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Math Monday: Make a Marble Run

By George Hart for the Museum of Mathematics


Many science museums feature a Galton board in which balls branch randomly left or right through an array of pegs and end up binned at the bottom in an approximation of a normal distribution. Here is a deterministic variation on that idea, in which there is a two-position gate at each juncture that causes each ball to go the opposite direction from the previous ball to visit the gate. If you use 64 balls, can you figure out how many will end up in each of the bins at the bottom? Karl Sims built this marble run and gives instructions on how to make your own, along with a clear explanation of its operation.


The side view below shows the tilt of the board and the final distribution of 64 marbles in the seven bins: 1, 6, 15, 20, 15, 6, 1. The mechanism forces each marble to take a different combination of the six left/right choices.



Gareth Branwyn is a freelance writer and the former Editorial Director of Maker Media. He is the author or editor of over a dozen books on technology, DIY, and geek culture. He is currently a contributor to Boing Boing, Wink Books, and Wink Fun. And he has a new best-of writing collection and “lazy man’s memoir,” called Borg Like Me.

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