In a mathematical competition, in which 6 problems were posed to the participants, every two of these problems were solved by more than 2/5 of the contestants.
Moreover, no contestant solved all the 6 problems.
Show that there are at least 2 contestants who solved exactly 5 problems each.

source: IMO 2005

(In reply to re(2): Is there an error of ways? by Steve Herman)

OK, I am going to edit my post.

Thanks.

Posted by Ady TZIDON on 2012-03-21 19:23:15