Visualising and representing

Here's a neat trick you can do with an 11 by 11 square...

What is the smallest number of additional squares that must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order 2?

Stephen stops at Darlington on his way to Durham. At what time does he arrive at Durham?

Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

When Andrew arrives at the end of the walkway, how far is he ahead of Bill?

A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?

After tennis training, Andy, Roger and Maria collect up the balls. Can you work out how many Andy collects?

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?