# Swimming Pool

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

Have you been to a swimming pool lately?

When you go swimming you might walk down some steps to reach the bottom, or you might use a ladder at the side of the pool.

Here's a picture of a set of steps and a ladder.

You'll probably notice that I've coloured the steps.

The first step into the water is light green, the second step is purple, the third red and so on.

The same is true of the ladder.

Later, I'll be thinking about numbering these coloured steps.

- Suppose your friend puts you on step $4$ and you only want to go a little way into the water so you head for the red step. Stepping down carefully, one step at a time, how many steps will you have to take?
- Now the next time you want to go into the water your friend takes you to step $2$ and you're going to step down carefully to the blue step at the bottom. How many steps down do you have to take?
- When you have finished swimming you take yourself to the yellow step and meet your friend on step $5$. How many steps, one at a time, do you have to take?

Maybe it's time to number these coloured steps.

I think I'll go for numbering them down from the water surface.

Can you invent your own way of numbering the steps which go under the water?

Use your finger to "jump" a step at a time up or down the ladder, counting as you go.

What number could you call the level of the water itself?

We had five solutions sent in altogether. Joe from St. Anne's school sent in a full solution as follows:

Pranesh from Holy Garden school also sent in correct answers for the three questions. We had a pleasant chatty note sent in by Charlie from Culford Prep School as follows:

You are absolutely right in your thinking, well done!

The following solution also came in but unfortunately no name or school was attached.

Finally, from Hotwells School:

**Why do this problem?**

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