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:
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.