Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

You need to find the values of the stars before you can apply normal Sudoku rules.