# A cool question

Gold Member
Prove that for every set of n numbers has a subset whose sum is divisible by n. I found this result very interesting. It's also fun to prove!

Must these numbers be in sequence? Like {4,5,6,7,8}, or could it be any set like {1,10}?

EDIT: Never mind...that was a silly question.

can this subset be 1 number? or does it have to be summable?

Gold Member
Both the set and subset can be any not emty set. But I forgot to mention that numbers can repeat themselves so that in this case {1,1,2,2,4} is a "set" of 5 numbers and to answer ices's question, {1} is a subset of it.

HallsofIvy
Homework Helper
No, that is NOT a "set" of 5 numbers! {1,1,2, 2,4}= {1, 2, 4} is a set of 3 numbers!
If you mean something else do not use the word "set".

CRGreathouse
Homework Helper
No, that is NOT a "set" of 5 numbers! {1,1,2, 2,4}= {1, 2, 4} is a set of 3 numbers!
If you mean something else do not use the word "set".
The result holds for sets. daniel_i_l's point was surely that the result naturally extends to multisets.

mathwonk