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Material added 07 07 07
Cloverfield, JJ Abrams, and Ethan Haas
The Untitled JJ Abrams project, ultimately a SF movie now codenamed Cloverfield (debuts Jan 8, 2008), has a puzzle site of sorts, So far, the puzzles are attractive but tedious. A trailer is in front of the Transformers movie, I've heard.
Puzzle Picnic
Johan de Ruiter: Some friends and I have been working on a website for WPC-like logic puzzles. Aside from solving puzzles, people can also design puzzles in our studio if they wish. You can find us at [Ed - many excellent logic puzzles here. Two other logic puzzle sites I like are Simon Tatham's Portable Puzzle Collection and].
Vortex Maze Construction
Would you like to make a challenging maze with many vortices? The paper by Jie Xu and Craig S. Kaplan, Vortex Maze Construction, gives an excellent overview of the problem, lots of insight, and lots of mazes.
The Angel Wins
On an infinite 2D board, a chess piece called the Angel can move up to n spaces each term. A piece called the Devil destroys one square each turn. If the Devil can surround the Angel with destroyed squares, the Devil wins. Who wins? in a recent paper, Peter Gacs argues that The Angel Wins.
Alice is Lost
Eric Harshbarger has made an online puzzle series called Alice is Lost, which has an Alice in Wonderland motif.
Science Videos
I'm always on the look-out for good free science videos. Why is it so? is one good set, which ran on Australian Broadcasting Corporation from 1963 to 1986. Freescienceonline is a blog that focuses on lectures. Science Daily occasionally adds new videos. Through Slashdot, I learned of, which has vetted science videos from YouTube. A nice puzzle video featuring Kate Jones from was made by Telepathic TV.
Denis Borris: a = 5 406 093 003, b = 14 612 920 778 542 779 004, c = 14 612 920 778 542 779 005, d = 7 645 370 044, e = 14 612 920 777 423 140 483, f = 14 612 920 777 423 140 485 has the property that abc and def are right triangles with the same perimeter, c-b=1, and f-e=2. There are five smaller pairs of triangles, all with a < 1 billion. Find them.
Rolling Block Flash Puzzle Game
Bloxorz is a fairly nice flash game with rolling block mazes, as championed by Robert Abbott of
Walking and Hopping Toys
Can an object walk down a mild ramp with no gears or batteries? peter Steinkamp shows many varieties of what he calls Unpowered Walkers and Hoppers.
3 Million Visitors
Dick Saunders Jr.: What date will you turn over 3 Million Visitors? I will guess July 4, 2007. [Ed - Hmmm... about 2969000 right now. Apologies for the length of the break. In 1991 I bought a house in Colorado for $17,777.77. Now on 7/7/7, I've closed on it (for more), and moved most of the things in it to my home here in Champaign IL. So I've done lots of packing, unpacking, cleaning, and truck driving. My mom was living in the Colorado house, and now doing comfortably in an assisted living facility.]
Material added 12 Jun 2007
Mr. Wizard passes
Mr. Wizard, Donald Jeffrey Herbert, is no longer with us (July 10, 1917 – June 12, 2007). The LA Times has photographs of his shows, and his story. He did some science shows I saw as a boy. When I met Bill Nye at AAAS, to convince the Numb3rs crew to use the pepper and soap experiment in one scene, Bill showed me a twist to the experiment, and mentioned that he originally saw it from Mr. Wizard.
Google U.S. Puzzle Championship - 14 Jun registration deadline
Nick Baxter: The Google U.S. Puzzle Championship is coming up next weekend--June 16. Winner gets a trip to Rio de Janeiro with the U.S. Puzzle Team. Anyone can enter -- but they must enter by June 14th (Thursday). [Ed - Anyone entering can expect to find many top-notch puzzles.]
Rubik's Cube in 26 Moves
Northeastern University computer science professor Gene Cooperman and graduate student Dan Kunkle have proven that any configuration of a Rubik's cube can be solved in 26 moves. The research from Cooperman and Kunkle improves upon the previous record by one move. The use of 7 TB of distributed disk as an extension to RAM for holding large tables and the development of faster computer moves using mathematical group theory were keys to their research efforts. For more details, see the paper, "Twenty-Six Moves Suffice for Rubik’s Cube."
