Games Theory is a pure strategic logic. Mathematicians enjoy the challenge of playing games where the rules are simple and the strategies complex. Explaining the strategies takes a strong command of clear language. Some mathematicians take it all the way to the Nobel prize. It was Games Theory which underpinned John Nash’s Nobel Prize for Economics. It was Games Theory which underpinned the 2005 prize again. The final game in this set is John Nash’s Hex. Books have been written on the strategies. Now we ask the same of the students! Don’t worry - they start simple!

Prime Fingers

Circle of Coins

Race to 100

Fifteen by Three

Pentominoes

Pile of Stones to Nim

The L-game

Five in a Row and Go!

Hex

Do you play draughts? If so, what has Smidgin done wrong?

Games, in mathematics, are defined by the rules:

1. There are two players.

2. The players move alternately - that is, they take turns to make their moves.

3. There are no dice or other chance devices. It is all skill and no luck.

4. Both players have all possible information about all the elements of the game.

5. The game can't go on for ever - there must be an end point.

6. There are no draws - there must be an outright winner.

7. The last player to move wins. You cannot lose on your move.

That cuts out Bridge (by rule 4), Chess (by rule 6) and Backgammon (by rule 3) among many others.

Bibliography: A list of the books which have served to inspire tasks within the EUMY Mathematics set.

Acknowledgements. The author would like to acknowledge the invaluable assistance of her mathematical models who appear throughout these tasks:

Epsilon-pi and Smidgin Ubiquitous

We call them Epsi and Smidge!