Shortcut back to Logo Maze Puzzle Logo maze puzzle:
analysis and solution by Gordon Collins


 

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Path networks in Logo Maze

Gordon Collins, puzzle solver extraordinaire, sent us the diagram above with the three subcircuits highlighted in different colors. He then transformed this pattern into a stretched string figure, below, by grabbing the two balls and pulling them apart. Numbers with asterisks are the balls.

Gordon Collins' maze analysis schematic

From this pattern Gordon was then able to deduce a minimum of 14 and a maximum of 64 moves! Here are some of his sample solutions:

  • The smallest number of moves is 14:
    1e, 1f, 1m, 1k, 1n, 2e, 2a, 2d, 2h, 2i, 3a, 3b, 3l, 3*. One can use 2f and 2b instead of 2e and 2a.

  • There are many ways to get there in 25 moves, one of which is:
    1b, 1h, 1i, 1d, 1c, 1l, 1k, 1n, 2e, 2j, 2k, 2b, 2d, 2h, 2g, 2l, 2m, 3k, 3j, 3e, 3f, 3d, 3c, 3l, 3*.
For the maximum, there are several choices for restrictions on the problem:
  1. cannot return to start or arrive at a given end point more than once;
  2. cannot arrive at a given endpoint from the same direction more than once (prohibits following both 2f2b and 2k2b);
  3. cannot use the same directed path more than once (prohibits following 2k2b twice);
  4. cannot use the same UNdirected full segment more than once (prohibits following 1m1d and 1d1m);
  5. cannot use the same undirected full segment more than once in succession (allows following 1m1d and 1d1m, just not one right after the other);
  6. and cannot use the same directed full segment more than once in all.
Gordon found the following maximal paths for the above:
  • 35 moves:
    1b, 1h, 1g, 1i, 1m, 1d, 1c, 1l, 1k, 1a, 1n, [ or ... i d c l m k ...] 2f, 2e, 2a, 2j, 2k, 2b, 2d, 2h, 2i, 2g, 2c, 2l, 2m, [2 other variations before d] 3a, 3k, 3j, 3e, 3f, 3g, 3d, 3c, 3b, 3l, 3*

  • 52 moves: (reaches all endpoints at least once)
    1e, 1f, 1e, 1*, 1b, 1h, 1g, 1j, 1g, 1i, 1d, 1c, 1l, 1c, 1d, 1m, 1k, 1a, 1n, 2e, 2f, 2k, 2j, 2a, 2j, 2k, 2b, 2a, 2d, 2h, 2i, 2g, 2c, 2l, 2m, 3a, 3k, 3j, 3e, 3f, 3g, 3d, 3c, 3b, 3a, 3b, 3l, 3*, 3i, 3h, 3i, 3*

  • 64 moves:
    1b, 1h, 1i, 1g, 1j, 1g, 1i, 1d, 1c, 1l, 1k, 1a, 1b, 1*, 1e, 1f, 1m, 1d, 1m, 1k, 1n, 1a, 1n, 2f, 2e, 2f, 2b, 2k, 2j, 2a, 2j, 2k, 2b, 2d, 2a, 2d, 2h, 2g, 2i, 2g, 2l, 2c, 2l, 2m, 3k, 3j, 3e, 3f, 3d, 3g, 3d, 3c, 3l, 3b, 3a, 3k, 3a, 3b, 3l, 3*, 3i, 3h, 3i, 3*

  • 41 moves:
    1e, 1f, 1d, 1c, 1l, 1k, 1a, 1*, 1b, 1h, 1g, 1i, 1d, 1m, 1k, 1n, 2f, 2e, 2a, 2j, 2k, 2b, 2a, 2d, 2h, 2i, 2g, 2c, 2l, 2m, 3a, 3k, 3j, 3e, 3f, 3g, 3d, 3c, 3b, 3l, 3*

  • 43 moves:
    1b, 1h, 1g, 1i, 1m, 1d, 1c, 1l, 1k, 1a, 1b, 1*, 1e, 1f, 1d, 1m, 1k, 1n, 2f, 2e, 2a, 2j, 2k, 2b, 2a, 2d, 2h, 2i, 2g, 2c, 2l, 2m, 3a, 3k, 3j, 3e, 3f, 3g, 3d, 3c, 3b, 3l, 3*



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