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## 'Sumo' printed from http://nrich.maths.org/

This game was invented by Tony Reeves who teaches at Christ's College in Brecon.

#### When Push Comes to Shove

- Sumo is a one dimensional representation of a Sumo wrestling bout.
- Each bout lasts a maximum of 6 turns.
- The ring is represented by a linear track seventeen spaces long.
- A counter is placed on the central space of the track at the start of the bout and is moved to the left or right depending on the outcome of each round.
- If the counter is pushed beyond the end of the track then the bout is over as one contestant has pushed his opponent out of the ring.
- Each player begins the game with 6 cards values 1 to 6 inclusive.
- Players simultaneously reveal their choice of card.
- If the cards are equal, no movement occurs.
- The player selecting the larger value card pushes the token a number of spaces equal to

THE DIFFERENCE BETWEEN the 2 card values MULTIPLIED BY THE LOWER of the 2 card values.

#### Examples

Higher Card |
Lower Card |
Movement |

6 |
4 |
(6 - 4) x 4 = 8 |

5 |
2 |
(5 - 2) x 2 = 6 |

4 |
3 |
(4 - 3) x 3 = 3 |

The greatest movement possible is 9 spaces (when 6 and 3 are the selected cards).

It is thus (just) possible to win on the first turn.

A player wins a bout by either:

Pushing the counter off the end of the track.

Ending the 6 turns with the counter in his opponent's half of the track.

An interesting variant is the introduction of a zero card to the initial allocation.