I am trying to solve a problem that states a certain number of points lets say 50, are in a 20cm cube. It then asks to prove that 7 are in a 10cm cube. How is this even pigeonhole? I've not done this kind of problem before.
I have tried breaking it up into 49 smaller cubes (holes) and therefore 1 or more point is in each. Then done the same with the 10cm cube but not made much progress.
A 10cm cube is $\frac{1}{8}$ of a 20cm cube, $7>\frac{50}{8}>6$, hence at least one 10cm cube will contain at least 7 points