25 10:59:05
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 (3)
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