Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

How many different triangles can you draw which each have one dot in the middle?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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.

How many possible symmetrical necklaces can you find? How do you know you've found them all?

How many different triangles can you make on a circular pegboard that has nine pegs?

How many symmetric designs can you make on this grid? Can you find them all?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?