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4

Part of 1999 Mexico National Olympiad

Problems(1)

distances of 10 centers in 8x8 board of unit squares

Source: Mexican Mathematical Olympiad 1999 OMM P4

7/28/2018
An 8×88 \times 8 board is divided into unit squares. Ten of these squares have their centers marked. Prove that either there exist two marked points on the distance at most 2\sqrt2, or there is a point on the distance 1/21/2 from the edge of the board.
combinatorial geometrydistanceboardcombinatorics