This page contains a Python script blocks.py for solving 2D and 3D
block puzzles. An example of such a block puzzle is
- Solve puzzles using the Z3 solver.
- Save puzzles in SMT format.
- Draw puzzles and solutions in VRML format. A WRL viewer is required to view them.
Below the pieces of the half-cube puzzle are shown.
A puzzle is stored in a simple textual format. Each line contains a piece of the puzzle. A piece consists of the 3D coordinates of the cubes of the piece. Hence, each line consists of triples of integer values.
The goal of a puzzle is stored in the same format as the puzzles. It should contain one piece only, which is the desired configuration of the puzzle.
The puzzles directory contains several examples of puzzles.
The goals directory contains target configurations of the puzzles.
If you have additional puzzles, please send them to [email protected], so that I can add them to the repository. A puzzle consists of a text file with the coordinates of the pieces, a text file with the coordinates of the goal, a name of the puzzle, and optionally a link to a description of the puzzle.
The Python package z3-solver must be installed, see https://pypi.org/project/z3-solver/.
The option --draw is used to create .wrl files that can be viewed
with a WRL viewer. The pieces of a puzzle can be drawn using a call like this:
python3 blocks.py --draw --pieces="puzzles/half_cube.txt" --grid
The option --grid puts the pieces in a 2 dimensional grid. This
is done to avoid collisions.
The option --scatter is used to move pieces away from the center
of gravity. This can be helpful to view the inside of a solution, as
demonstrated in the picture below.
A solution of a puzzle can be drawn using a call like this:
python3 blocks.py --draw --pieces="solutions/offroad_cube-4x4x4.txt" --scatter=0.5
A puzzle can be solved using a call like this:
python3 blocks.py --solve --pieces="puzzles/offroad_cube.txt" --goal="goals/4x4x4.txt"
The input consists of a file containing the pieces of the puzzle, and a file containing the goal of the puzzle. Note that some puzzles may take a long time to solve.
The option --transform can be used to compute and display all possible
orientations of the pieces. For example the call
python3 blocks.py --transform --pieces="puzzles/hara_cube.txt" --goal="goals/4x4x4.txt"
results in the output
Saving 144 piece orientations to file 'hara_cube-0.wrl'
Saving 432 piece orientations to file 'hara_cube-1.wrl'
Saving 432 piece orientations to file 'hara_cube-2.wrl'
Saving 192 piece orientations to file 'hara_cube-3.wrl'
Saving 432 piece orientations to file 'hara_cube-4.wrl'
Saving 384 piece orientations to file 'hara_cube-5.wrl'
Saving 144 piece orientations to file 'hara_cube-6.wrl'
Saving 144 piece orientations to file 'hara_cube-7.wrl'
Saving 288 piece orientations to file 'hara_cube-8.wrl'
Saving 288 piece orientations to file 'hara_cube-9.wrl'
Saving 324 piece orientations to file 'hara_cube-10.wrl'
These numbers give an indication of how complex the puzzle is.
The option --smt is used to save the puzzle in .smt format. For
example the call
python3 blocks.py --smt --pieces="puzzles/offroad_cube.txt" --goal="goals/4x4x4.txt"
produces a file offroad_cube-4x4x4.smt that can be used as input for an
SMT solver.
Thanks to Huub van de Wetering for providing the visualizations of the puzzles, and thanks to Alex Uuldriks for handing me Hara's Cube puzzle and challenging me to solve it.
https://diypuzzles.wordpress.com/tag/4x4x4-cube/
https://puzzlewillbeplayed.com/444/Gemini/
https://en.wikipedia.org/wiki/Tetromino
https://en.wikipedia.org/wiki/Pentomino