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Find the shape and symmetries of the two pieces of this cut cube.

Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Napoleon's Hat

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

Four Points on a Cube

Age 16 to 18
Challenge Level

Take a cube of side length one unit. A vertex of the cube and the centres of the three faces not containing that vertex form the vertices of a tetrahedron. What is the surface area of this tetrahedron?

Cube with tetrahedron inside.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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