Any puzzle where a team of pursuers must capture a team of targets, with movement limited to some given space. The goal is to find a winning strategy either for the pursuers or for the evaders.

A pursuit-evasion puzzle is any puzzle where a team of pursuers must capture a team of targets, with movement limited to some given space. The goal is to find a winning strategy either for the pursuers or for the evaders.

These puzzles are defined by

  • where the parties are constrained to (e.g. a plane, a sphere, the edges of a triangle)

  • the relative speeds of the pursuers and targets

  • whether or not either party is aware of the other's positions

  • a winning condition for the evaders (e.g. evade capture indefinitely, reach a winning region)

One of the more well known puzzles in this category is the Duck and the Fox (asked here in an equivalent form):

A duck is at the center of a circular lake, with a hungry fox waiting at the border. The fox cannot swim, but can run 4 times as fast as the duck can swim. As long as the duck touches the shore at a point where the fox isn't already waiting, then it can instantly fly away to safety. Will the duck be able to fly south for winter?

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