Material added 29 May 2007
Public Service Award from National Science Board
Numb3rs received a public service award from the National Science Board, so I went to Washington DC (see the full story at the Wolfram Blog). Here's a picture from the diplomatic reception room at the State Department. From left to right, Michael Trott (Mathematica Guidebooks), Ed Pegg Jr (mathpuzzle), Cheryl Heuton (Numb3rs series creator), Eric Weisstein (MathWorld), and Amy Young. If you'd like to hear my voice, I did a radio interview with Amy Young on NPR's Afternoon Magazine.
DROD: The City Beneath
If you like puzzles, you need to try DROD: The City Beneath. I found the predecessor, Journey to Rooted Hold, to be the best game I ever played. Now that I'm deep, deep into TCB (specifically, the Holding Vats), I have a new all-time favorite game. Truly a superb game (if you like thinking).
RSA Factoring Challenge Discontinued
Dick Saunders Jr.: At RSA Labs is the message "This challenge is no longer active." I suppose that will make the Cunningham Project the primary place for factoring challenges.
Turing Challenge Announced ($25,000)
Is there a universal 2,3 Turing machine? A resolution of the question either way will net you $25,000 from Stephen Wolfram, in the first Wolfram Research Prize.
Kurchan Squares Contest Results
In a Kurchan square, numbers 1 to n2 are arranged in a grid, and the difference between the maximal and minimal product is made as small as possible. The best known Kurchan squares have been greatly increased in the latest Al Zimmermann contest.
Crossword Compiler 8
If you'd like some assistance in making crosswords, Crossword Complier 8 is the best program on the market. The various puzzles I've had in the New York Times were made with the assistance of earlier versions of Crossword Compiler.
Knight's Tour Cube
Awani Kumar has made a 8x8x8 Semi-Magic Knight's Tour Cube. Harvey Heinz has other Unusual Magic Cubes. Awani has also written a GPJ article about Knights in 3D.
Material added 02:03:04 05/06/07
The Wolfram Demonstrations Project
A secret project I've helped with has been launched, the Wolfram Demonstrations Project. I wrote my Math Games about it. 1200+ mathematical demonstrations, all interactive and freely available with the Mathematica Player. Below is a piece of one of my demos, Circles and Ellipses.
Mathematica 6
Mathematica 6 has been launched. This was covered on MathWorld, Slashdot, Science base, the Wolfram Blog, Gizmag, the News-Gazette, and my Math Games column. Below is a snippet of the Mathematica 6 flash header.
New big primes
The 17 or Bust project has found a new Sierpinski problem solution: 19249×213018586+1, which has 3.9 million digits. That makes it the largest non-Mersene prime ever found.
Goldbach Verfied to 1018
Tomás Oliveira e Silva: The Goldbach conjecture has been verified up to 1018. Our prime gap computations are a by-product of our Goldbach conjecture verification effort.
Golly 1.2
The Game of Life exploration tool Golly 1.2 has been released. It features fast updates, huge universes, and a large library of examples.
Bill Clinton's NYT Crossword
On May 6, the Games and Puzzles section of the New York Times, under the guidance of Will Shortz, will be in a new, revamped format. The first crossword featured in this new section will be by crossword aficionado Bill Clinton, who was seen as a solver in the movie Wordplay. And here's the crossword: Twistin' the Oldies.
A Great Issue of Games Magazine
Lots of good game and puzzle magazine have folded lately. At the same time, Games Magazine has really been putting out a string of great issues. It starts with an Andrea Gilbert maze cover, and contains a Gottlieb-Selinker-Woodruff puzzle extravaganza, an incredible meandering crossword by Frank Longo, an article by Tom Cutrofello about puzzle designer Michael Toulouzas, and the usual collection of great puzzles.
Polyomino Magic Squares
Erich Friedman latest Math Magic ponders how multiple copies of a polyomino can be placed in a square so that every row and column has the same number of filled squares.
The Birmingham Mirror Maze
Adrian Fisher has posted a video of his latest mirror maze, at the Birmingham Sea Life Centre.
Livio Zucca explores packing tetrominoes into larger tetrominoes.
Alexandre Owen Muniz: On May 15, the US Postal Service is increasing the cost of a first class stamp to 41 cents. Here's something else you can do with 41 pennies. Two connected arrangements of coins are the same polycoin if you can transform one to the other by sliding coins without changing which coins are adjacent, or by a combination of flipping the arrangement and coin sliding. There are 13 pentacoins. I've found a 41 coin arrangement with the property that all of the pentacoins are contained within it, and if any coin is removed this
ceases to be true. I believe that no larger arrangement with this property is possible.
Factoring Cartoon
The online comic has a nice numbering factoring cartoon. I also liked their cloverleaf collection.
