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Math Games
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Material added 23 December 2009
Christmas Tree Lane
I recently visited Christmas Tree Lane after giving a math talk at Fresno State. I noticed that it's an anagram of thermal resistance, and dressed appropriately.
Christmas Tree Lane
Erich's Holiday Puzzles
Erich Friedman has put together a batch of Holiday Puzzles.
Erich Dec 2009
New Tightest Tetrahedra Packing
Back in August 2009, I put out a demo with a tetrahedra packing with density .782. That record didn't last long. The paper "Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra" by Amir Haji-Akbari, Michael Engel, Aaron S. Keys, Xiaoyu Zheng, Rolfe G. Petschek, Peter Palffy-Muhoray & Sharon C. Glotzer, published in Nature 462, 773 - 777 (2009), has found a packing with density 0.8502671806. The GlotzerLabWiki has a java demonstration and data. The new best packing shows quasi-crystal properties. A write-up is at Science Daily.
tetra packing
Facebook Puzzle Challenges
Derrick Schneider: Facebook has taken a page from Google and set up a bunch of puzzles for aspiring programmer employees. But even if you don't want to work there, the puzzles are available for anyone to try. Some thought-provoking challenges in there that are -- obviously -- heavy on the "write a program to solve this" attitude. Thought mathpuzzle readers might like it. [Ed- Some intriguing challenges here.]
The Prisoner
One of my favorite shows is The Prisoner, from the 1960's. I recently started going through the excellent Blueray set (it was on sale, but pricey again now). I also learned that AMC put the Prisoner series online.
Checkerboard Illusion vs Vacuuming
I quite liked how the Checkerboard Illusion vs Vacuum turned out.
Material added 30 November 2009
Polyform Semi-oddities
George Sicherman: As you were the first to encourage Mike and me in finding polyomino oddities, you may be interested in some polyform semi-oddities. So far I've found only partial impossibility proofs.
Recent Demonstrations (out of 5579)
Here are some of the interactive demos that have been posted at recently. Click on an image to go to the demo.
Ignobel Prize Festivities
The festivities of the 2009 Ignobel Prize are featured at this week's NPR program, Science Fridays.
Material added 29 November 2009
Puzzle collector Laurie Brokenshire in Daily Mail
An article about Laurie Brokenshire talks about his thousands of puzzles. I got a chance to try out many of them when I visited him in England, as part of a working trip with Adrian Fisher, the master maze maker.
Laurie Brokenshire
4D Magic Puzzles
Roice Nelson: The opensource Rubik analogue program MagicCube4D just had a major release supporting a huge number of new 4D puzzles.  General duoprisms, the 4-Simplex, the Dodecahedral Prism, and the 120-Cell all have twisty puzzles associated with them now. Even the 4D Rubik's Cube variants were extended, and allow up to 9 cubies-per-side!
4d Magic
Jan Zoon Heptacubes
Jan Zoon: I sent a Christmas card to Kate Jones and she mentioned I should also send the picture to you.

I call the figure Notre Dame. The lower block is composed out of four complete sets of Heptacubes. The White and Black Heptacubes are set in blocks of 31. The blocks are placed in such a way that they alternate each other. They form the lower half of the big block. The upper half of the big block is composed of the same heptacubes but now one set of brown - white pieces and the other set of white - brown pieces.

The middle part is composed of four complete sets of hexacubes. Again two sets one black and one white in cubes of (10x10x10 with one additional tetracube). Here the cubes are also formed out of sub-blocks which are alternately placed in such a way that you can see the way the are built. The next layer is formed by the sets of white-brown and brown-white hexacubes. On top you find the two towers, They are made of four complete sets of pentacubes. For the base all white and brown pentacubes are used. Above them are the white-brown and the brown-white pentacubes. So in total all possible heptacubes, hexacubes and pentacubes are used to make this picture.[click on the image to see a much larger version]
Jan Zoon
A problem of squares
Bernardo Recamán Santos: Find a four-digit square number which has at least one digit in common with every other four-digit square number. [A nice little problem.]
The Complete Works of J S Bach
One odd purchase I made recently was the Complete Works of J S Bach, for a little over $100. I picked up Beethoven and Mozart, too, while I was at it. After listening to thousands of works, I'm pretty firmly a Bach guy. His Cantanas, which stretches to 60 CDs, are incredible. Almost every Bach work seems to have something marvelous. Beethoven's major works are incredible (perhaps 20 CDs worth) -- but his minor works don't seem as compelling. Mozart's major works are also incredible -- but I find myself returning to Bach's minor works.
Material added 27 November 2009
Old papers
I cleaned out my house over the past few weeks, and came across a birth certificate for my grandmother, born as Cecelia Marion. I learned that her parents were Hormidas O. Marion, and Virginia Greenough. I'd only heard of Hormidas mentioned once by my mom, in relation to a particular gold nugget. As a trapper in Canada, the nugget is one of the things he brought down with him, to sell if he got desperate. He got a job as a dishwasher in Fort Pierre, and gradually earned enough money to buy a large island, which became a profitable orchard. He gave the nugget to Virginia as a present before they married. The island became a large portion of what is now Pierre SD. Her brother was Louis Greenough. He built the fifth car in the world, shortly after seeing the first car at a world's fair. He created the first motorized bus, and was indirectly responsible for some of the first auto safety laws, via cities banning him from driving any of his vehicles into city limits.
