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Math Magic Archive

Problem of the Month (July 2020)

Ten years ago, I published a set of Replacement Puzzles in GAMES magazine. This got me thinking, what is the longest possible length M of such puzzles with a unique solution, and how does it depend on S (the number of different symbols allowed), L (the maximum length of strings) and R (the number of transformation rules)?

Graph theorists use the word girth to represent the length of the shortest cycle in a directed graph. Given S, L, and R, what is the largest girth G that is possible?

You can see all the best known results here. Submit your answers here.

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