How to assemble 7 pieces into a cube
I recently came across an addictive puzzle for kids — Magic magnetic cube. It is a set of 7 blocks with different shapes and colours that have to be assembled into a cube.
Depending on the vendor the same shapes can be colored differently.
After trying a bit, I eventually manage to assemble the blocks into a cube. But every assembled cube seems different because I assembled them accidentally, rather than consciously. So I wondered how many distinct cubes can be assembled from those 7 blocks. It also seemed to me that the assembled cube had the orange block at a corner.
So I additionally wondered if the orange block, the tripod-like block, can be placed in a cube not at a corner.
To answer those two questions that somewhat bothered me, I decided to calculate the possible solutions.
It turns out that 480 unique cubes can be assembled from the building blocks. None of the calculated 480 cubes is a rotation of any other cube from the result set.