G3ode Puzzle
Nicholas Quaine: The G3ode puzzle is a polyhedron with tiles covering all facets but one. Each tile has two distinctively coloured sides. Any of the 3 tiles adjacent to the empty facet can be flipped into that space. The puzzle is solved when all tiles are flipped such that the surface of the puzzle is all one colour. G3ODE is copyrighted freeware, currently available for the Windows XP operating system.
Angel Problem Solved
Several paper have been published solving the Angel problem.
Cellular Automata Bottle Table
The video of cellular automata controlled bottles is quite neat.
Chinese University vs English University
This BBC article shows a Chinese test question and an English test question.
Material added 22 April 2007
The Klein Graph
Over at Wolfram Research, I've been working on graphs. In one book, I found a reference to the Klein graph, with 24 points each connecting to 7 others. I soon found many more beautiful references: Patterns on the Genus-3 Klein Quartic by Carlo H. Séquin, Klein's Quartic Curve by John Baez, The Eightfold Way: The Beauty of Klein's Quartic Curve by Silvio Levy, Klein's Quartic Curve by Greg Egan, Polyhedral models of Felix Klein´s Quartic, and Independence Numbers and d-Codes in the Klein and Related Graphs by Bellarosa, Fowler, Lijnen, and Deza.
Harder than Diamond
Diamond's long reign as the hardest known substance seems to be ending. Aggregated nanorods, fullerite, boron nitride, boron suboxide, boron-aluminum-magnesium (BAM) and rhenium diboride all seem to be as hard or harder. Did you know there are now 8 known allotropes of carbon? Below is an image of a grain of boron suboxide.
Numb3rs wins National Science Board Award
From The popular television drama series "Numb3rs," about an FBI agent whose brother, a genius mathematician, helps solve crimes in the Los Angeles area by using mathematical problem-solving techniques, will receive a National Science Board group Public Service Award for 2007, along with the program's co-creators, Nick Falacci and Cheryl Heuton.

The CBS Paramount-produced drama and its two collaborators will be honored for their contributions toward increasing scientific and mathematical literacy on a broad scale at a ceremony May 14 at the State Department in Washington, D.C. [Ed - so I'll be in Washington on May 14.]

"Numb3rs" is the first television series on which Falacci and Heuton have collaborated. Wisely bringing in several mathematicians as consultants, the producers were able to provide realism to the mathematical theories employed in the crime-solving cases of each episode. Experts say that the various theories and mathematical problems and equations used on the program are easily transferable to equivalent real-world situations. Cryptanalysis, probability theory, game theory, decision theory, principal components analysis, multivariate time series analysis and astrophysics are just some of the many disciplines employed in the series thus far. Working mathematicians of the Mathematical Association of America have recognized the accuracy and validity of the theories and their presentations on the program.
Bill Clinton to write NYT Crossword
On May 6, the Games and Puzzles section of the New York Times, under the guidance of Will Shortz, will be in a new, revamped format. The first crossword featured in this new section will be by crossword aficionado Bill Clinton, who was seen as a solver in the movie Wordplay.
Combinatorial Designs
I've recently been doing some combinatorial design work as well. has an excellent database. The other main public site is the La Jolla Covering Repository. After being down for awhile, a page on the Social Golfer Problem is now available. The chief book on the topic is the Handbook of Combinatorial Design. A great free online book on the topic is Combinatorial Generation, by Frank Ruskey. Ezra Brown wrote (at least) two great papers on the topic, about the Fano Plane and the (11,5,2) Biplane. A more difficult paper, but quite beautiful, is Antipodal Covers, by Aleksandar Jurisic.
Multimagic Squares Update
Christian Boyer: The April 2007 update of is online. You will see a new page on the first bimagic square of primes, but also some other news.
Hexagonal Spirallohedra
Russell Towle has made a great series of youtube videos about zonohedra. One of them is his video on Hexagonal Spirallohedra.
Logical Labyrinth
Eric Harshbarger had a puzzle party for his birthday. The A to Z puzzle is interesting -- what's the optimal list? The Logical Labyrinth is quite impressive.
Burrtools, Winedt, Great Stella
Various useful programs: BurrTools, for studying burr puzzles, has a new update. WinEdt 5.5, one of the best LaTeX editors on Windows, has just been released as a new version. Stella 4D was released with a price drop. There is no more comprehensive database of polyhedra that I know of -- I've found it a useful tool so far.
