The game of Sym

Class practical

This is a fun challenge, ideal as an extension activity or just for some mind-stretching for its own sake.

Apparatus and Materials

For each student group

• Beam with regular markings, simple
• Wooden prism block
• Metal loads, square and identical

Health & Safety and Technical Notes

Read our standard health & safety guidance

These items of apparatus are available from educational suppliers as part of a lever kit.

The square metal loads should have approximately the same diagonal length as the width of the beam.

Procedure

1. Start with the beam balanced with no square loads on it.
2. Take several square loads and arrange them on the balance, at marks on the balance, so that the beam is balanced. Make a sketch of that pattern.
3. Now put all the square loads in a single pile above the pivot.
4. Move two square loads, so that the beam is balanced again. You can put them at the marks on the beam, but not in between marks.
5. The object of the game is to reproduce the pattern that you sketched. You can only move two loads in each move. At the end of each move the beam must be balanced. The person who can do this in the smallest number of moves is the winner.

Teaching Notes

• This game was devised by a mathematical physicist, and can be absurdly simple or extremely hard. It is very suitable as an extension activity.
• It is a good idea to demonstrate the game first to would-be competitors, starting with a very simple pattern, so that the rules about moves are clear.
• Faster students will quickly learn how best to play the game. They shouldn't be allowed to discourage those who take a bit longer.

This experiment was safety-tested in October 2004