Hey, I read this question a while ago and was wondering if anyone could come up with proof for this question. Let a1,a2,a3,a4, and a5 be any distinct positive integers. Show that there exists at least one subset of 3 of these integers whose sum is divisble by 3. (Use the fact that every integer can be writtein in the form of 3k, 3k+1, 3k+2, where k isa int).

 

Thanks, this question has been bothering me for quite some time now

1. Work out all 5C3 possibilities. It's not hard, just tedious.

 

2. Appeal to the pigeonhole principle. needs a little ingenuity.

smells like homework

well it wasn't assignment work, its just that I read it in a textbook a while ago but couldn't really figure it out. Thanks for your input though