Total[({57, 399, 679, 995, 1167, 1293}^k)] == Total[({115, 299, 767, 925, 1205, 1279}^k)]
The above sum of powers works for k=1, 3, 5, 7, or 9.
Tito Piezas: Jaroslaw Wroblewski found the second soln to the above system! This is: [57, 399, 679, 995, 1167, 1293] = [115, 299, 767, 925, 1205, 1279]. There is also a 6.6 partition such that it is good for k = 1,2,3,5,7,9: [-1205, -767, -299, 399, 995, 1167] = [-57, -679, -1293, 115, 925, 1279] just like the first one found in 2000 by Shuwen. In summary, for optimal multi-grades, there are,
(k,4,4), k = 1,2,3,5 (completely solved as quadratic forms)
(k,4,4), k = 1,2,4,6 (as quadratic forms, and elliptic curve soln)
(k,5,5), k = 1,2,3,5,7 (as quadratic forms, and elliptic curve soln)
(k,5,5), k = 1,2,4,6,8 (with only elliptic curve soln)
(k,6,6), k = 1,2,3,5,7,9 (unknown)
(k,6,6), k = 1,2,4,6,8,10 (with only elliptic curve soln).
Science, Technology, Engineering, and Mathematics
Mythbuster went to the White House, as a part of an event promoting STEM.
The Earth with Saturn-like Rings
I found this video of Saturn-like rings for the Earth quite fascinating.
Sorting Contest Animation
Dick Saunders Jr.: You might like the animations at A Sorting Contest.
National Sudoku Championship
Wei-Hwa Huang and Thomas Snyder, authors of Mutant Sudoku, were featured in a Time video article on the event.
Lottery Comparisons
I recently tried to find lists of what lottery games were played, where. I wasn't able to find any pick-6 type lotteries with 43, 50, or 51 balls.
Lottery Games
3D Mandelbulb
A 3D version of the Mandelbrot set has gotten a lot of attention lately. A gorgeous rendering method is used.
Numb3rs reduced to 16 episodes in Season 6
For some reason, Numb3rs has been steadily losing its audience, and CBS has reduced the season order from 23 episodes to 16 episodes.
Material added 21 October 2009
Martin Gardner in New York Times Article
John Tierney: "For today’s mathematical puzzle, assume that in the year 1956 there was a children’s magazine in New York named after a giant egg, Humpty Dumpty, who purportedly served as its chief editor." See the rest of the article.
Wolfram Homework Day
Today, Wednesday Oct 21, is Wolfram|Alpha Homework Day. I'll be one of the dozens of people on hand to answer questions, from noon (CST) until the wrap-up 14 hours later. Feel free to send in any questions you like.
MathCamp Qualifying Quiz
The qualifying questions for MathCamp 2009 are a nice selection.
Golly 2.1
The cellular automata program Golly 2.1 has been released. Some extensions are also available. Tim Hutton wrote a turmites extension, and noticed that my wormtrails turmite got trapped in a cycle after 4.3 million steps, making it the best known "busy beaver" of 2-D Turing machines.
The Zen of Labyrinth
Robert Abbott: Dave Phillips wrote a new maze book called "The Zen of the Labyrinth." I reviewed it here:

I thought one of his mazes would look great on, so a GIF of the maze is the first attachment here. Dave says you have his permission to use the maze. These are the rules:

   Enter by the bottom red path and end on the center gray square.

   You may retrace your path but may not make a U-turn on a
   pathway. You must follow the paths in the order red, blue,
   yellow and then red, blue, yellow again, as needed, changing
   color on the white squares.
[Ed - I went ahead and picked up the book myself, and it's gorgeous. Every page is like a piece of art, and every one is an interesting maze-based logic puzzle, of many different varieties.]
Acute-dissected Squares and Cubes
A square can be divided into acute triangles. Can a cube be divided into acute tetrahedra? Various papers look at the problem, some with solutions with a large number of tetrahedra:Tiling space and slabs with acute tetrahedra, Acute triangulations of polyhedra and R^n, A Dihedral Acute Triangulation of the Cube, Triangulation of Simple 3D Shapes with Well-Centered Tetrahedra.
Can't Decide? Undecide!
Chaim Goodman-Strauss has written an excellent paper on undecidability for Notices of the AMS.
Material added 9-9-9
Lots of 9 news today. The Beatles "Revolution 9" almost never got onto the track, because the higher-ups thought it was too uncommercial. Now, it's the centerpiece of one of the biggest commercial campaigns of all time. For the Wolfram Blog, I wrote 9-9-9 about almost integers with lots of nines.
The Diabolical Box
One thing that slowed me down in recent weeks was Professor Layton and the Diabolical Box. This is a nice collection of about 150 puzzles, much like Professor Layton and the Curious Village. Many are familiar. For example, 10 of them are knight-tour and peg-jumping puzzles. But all nicely interactive, and there were a few I hadn't seen before.
