## Let's play Watanabe Jyanken

Janken (Rock-paper-scissors) is a traditional and popular method in Japanese daily life to decide one winner. However, we have to do Janken many times, if we select one winner among many people. Watanabe Janken can select one winner with only one time even if the number of people is large.

## How to Watanabe Jyanken

How to play Watanabe Jyanken is easy.

1. Assign a different number to each person from one to the number of the participants. For example, select any person, assign 1 to the person and assign 2, 3, 4...in order. The following figure is an example about four participants.

2. Let’s say " Watanabe Janken, Janken, Pon ! ." Everyone choose any number from 1 to the number of the participants and shows it simultaneously by her/his fingers.

3. Add all numbers (equivalent to all fingers) and calculate the remainder dividing the sum (the number of all fingers) by the number of the participants,. A person whose assigned number is equivalent to the remainder is the winner. Congratulation! (If the remainder is zero, a person whose assigned number is equal to the number of the participants (equivalent to the largest number) is the winner. )

Number 3 is the winner, since the remainder is 3.

（If the remainder is equal to zero, Number 4 (Dad) is the winner...）

## VIDEO in English

### Who can eats two Sushis ? Let's decide by Watanabe Jyanken !

## Why Watanabe Jyanken.

- We can select one person without any equipment. We use only by our fingers.
- Easy and fun !
- It is a fair method:
- The possibility of the winner is even if any one chooses her/his number at random.
- Every one cannot manipulate if the others choose their numbers at random.
- To select the number arbitrarily is a Nash equilibrium in game theory.