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NRICH: Sumo   A number game requiring a strategy.

Ages 7 – 11

#### When Push Comes to Shove

1. Sumo is a one dimensional representation of a Sumo wrestling bout.
2. Each bout lasts a maximum of 6 turns.
3. The ring is represented by a linear track seventeen spaces long.
4. 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.
5. 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.
6. Each player begins the game with 6 cards values 1 to 6 inclusive.
7. Players simultaneously reveal their choice of card.
8. If the cards are equal, no movement occurs.
9. If the cards are not equal, the player selecting the larger value card pushes the token a number of spaces equal to:

THE DIFFERENCE BETWEEN the two card values MULTIPLIED BY THE LOWER of the two 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

A player wins a bout by either:
Pushing the counter off the opponent’s end of the track.
Ending the six turns with the counter in the opponent’s half of the track.

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

Addition & Subtraction, Multiplication & Division
K-6

## Organization

NRICH (University of Cambridge)

Board/Card Game
Tutorial