DiabolicalBox Curious Village
Material added 7 Sep 2009
NPR Puzzle
The puzzle from NPR this week is mine. "This challenge comes with help from math puzzle expert Ed Pegg. Take the names of the first nine elements of the periodic table: hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen and fluorine. Select one letter from each of these names in order to spell a familiar nine-letter word. Hint: It's a word used in math." Send Answer.
Here's a similar puzzle that Will Shortz though was slightly too obscure: Take the names of the officially recognized planets in order, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. Select one letter from each of these names in order to spell a familiar eight-letter name. Hint: It's a name used in math. Answer.
Don Knuth on Puzzles
I had the pleasure of seeing Don Knuth speak at the International Puzzle Party. Around his neck he had a necklace of 12 disconnected L-trominoes based on unit squares, with the centers of each end joined by strings of unit length. He asked if it was possible to make a 6x6 square with the necklace of trominoes.
Knuth Puzzles   Knuth Necklace
After showing various cool tricks possible with polarized film on an overhead projector, he started his talk on how Boolean Decision Diagrams were great for solving puzzles. He used it to solve the Knuth Necklace problem, and then demonstrated his program for sliding block puzzles. He showed how BDD could solve Slitherlink, then introduced Skimperlink, which allows multiple loops, the goal is to find the minimum number of edges to satisfy all given constraints. Amusingly, Wei-Hwa Huang was helping with the slides, and showed a few impressive fast-solving techniques. Don announced an upcoming book, Selected Papers on Fun and Games, which will be out next year (Amazon doesn't list it yet). Speaking to Don later, he shared the quick puzzle with me: "f4e, s9, se5en, ??" I also asked what got him started, and he told me his story on how he won the Ziegler's Giant Bar contest as a boy, pretending to be sick so he could built up the winning word list - what are all the words you can make from 'Ziegler's Giant Bar'?. While he was doing it, he figured out algorithms that could save him time. For example, no reason to look through the C and D pages of the dictionary. Can you name a political party or animals that use all but 4 letters in 'Ziegler's Giant Bar'?
Oskar van Deventer Videos
I also had the pleasure of seeing Oskar van Deventer's latest creations. many of them are shown in the incredible series of videos under the name OskarPuzzle. Many of these puzzles are available for sale at the 3D printing shop Shapeways Oskarpuzzles. Some are also available at, for example James Stephens mentions that "Oskar's wurmm puzzle is now available from Puzzle Masters.   I am lucky enough to have one of the George Miller produced versions and think it is one of Oskar's best inventions (tied with about 20 other Oskar puzzles, of course, but that's still a pretty exclusive list for him). Oskar has also written up papers for a few of his puzzles, such as Topsy Turvy which mechanically recreates the sporadic M12 group (video). In addition to Shapeways, Oskar mentioned tools Solidworks, Meshlab (STL Repair), and Minimagics (Materialize). A favorite video of mine is the the Caution Cube, a geared puzzle that has drawn Oskar's blood.
George Miller Videos
George Miller, who runs the wonderful site, also has a puzzle video collection under the name MrPuzzleman. The videos of the Geary cube, Fire, and People Put-together (with Oscar) are well worth a look.
Erich Friedman Puzzles
Erich Friedman: Multi-Balance Puzzles, Pyramid Puzzles, Crypto-Product Puzzles, Weight Equation Puzzles, Gold Star Puzzles, and Packing Puzzles have been added to Erich's Puzzle Palace. For example, for Weight Equations, put a digit in each box so that the equation is true. The boxes should also balance, where each digit represents the weight of that box. (His entry on Packing Problems at Math Magic this month is also very nice.)
Weight Equation
Gary Foshee puzzle
Gary Foshee gave me this puzzle: "I have two children. One is a boy born on a Tuesday. What is the probability that both are boys?" Answer.
Nob Yoshigahara Puzzle Design Competition
The Floppy cube was the winner of the Puzzle Design Competition. My own entry, Super-Hamilton, didn't win any prizes, but seemed fairly popular. I have two copies left, available for $25+shipping. If there is enough demand, I'll ask Walter Hoppe to make up to 30 more, before I reach the 150 limit.
Floppy cubesuperhamilton
Tom Cutrofello Puzzle Blog
The latest Games Magazine has a great article on George Hart. Not all of Tom's columns get accepted by Games, and those go into his excellent Puzzle Blog, Gottasolveit.
New Densest Tetrahedron Packing
S. Torquato & Y. Jiao published (in Nature Vol 460, 13 August 2009) a packing method for tetrahedra with a packing density of 0.782021. Exact coordinates can be seen in their page of supplemental information.
tetrahedron packing
Squares vs Cubes
From Asim Shah: Find the two smallest numbers whose difference between their squares is a cube and whose difference between their cubes is a square. As a hint and encouragement, both numbers are between 3 and 12. The next such pair is 384, 640.
Water Retention in Magic Squares
Craig Knecht has work with Walter Trump on the water retention problem, and has some nice results.
