Posted by **ABCD** on Wednesday, May 29, 2013 at 4:28am.

Given the set of integers {1,2,3,…,801}, what is the maximum number of sets we could distribute these numbers into such that the sum of each set is exactly the same.

- Maths -
**MathMate**, Thursday, May 30, 2013 at 9:27pm
If we sum the sequence,

S=&sum i, i=1,801, we have

S=3²*89*401, as prime factorization.

Thus the largest number of groups is 401 sets, each sum would therefore be 801, as follows:

{1,800},{2,799}...{399,402},{400,401},{801} for a total of 401 sets.

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