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

He told how the cleric at St. John's Seminary on Kairiru had trained him to peruse and communicate in English a piece, and through him, he had learned of the Japanese occupation. Presently it appeared to be that quite possibly Hibiki 21 they were returning, and he could want recompense for his dad.

Posted by scsc dvhhn on 2022-06-06 02:20:03