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Math. competition, (Posted on 2012-03-21) Difficulty: 4 of 5
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

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Exactly 2/5 | Comment 7 of 9 |
As I suspected, exactly 2/5 of all pairs of questions can be solved for some numbers of contestants if all contestants solve exactly 4 problems.

For instance, if there are 15 contestants and each solves a different set of 4 problems, then every pair of problems has been solved by 6 of the 15 contestants.

  Posted by Steve Herman on 2012-03-21 20:22:59
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