MathDB
IMO Shortlist 2012, Combinatorics 3

Source: IMO Shortlist 2012, Combinatorics 3

July 29, 2013
combinatoricsmatrixExtremal combinatoricsIMO Shortlist

Problem Statement

In a 999×999999 \times 999 square table some cells are white and the remaining ones are red. Let TT be the number of triples (C1,C2,C3)(C_1,C_2,C_3) of cells, the first two in the same row and the last two in the same column, with C1,C3C_1,C_3 white and C2C_2 red. Find the maximum value TT can attain.
Proposed by Merlijn Staps, The Netherlands
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