Original video
Solution to question B

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

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

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

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.

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

• 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)

pip install -r requirements.txt
jupyter notebook

Run all cells in main.ipynb notebook.