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 2018)

Call a square of side n neighborly if it touches n other squares (at more than one point). Call a collection of squares neighborly if every square is neighborly. There are clearly neighborly tilings of the plane, as demonstrated by the tilings below. What other sets S of sides are possible? What about infinite strips?


{4}

{5}

{6}

Call a collection of squares k-balanced if it has an equal number k of squares of each size. If we have a finite k-balanced neighborly collection of squares, what is the smallest possible value of k?

Given a rectangle, how can it be tiled with squares to maximize the proportion of the squares that are neighborly? What proportion of squares an infinite strip of a fixed width can be neighborly?


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 Genealogy | Top Ten Lists | Mathematical Horoscope | Math Humor