Drifting in an ocean of arrows

Asked Jan 20 '16 at 00:47

Active Jan 20 '16 at 00:47

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Each cell in an infinite square lattice contains an arrow ponting to one of the eight cells adjacent to it. No two adjacent cells contain arrows differing in direction by more than 45°.

Suppose (starting anywhere) we trace a path by travelling in the direction of each arrow we hit. Prove that we never visit the same cell twice.

asked Jan 20 '16 at 00:47

rnaylor

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Closely related: Arrows on a Chessboard. – Mike Earnest Jan 20 '16 at 02:03
Because you said it is impossible... – Anthony Pham Jan 20 '16 at 02:29
@MikeEarnest I think it's close enough to count as a duplicate. If there is a loop on the infinite lattice, you can put a finite square around it and apply the logic from that question. – f'' Jan 20 '16 at 03:06

Drifting in an ocean of arrows

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