Maths
posted by ABCD .
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.

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.