Can you partition the numbers 1, 2, 3, ... nē in n separate subsets, each with n numbers, all subsets having the same sum?

I guess I could answer the problem with a "yes", but FK probably wants more detail than that. :)

Not a proof, but a process: Start from the outsides and work in
1 + n^2
2 + n^2-1
3 + n^2-2
...
n + n^2-n

Then continue building the n subsets in the same manner

For example: n=4
1 + 16 = 17
2 + 15 = 17
3 + 14 = 17
4 + 13 = 17
and so on makes the subsets
1 + 5 + 12 + 16 = 34
2 + 6 + 11 + 15 = 34
3 + 7 + 10 + 14 = 34
4 + 8 + 9 + 13 = 34

EDIT: Oh yeah, only works for even n!

Edited on August 28, 2005, 10:35 pm

Posted by Bob Smith on 2005-08-28 22:25:42