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 A problem

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pythag011
School Math Nerd
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Registration date : 2008-08-17

PostSubject: A problem   Wed Aug 20, 2008 9:39 pm

1. Determine if the set {1,2, ..., 96} can be partitioned into 32 sets of equal size and equal sum.

This was part a (The much easier part) of China Girls Math Olympiad 2008. It actually is not all that hard...

If anybody wants to know, this is the somewhat harder part:

b) Determine if the set {1, 2, ..., 99} can be partitioned into 33 sets of equal size and equal sum.


A hint for b:

Spoiler:
 

Clarification: The problem is just asking whether is it possible to divide the set into subsets with 3 elements each such that the sum of the elements in each subset is the same.
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FantasyLover
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Registration date : 2008-08-24

PostSubject: Re: A problem   Mon Aug 25, 2008 11:46 am

1)

sum of 1, 2, ..., 96 : 96*97/2=48*97, which is not a multiple of 32.

No, it can't be partitioned into 32 sets of equal size and equal sum.
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