I'm playing a video game right now and in it is a puzzle (see here). There are solutions to solving it (see here) on the Internet, but I'd like to know if this path is the shortest path (least amount of moves) possible to solve the puzzle.

The rules of the game are clear from the video. There is a grid of nodes. The border nodes are bounded with limited path choices. There are three moving bodies. The main one chooses a path that reflects the path choices of the other two. The aim is to guide the other two to land on certain nodes at the same time.


If the guardians face each other and Link, the player, moves in a way to make them collide they, in effect, stay in the same position and Link keeps his move: youtube.com/watch?v=ZNnSwc0w1oE#t=4m58s

Top-guardian-Link conga allowed: youtube.com/watch?v=oUh88KsZYCc#t=3m53s – Liz Wesley 21 mins ago

The game ends if the player jumps on a square that a guardian is set to jump on at the same time: youtube.com/watch?v=ZNnSwc0w1oE#t=2m55s

I'm seeking a shortest path proof based on this game's rules. Any help would be appreciated.

It is important to note that the top guardian moves in the opposite direction as link and the bottom guardian mimics Link's direction.

Daniel Wagner's 12-step Haskell Solution:

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Guardian Path Overlay:

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  • $\begingroup$ Original: math.stackexchange.com/posts/1245680/edit $\endgroup$ – Liz Wesley Apr 24 '15 at 2:42
  • $\begingroup$ Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the faq! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! $\endgroup$ – Michael E2 Apr 24 '15 at 2:46
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    $\begingroup$ Check out mathematica.stackexchange.com/help/on-topic. This is a site about a software product, not about proving things per se. If this is in fact a question about Mathematica, perhaps you could make clearer what aspect of the software program you need help with. $\endgroup$ – Michael E2 Apr 24 '15 at 2:47
  • $\begingroup$ This is probably a better link to the original: math.stackexchange.com/questions/1245680/… $\endgroup$ – Michael E2 Apr 24 '15 at 2:52