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Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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Making Maths: Triangular Ball

Make a ball from triangles!

Child's Play

Age 7 to 11 Challenge Level:

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows.

If you press the start button and fit the tetrahedron into the triangular hollow or the cube into the square hollow, it rings a bell.

It only rings the bell again if you then fit the tetrahedron or the cube into its hollow in a different way from any you have done before.

When you have fitted the shapes into the hollows in all the possible ways, the game is complete.

How many times does the bell ring in a complete game?