Math Magic is a web site devoted to
original mathematical recreations. If you
have a math puzzle, discovery, or observation,
please e-mail me about it. You can also send
answers to the problem of the month.
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.


Home | Math Magic | Packing Center | Puzzle Palace | Published Puzzles | Puzzle Collection
Friedman Numbers | What's Special About This Number? | Periodic Table of Mathematicians
Stetson University | Math Department | Teaching | Vita | Undergraduate Research | Ambigrams
Florida Mini-Golf | Movies | Places I've Been | Places I've Been E-mailed From | E-mail Me
Pictures of Me | My Math Genealogy | Top Ten Lists | Mathematical Horoscope | Math Humor