## Box World

#### Problem

In box world all the buildings are made from cubic box sections.

Not counting different orientations, how many distinct ways can you connect four rooms together?

#### Solution

There are 8 distinct ways of connecting four unit cubes.

How many distinct ways can you connect together five unit cubes?

What if you count different orientations?

Can you generalise?

Problem ID: 55 (Nov 2001) Difficulty: 2 Star