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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

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