Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

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

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

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

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

We received a variety of well explained solutions to this problem, starting with the specific and finishing with the general. Thank you all.

In this article, we look at solids constructed using symmetries of their faces.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.