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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

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

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CR: Review Problem Set
Problem 35CR
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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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