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Find a subset (Posted on 2005-08-24) Difficulty: 3 of 5
Given N integers a1, a2, ... aN prove there exists a (non empty) subset whose sum is a multiple of N. (Allow repeated numbers in both the original set and its subsets.)

See The Solution Submitted by Federico Kereki    
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Some Thoughts re: what is a subset? | Comment 2 of 6 |
(In reply to what is a subset? by Sir Percivale)

Right, the whole set is a subset of itself, though not a "proper" subset. The empty set is also a subset of any set, but isn't allowed here.
  Posted by Old Original Oskar! on 2005-08-24 19:09:05

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