New as of June 17, 2000:  Venn Polyominos, an original problem in combinatorial geometry
April 9, 2000:  W. R. Marshall and Casey Mann have pushed the envelope on Self-surrounding tiles:  see this page for a tile of Mann’s that self-surrounds five times!
February 18, 2000:  Urn problem
February 3, 2000:  In Self-surrounding tiles, new and corrected information
New as of January 8, 2000:  In Latin Squares, a link to Stephen Bennett’s website where you can find a Java applet for working that type of puzzle.
December 12, 1999:  Hip Solitaire
November 20, 1999:  Update on Self-surrounding tiles:  a tile that surrounds itself three times!
October 24, 1999:  Preliminary version of a new page on Self-surrounding tiles, to which I hope to add additional illustrations in the near future
 

Here are some links to people who present new mathematical problems and puzzles regularly:  Ed Pegg’s weekly Math Puzzle, Erich Friedmann’s monthly Math Magic

I’ve been writing puzzles for GAMES magazine freelance for almost twenty years, and lately I’ve begun writing a monthly puzzle column for the newsletter of the Chicago chapter of Mensa.  Someday I hope to collect these into a book.

A somewhat obscure, but interesting, corner of tiling theory, with an interesting unsolved question, involves self-surrounding tiles that will not tile the entire plane.  There are a few illustrations of such tiles that I’ve discovered, which as far as I know have not been published elsewhere.

Here are a few of my puzzles based on the beautiful Cairo tiling.

I also originated a puzzle type involving Latin Squares, a few of which were printed in the July 1996 issue of GAMES World of Puzzles.  I’m also interested in  Latin Squares as a topic of combinatorial math, and I’ve found some minor new discoveries.

Some miscellaneous original puzzles:  Domino triangle, Hip Solitaire, Twiddling Digits, Triamond dissection, Urn problem, Venn Polyominos

Numerology, of the sort practiced by Martin Gardner’s creation, Dr. Matrix, interests me.  I’ve written a story of a similar type which was printed in GAMES magazine, in their November 1999 issue.

Questions, corrections, comments:  Send me e-mail at  markthom@flash.net