Suppose you want to build a square pyramid made up of 30 spheres. So the bottom layer is a 4x4 square arrangement of touching spheres, and it has 3x3, 2x2 and 1x1 layers on top.
The building blocks you have are 15 di-spheres, i.e. they consist of two spheres stuck together.
At all times while building the pyramid, you want every sphere to be fully supported underneath, either by four spheres in the layer below or by the ground.
Is it ever possible to get stuck, where there is no possible way to complete the pyramid without first removing pieces?
This question arose when someone I know was trying to design a two-player game. It is not a very difficult puzzle, but fun to work out.