perplexus.info :: Just Math : Math. competition,

Math. competition, (Posted on 2012-03-21)

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: 3.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re(2): Is there an error of ways?

| Comment 5 of 103 |

(In reply to re: Is there an error of ways? by Ady TZIDON)

Ady:

I am pretty sure you meant to say that you meant to say that EACH POSSIBLE PAIR WAS SOLVED BY more than 4O% OF THE CONTESTANTS

I suspect that exactly 40% can be achieved without anybody solving 5.

Steve

Posted by Steve Herman on 2012-03-21 19:15:09

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