Math Games


Ed Pegg Jr., April 10, 2006

I liked the G4G7 column by my fellow columnist Ivars Peterson. I also liked Edward Rothstein's New York Times article. I have some extra notes, so I thought I might borrow a page from Paul Harvey, and give the rest of the story.

Wei-Hwa Huang put up his Sudoku presentation in his journal, so you can read his solving method there. Wei-Hwa was the last of many people I introduced in a rapid-fire presentation:

  1. The Math Factor podcast (XML) is a weekly feature by Chaim Goodman-Strauss, featuring 5 minute snippets of mathematical recreations.
  2. Lajos Szilassi and his Szilassi polyhedron.
  3. Emrehan Halici runs the PuzzleUp website, a weekly math puzzle competition. He is also a former member of the Turkish Parliament, and has authored the Mind Games column in newspaper Tubitak for 25 years.
  4. Kenneth Brecher runs Project Lite, an atlas of visual phenomena.
  5. Yossi Elran introduced Young@Science for the Weizmann Institute, and the Math by Mail Internet Club.
  6. Michael Kleber is an editor for the Mathematical Intelligencer, and showed off large models of possible isohedra.
  7. Istvan Orosz showed a number of his spectacular anamorphic pictures, some of them now in Masters of Deception by Al Seckel.
  8. Steve Sigur, who is working on the Triangle Book with John Conway.
  9. Serhiy Grabarchuk, who now runs the excellent Age of Puzzles site.
  10. Sándor Kabai, who has a large site dedicated to polyhedra and other mathematical symmetries.
  11. Siobhan Roberts, who recently finished the biography The King of Infinite Space : Donald Coxeter: The Man Who Saved Geometry.

Those are just some of the people I personally introduced. But I met many more people, and learned many things.

Eric Harshbarger gave his solution for arranging the standard 100 scrabble tiles into 4 5x5 squares, and showed some of the items and puzzles he's built for his puzzle parties.

Q U I L T   F J O R D   B I M A H   A G A T E
U N M E W   L A V E R   A V I S O   W A F E R
O R I B I   E L I T E   T O X I N   A Z O N S
T I N E S   Y O N I C   C R U D E   R O U G E
A G E N T   S P E A K   H Y P E D   D O L _ _

James Stephens of, in addition to talking about the methods he's used to program a computer to make puzzles, gave me a puzzle generated by his Fried Okra Perplexity series. Start with a 5x5 square, with coins as indicated, and one special coin. To move, select any coin and jump over one or more coins in an orthogonal direction, to the next vacant space. All coins remain on the board after jumps. Move the special coin to the upper left square.

Robert Wainwright discussed the status of Polyform Number Theory. In this problem, multiple copies of two polyforms are given, and the object is to find the smallest shape coverable by both. An example is shown of a hexomino and square. He offered a challenge with a particular heptomino and tromino.

Gary Foshee demonstrated the Maxwell Motor. It just needs a wire, battery, a screw, and a 1/4 inch cylinder magnet (Forcefield, Gaussboys, K&J Magnetics , United Nuclear). Let the screw and magnet dangle, then complete the circuit with the wire. The screw and magnet will start spinning very fast. (A bit easier if you use two hands.) If you properly understand the right hand rule, you can predict the direction the screw will turn.

Maxwell's Motor

Andrea Gilbert, the creator of, is one of the guest puzzlemakers for the $200,000 puzzle challenge Perplex City. The creators at Mind Candy Design also put out a general call for puzzle designers. She also had a wonderful walkthrough maze that I got thoroughly lost in.

Erik Hermanssen, creator of Deadly Rooms of Death, talked about The Appeal of Stepping Games. In addition to writing about his G4G7 experiences, he gave out a booklet of abstracted art. He also gave his entire presentation about stepping games in DROD.

I spoke to Rik van Grol, the editor of one of my favorite magazines, Cubism For Fun. A years subscription is now available via PayPal, by 18 euros to mariavangrol (at) . It's the best magazine around for mathematical and mechanical puzzles. I used the magazine extensively for my Modern Burr Puzzles column, a topic updated in a talk by Frans de Vreugd.

N. J. A. Sloane discussed seven staggering sequences in the Encyclopedia of Integer Sequences. I recently encountered a staggering sequence myself, while making updates due to the $500 Prime Generating Polynomial contest sponsored by Al Zimmermann. Dmitry Kamenetsky noticed that n6+1091 is particularly poor at generating primes. For n=1 to 3095, no primes are made. But n=3906, 4620, 5166, ... leads to primes. A check of OEIS led to A066386, a sequence discovered by D. Shanks in 1971.

George Hart discussed orderly tangles and polyhedral puzzles. He also talked about various methods of three dimensionsal printing, a topic also touched on by George Miller of Puzzle Palace and sculptor Bathsheba Grossman.

Jerry Slocum discussed Sam Loyd's greatest hoax, which is the subject of his new book, The 15 Puzzle. The meticulously researched book contains the definitive, illustrated history of one of the most popular and important mechanical puzzles of all time. The true story of the puzzle is given, including: How Sam Loyd's most successful hoax lasted more than a century; The real inventor and records of his patent application; and The story of how the puzzle came to be manufactured.

Robert Fathauer showed some of his edge to edge fractal tilings. He also displayed his latest items available for sale from

Highlights of a few treasure hunts were discussed. David Somers recounted his story of how some mathematics and three-dimensional imaging software gave him the solution for the Beetle in A Treasure Trove. Andy Latto gave highlights of the yearly MIT Mystery Hunt. The 2006 Mystery Hunt is now online.

Dennis Shasha talked about some of his online Scientific American columns, Puzzling Adventures.

One of my notes recommends that I check out Aaron Siegel's Combinatorial Game Suite. Looks fairly nice.

Brent Collins displayed several of his beautiful mathematical sculptures, which feature many symmetries and complex surfaces.

Robert Abbott, creator of Logic Mazes, gave an essay entitled What Logic is Not. You might want to solve his Twisty Maze first.

I talked about the Fano Plane, which will be the subject of my next column.

There was much more -- to get a taste, try the books based on previous Gardner Gatherings: A Lifetime of Puzzles, Puzzler's Tribute, and Tribute to a Mathemagician. The next book, based on the events based on G4G7, will be put together by me, of all people. I can't wait to see it.

Math Games archives.

Comments are welcome. Please send comments to Ed Pegg Jr. at

Ed Pegg Jr. is the webmaster for He works at Wolfram Research, Inc. as an associate editor of MathWorld. He is also a math consultant for the TV show Numb3rs.