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