I'wenty-one girls and twenty-one boys took part in a mathematical comp tition. It turned out that (a) Each contestant solved at most six problems, and (b) For each pair of a girl and a boy, there was at least one problem tha both of them solved. Prove that there is a problem that was solved by at least three girls and a

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Twenty-one girls and twenty-one boys took part in a mathematical compe-
tition. It turned out that
(a) Each contestant solved at most six problems, and
(b) For each pair of a girl and a boy, there was at least one problem that
both of them solved.
Prove that there is a problem that was solved by at least three girls and at
least three boys.
Transcribed Image Text:Twenty-one girls and twenty-one boys took part in a mathematical compe- tition. It turned out that (a) Each contestant solved at most six problems, and (b) For each pair of a girl and a boy, there was at least one problem that both of them solved. Prove that there is a problem that was solved by at least three girls and at least three boys.
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