Chessboard Attacking Chains
The Math Magic this month deals with Chessboard Attacking Chains.
New Crossword Record
Manny Nosowsky is mentioned in my Crossword Rules article. Jean-Charles Meyrignac brought to my attention an article by Manny where she does an examination a 19-cell crossword.
Material added 9 April 2007
DROD: The City Beneath
A few years ago I wrote a column about a great puzzle game. I finished it with "The game is huge, clever, well paced, and entertaining. I agree with the high praise that DROD: Journey to Rooted Hold has gotten so far -- this is the best puzzle game of all time." The game was received well for an independent game, and two years later, the sequel, DROD: The City Beneath, is now available. A PC demo, Mac demo, and Linux demo are all available. This sequel is a great continuation of DROD: JtRH. Highly recommended.
The Big Dig Litigation Graph
Joseph DeVincentis: What gets the Boston Globe to print (almost) the complete graph on 15 nodes the front page of its local section? A story about the lawsuits filed as a result of the tunnel ceiling collapse last year. The main story is The Big Tangle. [Each line represents two people suing each other.]
MayDay Mystery
Aaron Enright: Since the 1970's, strange notices have been printed on May Day. I must say that I'm intrigued by this webpage about the MayDay Mystery. Even if it's utter nonsense, I admire nonsense that can go on for this long.
11111 .... 111111 is prime!
Harvey Dubner: On March 28 I found a new probable prime repunit, R(109297), which consists of 109297 1's. It is effectively impossible to prove true primality at this time. The only known repunit primes are R(2), R(19), R(23), R(317), and R(1031). In 1999 I found the PRP repunit R(49081), and in 2000 Lew Baxter found the PRP repunit R(86453).
Material added 1 April 2007
Abel Prize for Srinivasa S. R. Varadhan
S.R. Varadhan has won the 2007 Abel Prize, "for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviation."
Bob Abbott on Mazes in Numb3rs
Robert Abbott: I finally finished writing my discussion of the episode of NUMB3RS that was about logic mazes. The writing took longer than I thought, probably because I was conflicted about whether to support the show or complain about it. I ended up complaining too much.
Come in - Go away
A reversible doormat is available. It's similar to the ambigrams of Scott Kim.
2007 World Sudoku Championship
The 2007 World Sudoku Championship is over. Thomas Snyder won, with Yuhei Kusui placing second. The instruction booklet has great descriptions for all manner of sudoku variations. Wei-Hwa wrote a blog item about the competition. Sudoku Puzzles from the competition preparations are available (34 pages!). Some other sudoku puzzles are maintained at Arthur Clarke's pages.
Tyler Hinman is Crossword Master ×3
For the 3rd time in a row, Tyler Hinman has won the American Crossword Puzzle Tournament.
Integer Distance Heptagon
Tobias Kreisel and Sascha Kurz have found a set of points, no three on a line and no four on a circle, so that all points are at integer distances from each other. It's an Integer Distance Heptagon. The existance of an integer heptagon has been a long-unsolved question. Is there an integer octagon?
Open Office 2.2 and Burrtools
I use Open Office, a spreadsheet - word processing - drawing program, all the time. They just came out with version 2.2. While I'm at it, Burrtools has another update.
The Hexagon on Saturn
Cassini Images Bizarre Hexagon on Saturn. That article from NASA reminded me of polygons in a bucket of water.(the same team wrote a paper). You can also compare hexagonal convection cells on flat surfaces.
Impossible Structures
Jean-Charles Meyrignac: Here are some of the impossible structures, though they appear to be impossible for construction but they are made possible.
Jeff Montanye: You may be interested in my site: [Very nice photographs of maze sculptures.
Puzzle Museum Curator
If you know puzzles really well, you can apply to be a curator. The Lilly Library at Indiana University, Bloomington, Indiana has just begun a search for a full time Curator of Puzzles to supervise the Slocum Puzzle Collection, which is being donated to the Library. The Slocum Room, which will house and display the puzzles, was opened August 2, 2006 and has a permanent display of the first group of about 500 puzzles. The remaining 29,500 puzzles, 5000 books and all the Slocum files will be donated to the Library over the next few years.
Lobster Point
George Sicherman: Rotary on a vertex is harder than it looks! (In other words, making a rotational oddity that works on a vertex is more difficult that the less constrained problem.)
Michael Trott's Quantum Views
Bohm's Quantum Mechanics may sound like a dry subject, but Michael Trott knows how to make almost any science topic beautiful. wrote about him in their article Quantum Views.
