Posted by ABCD on .
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,
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.