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Two men are trapped in an icy cave. Nowhere to go, except for two small holes in the ice, heading down. Only by working together, they can get deeper into the cave, hopefully finding a way out. Will they succeed or will they be stuck forever?

Rules: - Your goal is to let both players fall in a different hole (a brown circle). A player has no choice but to enter as they glide over it. If they fall in the same hole, they crash on each other and die. So this is impossible.

  • Each turn, one player can move either up, down, left, or right and glides into this direction until hitting a wall (black). The entire outside ring consists of walls.

  • A player that falls in the lava (orange/red) is dead, and the game can no longer be won.

  • If a player bumps into another player, it halts as if he hits a wall. This has no effect on the other player. So no two players can be on the same square. Of course, when a player has fallen into a hole, the other can not bump against him anymore.

My question is: What is the minimum amount of turns necessary? Of course, proving this by hand is laborious, so I only request the smallest number. No proof of minimality. First three tutorial mazes on a small 4-by-4-grid:

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The first has a minimal solution of 6 moves: Blue ↑, Red →↓, Blue ↓→↓.

The second maze has a minimal solution of 12 turns, and the third one of 13 moves.

Here are eight puzzles that increase in difficulty from left to right, top to bottom. They are computer-generated but rigorously playtested and proven to possible. The last four hold three players, but the rules remain the same.

The puzzles are on an eight-by-eight grid. With a little creativity, a chessboard might come in handy.

Good luck!

enter image description here

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    $\begingroup$ I have developed this puzzle a couple years back with some friends, and it is inspired by the old pokemon games. Later I figured out it is related to Ricolet's robots, but that was after coming up with all the rules etc. Do you think it is necessary to add this to the description? $\endgroup$
    – Derfellios
    Commented Mar 10, 2020 at 21:45

2 Answers 2

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First puzzle:

15 moves

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Second puzzle:

30 moves

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Third puzzle:

43 moves

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Fourth puzzle:

103 moves

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Fifth puzzle:

33 moves

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Sixth puzzle:

47 moves

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Seventh puzzle:

57 moves

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  • $\begingroup$ All three are correct! Five more remain. $\endgroup$
    – Derfellios
    Commented Mar 12, 2020 at 9:30
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    $\begingroup$ @Derfellios Four solutions added. Final solution still eludes me. When that battle is over, I'll find or confirm optimal solutions with a program. $\endgroup$
    – Daniel Mathias
    Commented Mar 12, 2020 at 19:03
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    $\begingroup$ You're getting close, but only the 6th one is in the minimal amount of moves. Can you improve the others a little more? The last one is difficult, and I have to admit this one was the only one I could not solve by hand. But the solution is quite nice. I have written a program myself and know the minimal amount of moves. $\endgroup$
    – Derfellios
    Commented Mar 12, 2020 at 19:04
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    $\begingroup$ @Derfellios I have minimal moves as (15, 30, 40, 100, 32, 47, 54, 69) but may not be able to update my answer for some time due to limited computer access. $\endgroup$
    – Daniel Mathias
    Commented Mar 14, 2020 at 14:48
  • $\begingroup$ No problem. I only requested the minimum amount of moves, and these are correct! I'm impressed. But I'm curious what your methods are. Pen and paper? A chess board as suggested, or a computer program? $\endgroup$
    – Derfellios
    Commented Mar 14, 2020 at 15:52
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This reminds me of the game Ricochet Robot.

Tutorial solutions

tu

Here's my initial solution for the first puzzle.

22 moves

p1

Second puzzle

41 moves

p2

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    $\begingroup$ You are pretty close! The tutorial puzzles are correct, but the other two solutions are not minimal. Are you able to find a shorter solution? $\endgroup$
    – Derfellios
    Commented Mar 11, 2020 at 9:47

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