Visualising and representing

Show that all pentagonal numbers are one third of a triangular number.

Which hexagons tessellate?

Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

Can you form this 2010-digit number...

Weekly Problem 37 - 2010
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?

What does Pythagoras' Theorem tell you about the radius of these circles?