Home > Just Math
| S.O.S. partition needed!! (Posted on 2011-04-23) |
 |
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 |
 | abcde | Jer | 2011-04-25 10:59:05 |
|
|
Please log in:
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:
|
