subsets

test out this rule:

for any 5 integers you can always find three of them 

that add up to a multiple of 3

the numbers can be as easy or tricky as you like (and could be negative)

e.g. 7   6   4  14  6

6 + 14 + 4 = M(3) and also:
6 + 7 + 14 = M(3)

a proof can be developed from a consideration of remainders after dividing by 3 (i.e. mod 3 arithmetic) and a consideration of the various options

also prove that in any 3 integers you can find two that sum to an even number

in any 6 integers you can find four that sum to a multiple of 4