"Amida-kuji" is Japanese for "network lottery."  According to Bob Stanton, it is used in Japan to choose turns in games and assign prizes.  You start with as many vertical lines as there are people.  Here is what we would have with six people numbered 1 to 6.  The prizes are placed at the other end of the lines in any order. Now you draw some "random" horizontal lines to connect pairs of adjacent vertical lines.  The only  rule is that no two of the horizontal lines can touch.  So the solid horizontal lines below are allowed, but not the dashed line.  The number of lines you draw is up to you, but to make it interesting you should have at least one horizontal line between each pair of adjacent vertical lines. To decide Player 3's prize you start down line number 3 until you reach a horizontal line and follow that line over to the adjacent vertical line, follow that line down to the next horizontal line and go across again, etc.  In this case Player 3 gets the book. Will each person get a different prize no matter what horizontal lines are added? Is there a way to place horizontal lines to make any assignment of prizes you want? Making Mathematics Home | Mathematics Projects | Students | Teachers | Mentors | Parents | Hard Math Café | Amida-kuji Project Description | Prerequisites | Warm Up Problems | Hints | Resources | Teaching Notes | Extensions | Results |
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