Wannabe Cube Dissection

Original video
Solution to question B

Wannabe Cube

Wannabe cube is cuboid with sequential integer lengths (e.g. $41 \times 42 \times 43$)

Questions

Question A

Is there any dissection of 3D wannabe cube by smaller distinct wannabe cubes apart from cuboid $5 \times 6 \times 7$?

Question B

Can $41 \times 42 \times 43$ wannabe cube be dissected?

Answers

Question A (not solved)

All 3D cuboids up to $45 \times 46 \times 47$ can't be dissected in smaller cuboids except for $5 \times 6 \times 7$. 43rd-45th wannabe cubes are not shown in the notebook in the repository but were checked by running code in the notebook for them separately.

Question B

No, it can't be dissected. Prove by program which uses SAT solver under the hood.
See main.ipynb for details.

Dependencies

• z3-solver
• jupyter (can be removed by refactoring into the script)
• tqdm (can be removed by removing progress bar)
• numpy (can be removed after refactoring of answer printing, nothing really important depends on it)
• more-itertools (can be removed by changing more_itertools.distinct_permutations to itertools.permutations, but don't want to use unoptimized permutations function)

Reproduction

pip install -r requirements.txt
jupyter notebook

Run all cells in main.ipynb notebook.