American Go E-Journal

Go Spotting: Go and Polyominoes

Sunday July 25, 2021

by Xinming Simon Guo

My former math instructor, professor George Litman from National Louis University, recently invited me to visit his personal library. There, I found a mathematics book he purchased in 1995: Polyominoes: Puzzles, Patterns, Problems, and Packings. In the preface, the author, Professor Solomon Golomb, mentioned that polyominoes were first observed in patterns formed by 5 connected stones/markers on a Go game board in 1907.

Coincidentally, I also discovered these patterns in 2011 on the Go board, but I didn’t know they were polyominoes. In a Go game forum, I posted a puzzle about the possible shapes formed by 8 connected stones, which proved to be too challenging at the time. So I changed the difficulty level to 6 stones (Hexomino), and found all 35 shapes.

The unexpected discovery about polyominoes has led to the formal integration of these shapes into my Go and Math curriculum. The photo below captures all the shapes of pentominoes (5-stone string):

Photo by Jane online summer camp student Jane, 2020

By the way, there are 363 shapes of octominoes (8-stone string), a number arrived at by adding an extra stone based on 7-stone strings, removing duplicates, and counting the distinct shapes. No formula has been found yet to calculate the number of shapes.

Categories: Go Spotting,Main Page