Water Retention
Triangular Clock
Jörg Pretz: I have new idea for a binary clock. You can look it it under which has a detail PDF document.
triangular clock
4A = 6V
George Sicherman has shown that 4A = 6V.
Yahoo MathPuzzle Group
A link for the MathPuzzle Yahoo group is at .
Material added 28 Jul 2009
Droste Effect Music videos
There are two excellent music videos showing off the Droste Effect. Wild Beasts and Clap Your Brains Off.
Wild Beasts
Symmetry Festival
The Symmetry Festival 2009 takes place in Budapest, 31 July - 5 August You can watch all plenary events of the Symmetry Festival 2009 on-line, Central European Time (GMT +2), Aug 1 - Aug 4.
Material added 26 Jul 2009
Mirror Array
Edmund Harriss built a mirror array using acrylic mirrors bent in just one direction. It gives some nice results.
mirror array
Gravity Based Puzzles
Inventor P. C. Houlis let me know of some gravity based puzzles that he invented, along with some videos (Cubedron, Krystalledron, Icosedron, and Puzzle Ninja, ). He also has the kastellorizo youtube channel.
Yahoo MathPuzzle Group
I know I should join Twitter and various other sites, but I still rely on the Yahoo MathPuzzle Group to send out notices that I've made an update. With any luck, I'll be doing them more regularly now (though I keep saying that).
Talk to the Times
Will Shortz to a week and answered a lot of questions about crossword puzzles and his methods.
Red Green Blue Maze
Chris Lusby Taylor: I've just been asked to do something for a local school's playground. I planned to use the existing paving slabs as squares but then found that they're laid in an offset pattern, so each has six neighbours.

Enter at the top, cross the blue, green, and red bars, and keep this sequence until you exit at the bottom. Or enter at the bottom, and cross the red green and blue bars, and keep this sequence until you exist at the top.
Demonstrations Site
The Wolfram Demonstrations Project now has over 5000 entries. George Beck and Conrad Wolfram both blogged about it. Many of the flash videos have been added to YouTube.
Truck PackingPolya FillingPentagon TilingsShaping a road
Galvagni Figures
George Sicherman: I've posted Galvagni figures for polyenns and polydecs.
Various items at Amazon
Some of the books, games, magazines and puzzles I've ordered from Amazon in the past six months. I'm always interested in hearing about obscure recreational math related sites, books, puzzles, and games, so always feel free to write me.
SpherePackingThe ElementsTwisted RailsConfigurationsBob Hearngames of no chanceDiabolicalBoxCast DuetStratumHead StressFire and IceIMO CompendiumGames MagazineMathematical GamesMathWorldMathematical WizardryPied Puzzler
One puzzle game I haven't been able to find anywhere yet is Anti-virus, by James Stephens and Oskar van Deventer. Online, this is their Bulbous Blob puzzle, long one of my favorite puzzle series.
Mondrian Knight
Julian Courtland-Smith (inventor of Survive!): Please find enclosed 'Mondrian's Knight's Tour' with numeric solution. As a designer, I am obviously interested in the history of art. One of my favourite artists is Mondrian. Looking back, his work looks passe compared with today's modern art, but he did set the tone for the modern architecture of the twenties and thirties which is still enjoyed and practised today. When looking at his art, it becomes obvious Mondrian would not have simply painted a knight's tour on one canvas as this would have obliterated the obligatory white spaces so beloved by him. Therefore, I trialed a few ideas and do believe that this two canvas problem/solution matches his style. (Puzzle in ODG format).
Mondrian Knight
New Packings and Coverings
I was just looking at Erich's packing page, and was amazed at some of the recent improvements. His latest Math Magic deals with Weightominoes.
8 triangles in a circle (April 2008) 8 triangles in a hexagon (May 2008)
9 triangles in a square (July 2008) 6 triangles in a triangle (August 2008)
2 squares covering a triangle (March 2009) 6 triangles covering a square (April 2009)
5 squares covering a circle (April 2009) 5 triangles covering a circle (June 2009)
China Labyrinth
There are 64 possible patterns of black and white around a hexagon. At Mindsports is an amazing solution that combines all of them.
New Elliptic Curve Cryptography Record
Joppe W. Bos, Marcelo E. Kaihara, Thorsten Kleinjung, Arjen K. Lenstra and Peter L. Montgomery have set a new record in Elliptic Curve Cryptography.
Long, Perfectly Packed Rectangles
Brian Trial: Here are some new results that Stuart Anderson was kind enough to render and display on his web site: SPSR with integer aspect ratios 13:1 up to 18:1.
Puzzle-Up Five
The fifth annual Puzzle-up has just started, a 24 problems/24 weeks competition where each week a different problem is put accross for you to think on and try to solve.
Candy Fabrication
The Candyfab 6000 is an intriguing method for printing 3D shapes in sugar.
Candy Dodecahedron
Thérèse Eveilleau, whose Magic Maths is very nice, has put Tetrapentos online. The pieces can be moved with mouse and arrow-keys.
Poker Odds
I've been studying various variants of Poker recently, trying to figure out good sets and matching odds for things like a five-color deck. These could be used to improve various very popular Poker Odds webpages.
