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Rooks and pawns

Source: Tuymaada 2018 Senior League/Problem 2, Junior League/Problem 3

July 20, 2018
Tuymaadacombinatorics

Problem Statement

nn rooks and kk pawns are arranged on a 100×100100 \times 100 board. The rooks cannot leap over pawns. For which minimum kk is it possible that no rook can capture any other rook?
Junior League: n=2551n=2551 (Proposed by A. Kuznetsov) Senior League: n=2550n=2550 (Proposed by N. Vlasova)
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