Galton/Plinko Board Reimagined for Differentiated Modeling

Choose the one YOU like

My interest in the Galton Board (Plinko Game) is refreshed by my colleague, Dr. Grant Miller, who suggested that I flatten the previous Marble model and then use transparency sheets (remember those plastic sheets we used for overhead projectors?) to seal the board. After a few experiments with different "nail" shapes, I found hexagonal ones yielded the best results. The gaps between the hexagonal branching points is 7mm, allowing the use of small seeds such as rice or mung beans. The transparency sheets can be glued on with super glue or clear grip contact adhesive, and then trimmed. One board can be used to explore the binomial distribution. Two boards can be glued together for an hour-glass-like model, with seeds sealed inside. I also added from initial numbers for those who want to make connections to the Pascal Triangle.

Mathematically, a n-layer Galton board is the same as "tossing n fair coins". Note that the seeds are collected at the (n+1)th layer. For example, for the 6-layer board, there are a total of 2^6= 64 pathways for a seed, of which one leads to the leftmost slot and one to the rightmost one. To find the number of pathways to the third slot from the left, a seed needs to make two right turns: C(6, 2) =15, which is the same as making 4 left turns: C(6, 4). An equivalent question is, "When one tosses six coins, how many ways can one get two heads (or four tails)?"

References

1. https://www.thingiverse.com/thing:2747357
2. https://www.thingiverse.com/thing:3098530