Capture the Cat
A game called Capture the Cat has been making the rounds. It's always possible to win, as shown by Adam Holers.
Material added 21 Jun 2009
Holey Megaminx
A hollow but functional Rubik's cube won a puzzle design competition recently. The high-end of rubik-type puzzles has been the dodecahedral Megaminx. Designer Lee Tutt has made a Holey Megaminx, and it is being made as a limited release.
If you put magnets in small plastic capsules so that they can move in a restrained way, then glue those into polyhedra, they will attach together in a very nice manner. The Dodek Puzzle is based on this, a matching puzzle based on the dodecahedron, with extremely high quality magnetic pieces. These can be crushed and reassembled in about 5 seconds, which makes for an excellent figidity toy. The two puzzles are also excellent. In addition, this is the first mass-produced toy entirely made in the US that I've seen in awhile. A bit larger and heftier than a Rubik's cube. Highly recommended.
Latin Hexagon
Wei-Hwa Huang posted a nice Latin Hexagon on his site.
New Al Zimmermann Contest and Site
At Al Zimmermann's Programming Contests, a new contest has started, Son of Darts.
Harvey Heinz's Magic Squares Site
Harvey Heinz's excellent site on magic squares, magic stars, and other objects, had an uncertain future at the soon-to-die Geocities. A copy of his site is now at
Anthill Substructure
A youtube video, several tons of cement, and lots of digging reveals an ant colony structure.
Conan Boron Rant
Back in February, Conan went on a rant against Boron. Boron has 4 forms, not three.
Magic tricks with Math
Peter McOwan has made various videos linking magic tricks with math.
The Problemist
A few thousand chess problems are collected in the Problemist Collections.
New Pattern found in Prime Numbers
Benford's law is a well known feature of statistics. A similar phenomenon has been found in prime numbers.
Material added 14 Jun 2009
A Collection of Algebraic Identities
Tito Piezas: Could provide a link to A Collection of Algebraic Identities? After all, solving Diophantine equations is a form of a puzzle too. [An encyclopedia's worth of work -- very nice]
New Mersenne Prime
A new Mersenne Prime has been discovered: 2^42643801 - 1. It's not the largest. MathWorld has the story.
World Puzzle Championship US Qualifier
Signup for the World Puzzle Championship 2009 US Qualifier is now open. There is also a practice test. The qualifier, put together by Nick Baxter, always has about ten pages of great puzzles.
Math Magic
Erich Friedman: the smallest square (not divisible by 5, 7, or 8) that can be tiled with squares of sides 5, 7, and 8 was  found by Brian Trial at this month's Math Magic. [Ed- Other news from Erich: 7, 10, 11, the largest circle coverable by five unit squares, and 15 points in a Heilbronn square. He's also added 3 new puzzle types at Erich's Puzzle Page.]
Squares5 7 8
Configurations of Points and Lines
Branko Grünbaum latest book, Configurations of Points and Lines, is a gorgeous gem of a book. collecting all the known information about configurations. In a 4-configuration, for example, there are four lines through every point, and four points on every line. In an extended Euclidean geometry, an 18-point 4-configuration is possible. The figures below all all work as 4-configurations without points at infinity. Amazingly, the first geometric 4-configuration was found in 1990, the second one below.
The first 5-configuration was found in 2007 by Leah Berman. 5 lines through each point, 5 points on each line.
Incidently, Branko's classic Tilings and Patterns is being reissued in paperback at the bargain price of $27.
Simon Tatham's Portable Puzzle Collection
One of the best sites I've seen for puzzles is Simon Tatham's Portable Puzzle Collection. I've seen it before, but didn't have the time at that moment to try it. Recently, I noticed they were all available as a batch install for Ubuntu Linux, and tried all of them. This is a great collection of puzzle games, with Black Box, Bridges, Cube, Dominosa, Fifteen, Filling, Flip, Galaxies, Guess, Inertia, Light Up, Loopy, Map, Mines, Net, Netslide, Pattern, Pegs, Rectangles, Same Game, Sixteen, Slant, Solo, Tents, Twiddle, Unequal, and Untangle.
More on the Klein Quartic
On a whim, I mapped the 24 points of the Klein graph onto a heptagonal tiling (PDF).
Klein Graph
Material added 15 May 2009
Burr Puzzles and Numb3rs
Bill Cutler and burr puzzles get a mention in tonight's season finale of Numb3rs. For many links, see my write-up below, or the current
Tiling Pentagons
I recently added Tiling Pentagons to the Wolfram Demonstrations Site. I give exact solutions for all 14 families. A must program to try for anyone that likes neat tilings.
The new computational knowledge engine Wolfram|Alpha launches tonight.
Material added 3 May 2009
CRC Encyclopedia of Mathematics, 3rd Edition
The third book that kept me busy: Eric Weisstein's CRC Encyclopedia of Mathematics, 3rd Edition. It's a huge, three volume encyclopedia, all of it available at Wolfram MathWorld. I assisted with the update, compiling the comments and suggestions of thousands of MathWorld visitors, allowing for just as many additions and corrections.
