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.

  • 4
    $\begingroup$ Closely related: Arrows on a Chessboard. $\endgroup$ Commented Jan 20, 2016 at 2:03
  • $\begingroup$ Because you said it is impossible... $\endgroup$ Commented Jan 20, 2016 at 2:29
  • $\begingroup$ @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. $\endgroup$
    – f''
    Commented Jan 20, 2016 at 3:06


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