david.017 Posted February 12, 2006 Share Posted February 12, 2006 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 Link to comment Share on other sites More sharing options...
matt grime Posted February 12, 2006 Share Posted February 12, 2006 1. Work out all 5C3 possibilities. It's not hard, just tedious. 2. Appeal to the pigeonhole principle. needs a little ingenuity. Link to comment Share on other sites More sharing options...
ydoaPs Posted February 12, 2006 Share Posted February 12, 2006 smells like homework Link to comment Share on other sites More sharing options...
david.017 Posted February 13, 2006 Author Share Posted February 13, 2006 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 Link to comment Share on other sites More sharing options...
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