Tuesday, July 19, 2005

International Math Olympiad

Here is an interesting problem from this year's International Math Olympiad:

In a mathematical competition 6 problems were posed to the contestants. Each pair of problems was solved by more than 2/5 of the contestants. Nobody solved all 6 problems. Show that there were at least 2 contestants who each solved exactly 5 problems.
(HT: Ars Mathematica)
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