I found this one in an old magazine: enter image description here

A rabbit is chasing a turtle (or tortoise, whatever you prefer!). Each of them makes one move at a time and they are only allowed to land on adjacent vertices and only on the grid. The rabbit goes first. Will it ever catch the turtle (obviously after a limited number of moves)?

I don't see any way of approaching this via any theory, although I am not good at maths. Having tried (almost) every possible move (on paper), it seems that the turtle can always be one step ahead.

I believe the tricky point is the triangle, but I don't know how to make use of it!

Any help is very welcome!

  • $\begingroup$ At a first glance, it is a "no". $\endgroup$ – Pradeep Suny Oct 26 at 11:50
  • 2
    $\begingroup$ There is a theory about evasion-games on graphs, commonly referred to as "cops and robbers", where graphs are categorized based on advantages (more rabbits, more moves, etc) and disadvantages (special robber-edges, etc) the cops (in your case the rabbits) need to have, to catch the robber/turtle $\endgroup$ – Laray Oct 26 at 12:19
  • $\begingroup$ Do both have to move, or can they decide to not move. And I suppose the rabbit goes first. $\endgroup$ – M. Winter Oct 27 at 21:38

The rabbit should move up on this first move and then go around the triangle. If the dots were numbered consecutively around the outside of the grid, the starting position has both animals on, say, odd numbered points. As long as they are both on points of the same parity , the rabbit can't catch the turtle. But when he goes around the triangle, he changes parity and can then easily trap the turtle.

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