This question is from the German mathematics competition Känguru der Mathematik. In this competition students have to solve 30 mathematical tasks like this in 90 minutes without calculator. Actually they are given 5 possible answers, but for this community a bit of additional challenge does not hurt.

You are given a cube with unknown edge length. A point $M$ inside the cube with unknown coordinates appears. Now imagine 6 pyramids inside the cube with each cube face being the base of one pyramid and $M$ being their common apex. The volumes of 5 of the 6 pyramids are 2, 5, 10, 11 and 14. What is the volume of the sixth pyramid?

This question is from the German mathematics competition Känguru der Mathematik. In this competition students have to solve 30 mathematical tasks like this in 90 minutes without calculator. Actually they are given 5 possible answers, but for this community a bit of additional challenge does not hurt.

You are given a cube with unknown edge length. A point $M$ inside the cube with unknown coordinates appears. Now imagine 6 pyramids inside the cube with each cube face being the base of one pyramid and $M$ being their common apex. The volumes of 5 of the 6 pyramids are 2, 5, 10, 11 and 14. What is the volume of the sixth pyramid?