Challenge Level

Most swimming pools are surrounded by tiles of some sort, like the pool in the photo above.

Imagine that we number the tiles around the pool.

In the image below, the pool takes up a 5 by 5 square and the space around the pool is five tiles wide:

Can you describe how the tiles are numbered?

Think about a series of numbers that you know about, for example square numbers, prime numbers, triangle numbers...

Explore where those numbers occur in the path around the pool.

What do you notice?

What happens if you look at the path those numbers make around a different sized pool? (You may find it useful to print off this sheet which includes pools of different sizes up to 7 by 7.)

Please let us know what you discover!