## Pathed Pathways

#### Problem

A pathway measuring 5 m by 2 m is paved with stones measuring 2 m by 1 m. One way in which the pathway could be paved is as follows.

How many different ways can the path be laid?

#### Solution

The pathways can be paved as follows.

There are 8 ways of paving a 5x2 pathway with 2x1 paving stones.

How many ways can you pave a 2 x n pathway using 2x1 stones?

What about different width pathways?

(Hint: Keep the length of the stones equal to the width of the pathway.)

Problem ID: 57 (Dec 2001) Difficulty: 1 Star