Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

Watch the video to see how Charlie works out the sum. Can you adapt his method?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

A collection of short problems on patterns and sequences.

How many diagonals does a regular icosagon (20 sides) have?