| Amidakuji (阿弥陀籤) is a Japanese method of lottery designed to create random pairings of
arbitrary numbers of two sets of things, each with an equal number of elements.
Process
As an example, consider assigning parts in a play to actors.
- To start with, the two sets are enumerated horizontally on a board. The actors would go on top, and the parts on bottom.
Then, vertical lines are drawn connecting each actor with the part directly below it.
- Next, each actor adds a horizontal line to the board. Each line must connect two adjacent vertical lines, and must not extend
another horizontal line.
- Once this is done, the vertical lines are traced from top to bottom. As you follow the line down, if you come across a
horizontal line, you follow it to the adjacent vertical line on the left or right. You continue until you reach the bottom of a
vertical line, and the top item you started from is now paired with the bottom item you ended on.
Mathematics
Part of the appeal for this game is that, unlike random chance games like rock, paper, scissors, amidakuji will always create a 1:1 correspondence, and can handle arbitrary
numbers of pairings (although pairing sets with only two items each would be fairly boring).
It also works regardless of how many horizontal lines are added at a time. Each person could add one, two, three, or any
number of lines, and the 1:1 correspondence would remain.
External links
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