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 Make it equal (Posted on 2010-05-26)
Divide the set {1,2,3,4, ....,n} into three disjoint subsets A , B , C whose sums of elements are equal. For what values of n it is feasible?

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 Doesn't work for n = 10 | Comment 2 of 7 |
Daniel:

I didn't understand your argument, so I can't tell you where you went wrong, but you are certainly wrong someplace.  This is not possible for all even n >= 6.

Consider n = 10
The total of 1,2,3 ... 10 is 10*11/2 = 55, which is not divisible by 3.

Clearly, a pre-condition is that n*(n+1)/2 is divisible by 3, which is only the case where n = 3k or n = 3k+2.

We can rule out 3 and 4, so the only numbers that might work are 6,8,9,11,12,14,15, etc.

I suspect they all work, but can't look at it right now.

 Posted by Steve Herman on 2010-05-26 18:20:31

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