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Rooks that can not see well

Source: Saint Petersburg MO 2020 Grade 11 Problem 2

May 7, 2020
combinatorics

Problem Statement

A short-sighted rook is a rook that beats all squares in the same column and in the same row for which he can not go more than 6060-steps. What is the maximal amount of short-sighted rooks that don't beat each other that can be put on a 100×100100\times 100 chessboard.