## The game of Sym

Practical Activity for 14-16

**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

- Start with the beam balanced with no square loads on it.
- 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.
- Now put all the square loads in a single pile above the pivot.
- 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.
- 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*