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69th Belarusian Mathematical Olympiad

Belarus counting and probability

Problem

Each cell of an table is filled with one of the two signs: «+» and «-». For each from to the amount of pluses in the first rows is greater than the amount of minuses in the first columns. Find the maximal possible number of minuses in the table.
Solution
Answer: .
Final answer
floor((n^2 - 1)/2)

Techniques

Coloring schemes, extremal arguments