This is a solver for a logic puzzle. The puzzle consists of 25 identical pieces of the following shape:
| X | X | X | X |
|---|---|---|---|
| X |
The goal of the puzzle is to combine then to fill a 5x5x5 cube.
The algorithm uses backtracking to find a solution. It iterates over the empty slots in the following way:
- Left to right (x - WIDTH)
- Back to front (y - DEPTH)
- Bottom to top (z - HEIGHT)
For each empty slot, it tries to insert a piece n.
To fill the next slot [x,y,z], the following 24 configurations are possible:
- [x,y,z], [x+1,y,z], [x+2,y,z], [x+3,y,z], [x+1,y+1,z]
- [x,y,z], [x+1,y,z], [x+2,y,z], [x+3,y,z], [x+2,y+1,z]
- [x,y,z], [x+1,y,z], [x+2,y,z], [x+3,y,z], [x+1,y,z+1]
- [x,y,z], [x+1,y,z], [x+2,y,z], [x+3,y,z], [x+2,y,z+1]
- [x,y,z], [x-2,y+1,z], [x-1,y+1,z], [x,y+1,z], [x+1,y+1,z]
- [x,y,z], [x-1,y+1,z], [x,y+1,z], [x+1,y+1,z], [x+2,y+1,z]
- [x,y,z], [x,y+1,z], [x,y+2,z], [x,y+3,z], [x-1,y+1,z]
- [x,y,z], [x,y+1,z], [x,y+2,z], [x,y+3,z], [x,y+1,z+1]
- [x,y,z], [x,y+1,z], [x,y+2,z], [x,y+3,z], [x+1,y+1,z]
- [x,y,z], [x,y+1,z], [x,y+2,z], [x,y+3,z], [x-1,y+2,z]
- [x,y,z], [x,y+1,z], [x,y+2,z], [x,y+3,z], [x,y+2,z+1]
- [x,y,z], [x,y+1,z], [x,y+2,z], [x,y+3,z], [x+1,y+2,z]
- [x,y,z], [x,y,z+1], [x-2,y,z+1], [x-1,y,z+1], [x+1,y,z+1]
- [x,y,z], [x,y,z+1], [x-1,y,z+1], [x+1,y,z+1], [x+2,y,z+1]
- [x,y,z], [x,y,z+1], [x,y-2,z+1], [x,y-1,z+1], [x,y+1,z+1]
- [x,y,z], [x,y,z+1], [x,y-1,z+1], [x,y+1,z+1], [x,y+2,z+1]
- [x,y,z], [x,y,z+1], [x,y,z+2], [x,y,z+3], [x-1,y,z+1]
- [x,y,z], [x,y,z+1], [x,y,z+2], [x,y,z+3], [x,y-1,z+1]
- [x,y,z], [x,y,z+1], [x,y,z+2], [x,y,z+3], [x+1,y,z+1]
- [x,y,z], [x,y,z+1], [x,y,z+2], [x,y,z+3], [x,y+1,z+1]
- [x,y,z], [x,y,z+1], [x,y,z+2], [x,y,z+3], [x-1,y,z+2]
- [x,y,z], [x,y,z+1], [x,y,z+2], [x,y,z+3], [x,y-1,z+2]
- [x,y,z], [x,y,z+1], [x,y,z+2], [x,y,z+3], [x+1,y,z+2]
- [x,y,z], [x,y,z+1], [x,y,z+2], [x,y,z+3], [x,y+1,z+2]
These configurations were derived manually.
They represent the 24 different orientations of a block.
Disclaimer:
While the solution is relatively concise and straightforward, it is not very efficient.
It took roughly an hour, before the first solutions were found.