Given 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?

[When n = 8, the example {1,2,3,6},{4,8},{5,7} shows that the largest k is at least 3.]

The smallest possible sum is n and the next smallest possible sum is n+1, since n must itself be in some box. 

Posted by Rosie Terry on 2019-01-31 02:35:43