In detail

The cube through the cube

The cube through the cube

We have two identical solid cubes, Is it possible to make a hole in one of the cubes so that the other cube can pass through it?


The solution involves making a hole slightly larger than the width of the cube by looking at it from one of its vertices, as shown in the image, so that the other cube can pass through it without problems.

If we look at the cube from one of its vertices (that is, with the visual in the direction of the main diagonal; for clarity, it has been drawn a little bit deviated) we will see the attached figure, which is a regular hexagon whose side is that of the Cube. Given the dotted rectangle, BC can be as close as we want to the diagonal of a face, and AB will always be larger than the side. Therefore, inside it fits a square with the same side as the cube. Drilling it according to the square, another cube will pass perfectly through the hole.