7 Mar 2020

The fun method of choosing a winner - Amidakuji

I've been here in Australia since 2011 and have noticed one thing. I haven't seen Amidakuji that is very common in Japan.

Amidakuji is convenient when you need to choose someone who will win a prize or prizes. For example, if there are four people and only one piece of cake remains, one guy can eat the cake. (Please do not say cutting a piece of cake into four.) Japanese people have two ways to solve this situation, one is Janken (Rock paper scissors) and another one is Amidakuji.

Firstly, you need to draw vertical lines the same as the number of people. There are four people, so draw four lines. There is only one piece of cake, so, make one cake mark somewhere under the line. 
Draw several horizontal lines between vertical lines, as many as you want.
However, there is a rule, you cannot exceed a vertical line with a horizontal line which means you cannot overlap the start and end point of a horizontal line with any other horizontal lines. For instance, if it would be a road, it wouldn't be a crossroads.
The next step is hiding the bottom part on which the cake mark has been drawn. The last step is depending on you. If you want to make it certain to be fair, you can ask attendees to add several horizontal lines as they want. Then all the preparation is done!

You ask the attendees to choose one of the vertical lines and write down their names. All right, it's fun time from here!
Pick up one of the names and trace the line from the top. When you meet a horizontal line, you must follow it. (Refer to the picture below) Follow the lines according to the rules and reach the bottom. If there is the cake mark, that name's attendee wins.

The interesting fact is each start point (the place where the name is written) doesn't duplicate with other end points. The picture below describes the easiest way to understand how it works.
I better tell you one more way of drawing horizontal lines. This is the one which Juno did when he was small. It's not common but maybe there are people who do the same. As I have written, the horizontal line should be drawn between two lines and not allowed to exceed a line. However, you can draw a horizontal line outside the amidakuji. Please have a look at the picture below. This looks like cheating, but it works.
It seems like Amidakuji stimulates mathematicians' interests. Some mathematicians have written about Amidakuji. If you are interested in it, please google it.

I'm going to continue to write about something interesting, especially information I can get from Japan. Unfortunately, most Japanese companies and creators don't have English pages on their website. I would be happy if I could introduce something fun to more people.


  1. I did not know this puzzle game to select winners. I will try it with my friends. It is good to see the variation in the video, where the middle is covered and only the top and bottom are seen. Also, to win a car seems like the most fun. :-)

    1. Hi Kathleen,
      Thanks for coming by to read my blog. I know you are interested in Japanese culture, so I will explain little more about Amidakuji. It seems like Amidakuji started about 600 years ago. At the time, Amidakuji was not vertical lines, it was radial lines. The etymology is related to Buddhism. Buddhist statues called Amida Nyorai has radical several lines on its back (https://www.rakuten.ne.jp/gold/garandou/add/butuzou/bu-025.html) and those lines are etymology of Amida kuji. Kuji means lottery.