Math puzzles - the questions
1. [The summation problem]
Given n integers a1, a2,., an (not necessarily distinct and not necessarily positive), show
that there exists k, 1 <= k <= n, such that the sum of some k of the given integers is
divisible by n, that
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Three friends divided some bullets equally. After all of them shot 4 bullets the
total number of bullets remaining is equal to the bullets each had after division.
Find the original number divided.
Assume that initial there were 3*X bullets.