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This is a preliminary 4x4 model of a 3D maze where a single die is rolled around from the start square to the finish square. This maze provides loops, dead ends, reversing paths, and traps which have no exit. The die always starts on the square marked START or S with the 1 pip side Up and the 2 pip side facing North. The die cannot occupy a blocked square. The die can be rolled North, South, East or West as many squares in the same direction as the maze boundaries allow, or until it is stopped by a blocked square on itís same level. After the die is rolled it is moved to the square directly above or below on the level that corresponds with the number of pips on the top of the die. The orientation does not change during the Warp to the new level. If the square on this level is blocked then this would not be a legal move and the die is placed back on the original square and with the original orientation. The challenge is to move the die to the FINISH or F square. Of course to finish on level one, the 1 pip side must be up!

I also provide a 2D representation of the maze. I prefer to use this one to actually move the die around. Itís much easier to picture. If a square shows a 3 and a 4 then the squares directly below on level 3 and 4 are blocked. S1 means that the start is on level one and F1 means that the finish square is on level 1.







In the example I try to move 1 East from the start. This square on level 1 is not blocked, but since the die would warp to level 3 , the number of pips on the top of the die now, this is not a legal move. I then try to move 2 East from the start. There is no blocked square on level 1 stopping me from moving 2 squares, but again the die would warp to level 6 and this square is blocked on level 6. Then I try moving 3 East. Nothing blocks me on level 1 and when the die warps to level 4 the square is also open. I have made the first move- 3East or 3E. The die is on level 4 with the 4 pip side up and the 2 pip side North. My second move cannot be to the 1, 2 or 3 West because that direction is blocked on level 4. I could move 1 South or 3 South, but not 2 South since that square is blocked on level 3. A solution to this maze is 1S 1E 1S 1E 1S 1E.


The Real Maze


















This one has a few solutions, the least of which has 26 moves

Good Luck!

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Last updated: 07/30/05.