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 (December 2016)

For a configuration of unit squares on a grid, let the adjacency number of a square be the number of (horizontally, vertically, or diagonally) adjacent squares. We call a connected configuration of squares equally adjacent if every number that is an adjacency number for the configuration has an equal number of squares with that adjacency number. For example, here are the smallest known equally adjacent configurations for the non-empty subsets of {1,2,3}:

What subsets of {1,2,3,4,5,6,7,8} have equally adjacent configurations? What is the smallest configuration representing each one? What are the solutions for the hexagonal grid? There are too many subsets of {1,2,3,4,5,6,7,8,9,10,11,12} to fully consider solutions on the triangular grid, but what about the one-element and two-element subsets?


You can see all the best known results here.

Submit your answers here.

Weekly Puzzle Sites: | Ken Duisenberg | NPR | Puzzability | The Griddle | Puzzle Picnic | Nick's |
Other Puzzle Sites: | MathPuzzle.com | IBM | Retrograde Analysis | Puzzle Palace | Terry Stickels |
Interactive Puzzle Sites: | Click Mazes | Puzzle Beast | Logic Mazes | Color Shift | Grid 1 | 2 | Boomshine |
Physics-Based Puzzle Sites: | Perfect Balance 1 | 2 | Assembler 1 | 2 | 3 | 4 |
| Color Infection | Redstar Fall 1 | 2 | Fantastic Contraption |
Colleges with Puzzles: | Macalester | Missouri State | Purdue |
Great Math Sites: | Geometry Junkyard | Math World | Mathematician Biographies |
| Integer Sequences | Inverse Calculator | Geometric Dissections |
Recreational Math Sites: | Mike Keith | Harvey Heinz | Primes | GIMPS |
| Polyforms | World of Numbers | Soup Kitchen |


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 Geneology | Top Ten Lists | Mathematical Horoscope | Math Humor