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: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.7: Problem Solving: Consecutive Integers
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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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