### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

### Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

# Sea Level

##### Age 7 to 11Challenge Level

Well, here's a pretty scene, the underwater creatures and the tall lighthouse joined by a seagull and a cloud in the sky.

There are black markings all the way up the lighthouse and on the support for the lighthouse going down to the sea bed. These markings are $1$ metre apart. I have left the numbering for you to do.

The sea level is of course "$0$" and then positive numbers going up and negative numbers going down to the sea bed.

If we think about the mouths of the creatures then we can see how much deeper they are from each other, or what distance they are apart.

For example the (mouth of) the fierce looking blue and white fish near the middle is $1$ metre deeper than the (mouth of) the golden yellow fish.

1. What number should be where the light shines from the lighthouse?
2. What number should be where the (head of the) seagull is?
3. What number should be where the (mouth of the) red crab, near the bottom, is?
4. How far is it down from the (head of the) seagull to the (mouth of the) yellow fish?
5. How far is it from the turtle, near the surface of the water, to the crab?
6. There's a little brown sea-horse to the right of the lighthouse support. How far from the surface is it?
7. How high above the sea level is the seagull flying?
8. How far is the seagull from the sea-horse?
9. How high is the pointed end of the cloud?

It would be interesting to know how you arrived at your answers.