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?
