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Age 14 to 16

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9 identical squares of side 2 units are separated by empty strips also of 2 units width.

What is the shortest route from A to B, assuming you can only go around the edges of the squares?

Now, consider 27 identical cubes of side 2 units which are separated by corridors also of 2 units width. What is the shortest distance from A to B?

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?

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?