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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