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Pairs of students in same row and of same sex not greater 11

Source: CWMO 2003, Problem 8

December 27, 2008
inequalitiesfunctionvectorgraph theorycombinatorics unsolvedcombinatorics

Problem Statement

1650 1650 students are arranged in 22 22 rows and 75 75 columns. It is known that in any two columns, the number of pairs of students in the same row and of the same sex is not greater than 11 11. Prove that the number of boys is not greater than 928 928.
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