- You are given a 4×4×4 cube consisting of 64 unit cubes. You are to remove exactly one of the unit cubes so that the remaining 63 unit cubes can be filled with 21 3×1×1 boxes. Where must you remove the unit cube from in order to do this?
- You are given a 5×5×5 cube consisting of 125 unit cubes. You are to remove exactly two of the unit cubes so that the remaining 123 unit cubes can be filled with 41 3×1×1 boxes. Where must you remove the two unit cubes from in order to do this?