For a positive integer n, what is the largest k such that
the numbers 1,2, ... ,n can be put into k boxes so that
the sum of the numbers in each box is the same?

(In reply to

Possible solution by Jer)

Please edit your second line:

{1,n}, **{2,n-1}...** {k,n-k+1} ... {n/2,1+n/2}}