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Kenneth Rosen Edition 7 Exercise 6.2 Question 24 (Page No. 406)

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Suppose that $21$ girls and $21$ boys enter a mathematics competition. Furthermore, suppose that each entrant solves at most six questions, and for every boy-girl pair, there is at least one question that they both solved. Show that there is a question that was solved by at least three girls and at least three boys.
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