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### Number and algebra

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# Sliding Puzzle

This puzzle is an old favourite. The aim of the game is to slide the green square from its starting position, in the top right hand corner, to the bottom left hand corner in the least number of moves. You may only slide squares up, down, left or right and not diagonally.

Try first on a small two by two grid and then as you become more confident, alter the size.

Can you find a strategy?

You may like to have a look at the problem Changing Places for some helpful hints.

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Age 11 to 16

Challenge Level

- Game

This puzzle is an old favourite. The aim of the game is to slide the green square from its starting position, in the top right hand corner, to the bottom left hand corner in the least number of moves. You may only slide squares up, down, left or right and not diagonally.

Try first on a small two by two grid and then as you become more confident, alter the size.

Can you find a strategy?

You may like to have a look at the problem Changing Places for some helpful hints.

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?