## Hollow Cube

#### Problem

A cube measuring 3 3 3 is made up of 27 smaller cubes and has a 1 1 square hole pushed right through the centre of each face so that you can see straight through the cube from every side.

The number of small cubes remaining is 20.

If a 5 5 5 cube has 3 3 square holes pushed through the centre of each face, how many smaller cubes would remain?

Problem ID: 27 (Dec 2000) Difficulty: 1 Star