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6.

Part of 2022 Polish Junior Math Olympiad First Round

Problems(1)

2022 Polish Junior Math Olympiad First Round P6

Source:

5/21/2023
In each square of a 10×1010\times 10 board, there is an arrow pointing upwards, downwards, left, or right. Prove that it is possible to remove 5050 arrows from the board, such that no two remaining arrows point at each other.
combinatorics