CRC Encyclopedia
Similar Polyominoes
I've been playing around with polyforms a lot recently. One good paper is Michael Reid's Tiling With Similar Polyominoes, which was expanded some with the October 2002 Math Magic. I used Burr Tools to try out some of the problems at Torsten Sillke's packing site, and at Puzzles will be Played. One puzzle example I made -- all the 2-7 square polyominoes with rotational symmetry can be fit into a 10x13 rectangle. One solution is below, with the center of rotational symmetry given for each of the pieces. You can also look at the Steady State cube from microcubology.
Void Cube and other Variants
The 2007 winner of the Nob Yoshigahara Puzzle Design Competition was the Void Cube (youtube), by Katsuhiko Okamoto. These are now available at Easier to order are some of the exotics now available at The mirror block (yousaytoo) is another variant.
Mad Science
In addition to introducing the Bacon lance, Theo Gray's book Mad Science is finally out. Glorious pictures and wonderful write-ups walk you through the wonderful experiments that Theo has tried. I've helped him with a few of them, and suggested others, some of which later wound up on Numb3rs. Our Sodium party wound up getting a write-up in Playboy magazine. (When I was younger, I never imagined I could get into Playboy by doing science experiments). Over at Amazon, try a random sample from Click Inside. More is at his site
mad science
Lasercut Binary Addition
M. Oskar van Deventer: I made a minimalistic binary adding machine. It has two laser cut plates and steel balls running between them. That is all. Here is the YouTube video. The object is a mechanical puzzle aimed at 6-10 year olds. [Ed - Another fantastic Oskar invention. To see many more, check out the May 2009 College Mathematics Journal. It's a Puzzle issue, with lots of great columns by Oskar, Martin Gardner, and Stewart Coffin.]
World Sudoku Championship
Vladimir Zahoransky: I visited World Sudoku Championship held in Slovakia in Zilina. It was fantastic event. Snyder, Kusui, Bertrand, Novotny and Ondrousek all made mistakes in the semi-final. The block was 45 minutes for 4 puzzles, but these 4 puzzles were very, very hard. I used my binoculars to watch the progress of all the contestants. Snyder solved only two puzzles, so his chances at the final were very theoretical. Bertrand had troubles too, only two puzzles. Novoty and Ondrousek solved 3 puzzles. Final part was crazy. Organizer made one mistake and all the contestants struggled with different methods for solving a superhard puzzle. At the end, the Slovakia team scored the golden medal, the Czech team claimed second and Hungarian came in third. Individual part ? polish solver presented best concentration. I have a lot of photos from WSC. I got Thomas Snyder's sign as a souvenir. The puzzles can be seen at, with the English version of puzzles about 2/3rd down the page under "competitions & results". One of the puzzles came from Steve Schaefer, who runs
Puzzle Design Competition
The 2008 Puzzle Design Competition results have been up for awhile. If you have an idea for an entry for the 2009 competition, you have until June 30 to enter.
Games Collection
At my local gameshop, I recently found examples of The Games Collection, all for under $20. These are excellently made wooden games. I've been trying out Creeper, Megalith, and Fire&Ice.
Game Playing
Do you know how to play Lines of Action, Amazons, and Go? If not, sites like Boardgamegeek can help you to catch up. some of the best of these games are available for play at iggamecenter and Three new games I was unaware of are Dragons, Attangle, and Yavalath.
Rick's Tricky Six
The paper Rick's Tricky Six by Alex Fink and Richard K. Guy is a fantastic linkage of the 15 puzzle, Moebius transforms, edge colorings, projective planes, icosahedra, the Hoffman-Singleton graph, Steiner systems, and the Golay code.
The Griddle
David Millar: I've added a comments feature on puzzle pages at The Griddle ( Hopefully it will help me get good feedback on the kind of puzzles people like to solve. I'll also be releasing my 350th puzzle page soon, and perhaps something else big on my 21st birthday, like some puzzles with a "21" theme. (21 is a triangular number - brilliant! I'm already thinking of some kakuro and sum sudoku.)
18 Black Squares
Jean-Charles Meyrignac: A new record for fewest blocks in a crossword, by Kevin G. Der: Also well worth a look are the main site, and the grid art section.
Tierney Lab
At the New York Times, I should soon have a puzzle in TierneyLab, with a Hamilton-path based puzzle.
The Cube
Jerry Slocum points to a recent video of a person paging through his book The Cube, which is also available at Amazon. Published by the same company that also published mad Science, above.
Wymondham College Math Links
Graham Colman sent a link to the Wymondham College website, and I spent a while checking out the very interesting links and items.
I recently attended EbertFest, and saw Sita Sings the Blues, by Nina Paley. Then, she dropped by my office, as a friend of Theo Gray, they both went to the same school. After seeing some of my puzzles, she pointed me to her short film Fetch, which is loaded with dozens of perspective tricks and impossible objects.
Bridged Polyforms
Bernd Karl Rennhak has made some beautifully curved figures that he calls bridged tritans.
New Polyform Oddities
George Sicherman: This full oddity for the Z pentomino is considerably smaller than the previous one.  It has 73 tiles. [George has also found a new Galvagni figure.]
