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(242) 6

Part of 1989 Tournament Of Towns

Problems(1)

TOT 242 1989 Autumn A S6 at least 1 star in each column in m x n array

Source:

3/12/2021
A rectangular array has mm rows and nn columns, where m<nm < n. Some cells of the array contain stars, in such a way that there is at least one star in each column. Prove that there is at least one such star such that the row containing it has more stars than the column containing it.
(A. Razborov, Moscow)
combinatoricstable