Triangles in a Square
This problem is inspired by this geometry puzzle on Twitter. The original problem asks to find the ratio between two equilateral triangles fitted into a square. Let’s generalize it.
Numbers of Polycubes
Let’s define polycubes as three dimensional shapes made up of unit cubes connected by shared faces.
Flattening Cubes
We want to flatten the outer shell of a cube without tearing or stretching the surface.
Cube Solids
For all questions in this problem, let’s ignore the effects of gravity, which means higher unit cubes can float in space without lower unit cubes to support them.