5Z Oddity
Curly Cube
A new metal puzzle at puzzlemaster: Curly Cube. Also looking very interesting are Metroville and The Ball Puzzle.
Jack Good Obituary
Mathematician Jack Good, a colleague of Alan Turing, recently died at age 92.
Foxtrot Puzzle
Bill Amend recent put a puzzle in Foxtrot.
Mathematics of Mirrors
A Philadelphia Inquirer article discusses the mathematical mirrors of Andrew Hicks.
Terry Stickels: Here's something from my friend Robert Webb, an Australian buddy who has worked with me on several projects: Dodecamorph.
Recent demonstrations
Recent Wolfram Demonstrations of note include Cayley tables, Finite Field tables, Look and Say Vectorgrams, Solar System Mandalas, Packing Squares with side 1/n, Coin Flips, and Fibonacci Number Interpretations.
Math Reference Sheets
Cody Miller: We just released our new free math reference sheets and this resource maybe valuable to your readers. These free reference sheets cover algebra, geometry, trig, and calculus. There are 6 sheets in all. Our goal at ecalc is to provide good free math resources to students and professionals.
80 Vertex Polytope
Someone was just asking about this, and I could remember where I'd seen it. From Math in the Media by Tony Philips: Eric Altschuler and Antonio Pérez-Garrido published an article in Physical Review last year (E 76 016705 (2007)) in which they described "a four-dimensional polytope, new to our knowledge, with a high degree of symmetry in terms of the lengths of the sides." They found the configuration "by looking at the ... problem of finding the minimum energy configuration of 80 charges on the surface of the hypersphere S3 in four dimensions" with the energy function Σ(1/rij) where rij is the distance between the i-th and j-th points, and the sum is taken over all pairs of distinct points. (They remark that they cannot prove this is actually a global minimum, but add that "even good local minima can be interesting or important configurations.") The other N for which they found symmetric configurations are 5, 8, 24 and 120; corresponding to the 4-simplex, the dual of the 4-cube, the 24-cell and the 600-cell. The authors give a method for visualizing their 80-vertex polytope in terms of the Hopf map S3 --> S2. They triangulate S2 with 16 equal equilateral triangles: 4 abutting the North Pole, 4 the South, and a band of 8 around the Equator. This polyhedron has 10 vertices. Each of these vertices corresponds to a circle of the Hopf fibration, along which they describe explicitly how to place 8 of the polytope's vertices. Another description of the 80-vertex polytope was published by Johannes Roth later in the same journal (E 76 047702 (2007)).
Optimal Packing of 6 Circles
A student project led to a great paper: Optimal packing of 6 circles in a flat torus.
Invisible Car
An impressive illusion by artist Sara Watson resulted in an invisible car.
Replica Narwhal Tusks
If you would like to get a replica of nature's most amazing spirals, Bone Clones has narwhal tusks.
Langton's Ant video
A great video by aldoaldoz discusses many varieties of Langton's ant.
Games and Puzzles Miniconference
Matthew Kolokoff: Ed! Why aren't you at the Games and Puzzles Mini-Conference, right now? Ok, I think it's in Israel, but that's no excuse. [Ed - looks like it was a great event.]
Material added 9 Mar 2009
Mathematica Home Edition
For years, recreationalists have wanted a less expensive version of Mathematica. Mathematica Home Edition is now available for $295.00. It's pretty much designed for at-home users, without some of the advanced capabilities more attuned to commercial usage.
My Second Gardner Tribute Book
Mathematical Wizardry for a Gardner, edited by Ed Pegg Jr, Alan Schoen, and Tom Rodgers, is now available for pre-order at Articles were contributed by Gary Chartrand, Jeremiah Farrell, Stanley Eigen, David Lister, Istvan Orosz, George I. Bell, Bob Harris, Derek Kisman, Richard Guy , Alex Fink, Rodolfo Kurchan, Peter Gabor Szabo, Matthew H. Baker, Aviezri Fraenkel, Thane Plambeck, Dick Hess, Mogens Esrom Larsen, Istvan Lenart, Colm Mulcahy, David Rhee and Jerry Lo, Robert Bosch, Stanley Eigen, Chaim Goodman-Strauss, George W. Hart, Akio Hizume, Robert Barrington Leigh, Ed Leonard, Ted Lewis, Andy Liu, George Tokarsky, Karl Schaffer, and Lajos Szilassi.
Puzzles on
Another thing keeping me busy has been weekly puzzles on I wrote a blog item about the puzzles so far.
Math Genius
Stephen Wolfram has announced Wolfram|Alpha, another project I've spent some time on.
MathWorld Updates
And another biggie, I've been working with Eric Weisstein to update Wolfram|MathWorld. Long lists of updates for January, February, and March. Sorry for the long delay in an update here, I'll try to get to all the material that's been sent in soon.
Material added 12 Jan 2009
Happy 1 * 2 - (3 - 4 - 5) * 6 * 7 * 8 - 9
Denis Borris notes the above, made with only multiplication and subtraction. I noted that 2010 made all but four letters of "counting down the days," and Will Shortz used it. This is a really late update for me. The December ice storms caused me to lose about 3 days of vacation, due to a lot of very large branches on my fence, house, and around my yard. I worked on two Numb3rs episodes, and caught up on my columns for Japan Airlines. I did a lot of reading of mathematical books and papers that have been accumulating. And I finished off my second Gardner tribute book. Apologies for the delay.
My First Gardner Tribute Book
Homage to a Pied Puzzler, edited by Ed Pegg Jr, Alan Schoen, and Tom Rodgers, is now available for pre-order at Amazon. Articles were contributed by Robert Cotner, David Meyers, Jerry Slocum, sarah-marie belcastro, Carolyn Yackel, Peter Hilton, Jean Pedersen, Byron Walden, Sandor Kabai, Louis Kauffman, Michael Longuet-Higgins, NJA Sloane, Peter Gabor Szabo, Zsofia Ruttkay, Oskar van Deventer, David Dillon, Jeremiah Farrell, Yossi Elran, Robert Friedhoffer, Judith Morrel, Robert Fathauer, Adrian Fisher, Markus Gotz, Serhiy Grabarchuk, Thomas Hull, Kate Jones, Rodolfo Kurchan, Mogens Esrom Larsen, Earnest Hammingway, Ann Schwartz, Jeff Rutzky, Norton Starr, James Stephens, and Robert Wainwright.
Mathematica 7 Reader launches
Jeff Bryant blogs about the new Mathematica 7 Reader, and a couple hundred new math demonstrations (now 4406). Some notable new demos include Manipulating Graphs, Irrational Tiling, Alternating Subtriangles, Truel World, Lattice Circles, Earth's Second Moon, Isotope Browser, and Gambler's Ruin. Another recent blog item concerns the Yellowstone Earthquakes.
Plane Boarding
Dick Saunders Jr: John Paulos is always coming up with something interesting!  He shows plane boarding can be cut to 1/6 the time.
Circles of Descartes, Mod 12
Playing around with my Circles of Descartes program, I noticed that any integer solution, mod 12, had only 4 different values, either 0149, 0589, 367A, or 236B (where A=10 and B=11). I wondered about the minimal set of circles that would cover all integers, but didn't find it. Likely, there are other moduli that are also important. Click on any image for a much larger visualization.
Melbourne Museum
Kiki Tanousis: Thanks for plugging our city. You might want to include the cube attached to the Melbourne Museum.
Z Oddity
George Sicherman: This oddity for the Z pentomino has 125 tiles and full symmetry.
Z oddity
Late Christmas Tree
Serhiy Grabarchuk: Here is a Strimko inspired Christmas tree.
Strimko Tree
La Ora Stelo
Jacques Ferroul: I added some pages : flowers, witch's hats, pentagona series. [Ed- A gorgeous series of pages.]
#1 Job: Mathematician
According to the Wall Street Journal, the #1 Job is Mathematician.
The Unitarity Triangle
In the latest Particle Physics Booklet (free), one new section is about the Unitarity Triangle, based on the CKM Matrix, which describes the difference between matter and antimatter. In order for the Standard Model to work, the Unitarity Triangle has to be perfect.
Unitarity Triangle
The Tiling Listserver
Brian Wichmann has added a series of improvements to the Tiling Database.
Tesla Coil Music and Lenz Forces
Lots of interesting music made with huge Tesla coils has been posted to Youtube, including Sugarplum, Nintendo Theme, Tocatta and Fugue, Creepy circus. The site has more. Did you know that near an MRI, a block of aluminum will fall slowly due to Lenz forces?
Fractals with Apophysis
The article 40 Amazing Fractals, using the program Apophysis, shows many gorgeous images.
Penrose Sudoku
Wei-Hwa Huang has posted a Penrose-base Sudoku on his blog. With Slocum, Singmaster, Gebhardt, and Hellings, he's also written the book The Cube, about the Rubik's cube (page 5). The same publisher will put out Theo Gray's Mad Science (page 8). Both books will come out in the spring.
Erich Friedman's Xmas Puzzles
Erich Friedman made five great X-mas themed puzzles. For example, Cut the ornament into 24 equal shapes. Four of the shapes have already been cut to start you off (see his link for the answer). His Math Magic this month combines polyominoes and chess pieces.
Paterson's Worms Update
Benjamin Chaffin: Hope all's well with you. I haven't had much time for math fun lately, but I did manage to update my page on Paterson's worms. I now have pictures of every worm, including close-ups around the origin so you can see the individual line segments. It's fun to just scroll through and look at all the different shapes.
Golly 2.0 Released
For explorations of Conway's Game of Life and similar automata, Golly 2.0 is now available. Golly now supports multiple algorithms, and universes with more than 2 cell states.  Tom Rokicki has extended Gosper's hashlife algorithm to allow up to 256 states, and that means Golly can handle many new types of CA. Andrew Trevorrow has added many more improvements.
Site Goals
Martin Gardner celebrates math puzzles and Mathematical Recreations. This site aims to do the same. If you've made a good, new math puzzle, send it to My mail address is Ed Pegg Jr, 1607 Park Haven, Champaign, IL 61820. You can join my moderated recreational mathematics email list at