Material added 21 Mar 2007
I'm fascinated by what tiny programs can do. My new favorite is a 4K program called synchroplastikum, by calodox. It unspools into an intricate 1 minute movie with kick-ass music. The 19K image below does not do justice.
Puzzler Scott Weiss make Jeopardy history
The first 3-way tie in Jeopardy history occurred recently. A frequent maker of puzzle extravaganzas, Scott Weiss (National Puzzler League member Squonk) decided to be nice to both of his opponents. In game theoretic terms, he already knew he could beat them, so he had a choice between two known opponents, or two unknown opponents. More is mentioned at Heaneyland. A video of the closing event is at Youtube.This weekend, he'll be at the American Crossword Tournament, hosted by Will Shortz
Kakuro article by Will Shortz
In his NYT article "A Rush of Excitement", Will Shortz shows his puzzle historian chops by tracking down the first publication of Kakuro. "Invented by a Canadian building constructor, James E. Funk, it was first published in the United States in 1950 in Official Crossword Puzzles magazine under the name “cross sums.” Gradually, cross sums grew in popularity and became a regular feature in Dell puzzle publications. The publisher Nikoli picked it up in the 1980s, renamed it and spurred its international growth."
Nikoli article by Martin Fackler
In another NYT article, "Inside Japan's Puzzle Palace," the history of Nikoli is discussed. Virtually all of the current puzzle crazes were initially invented of nurtured by Nikoli, the leading publisher of puzzles in Japan.
Japan Puzzlers Article by Mariko Yasumoto
One of the reasons puzzles are so popular in Japan right now is their strong link to brain health. If you solve a puzzle every day, your brain will be much healthier. The Washington Post article "Aging Japanese Keep Their Minds Moving" discusses more of the research behind heightened puzzle popularity.
Lie Algebra E8
An MIT announcement claimed the calculation of a character table for Lie algebra E8. More information is at To do this, they computed Kazhdan-Lusztig-Vogan polynomials for the split real form of E8, which has 453,060 irreducible representations.
Crossing Number 7
I'm preparing an article about crossing numbers in cubic graphs.The first graph below is the Desargues graph, which has crossing number 6. If you look closely, you'll see that the edges cross over each other in six places. I found this particular embedding, and it looks really nice. Graphs 2-6 are smallest graphs with crossing number 7, found by Geoff Exoo. These embeddings here look terrible. Can anyone find really nice embeddings? Some of the programs you can use to move points around are Compass and Ruler, Geogebra, Geonext, Openeuclide, and jgraphed. It wouldn't surprise me at all if a 10-year old found an unbeatable embedding, and that became the standard. Send embeddings.
Bogusia Gierus: I developed a new math puzzle called Hexa-Trex. The object of the puzzle is to find a path through ALL the tiles to make a math equation. A tile can be used more than once, but no immediate backtracking is allowed . Two or three digit numbers can be made from individual digits. This simple concept makes for a challenging at times puzzle. I try to post a new puzzle each day on my website.
Material added 10 Mar 2007
The Crosshatch Puzzle
Richard Saunders, Jr.: I wanted to suggest a puzzle to you of my own. You need 16 squares of paper: 9-single diagonal (corner to corner), 3-two diagonals (intersecting, both corner to corner), 4-blank. Make one big square with five lines. Send Answer.
Searching for Kurchan Squares
The latest Al Zimmermann Programming Contest involves Kurchan Squares. These are multiplicative squares with consectutive numbers. The Kurchan square can be considered the one which is closest to being magic. There is also a page at Prime Puzzles.
The 11-Cell
In Discover Magazine, the latest Jaron's World column talks about the 11-cell, a four-dimensional self-dual abstract regular polytope. As a graph, it's K11, the complete graph on 11 vertices.
Flatland: The Movie
For more 2-dimensional fare, clips and trailers from Flatland: The Movie are available. Martin Sheen (West Wing), Kristen Bell (Veronica Mars), Tony Hale (Arrested Development), supply the some of the voices.
Tilings w/o Corners
Erich Friedman: Many cool tilings at the Math Magic page. Reid, Hamlyn, and Sicherman obviously have better tiling programs than I do.
Old Islamic Tilings
Some pentagonal tilings caused a large stir recently: "Medieval Muslims made stunning math breakthrough". It got mentioned on Slashdot. There is a mathematical discussion. The discussion seems to be unaware of Kepler's Monsters, another pentagonal tiling of that era. It's doubtful that they cared about or understood aperiodicity. Related are the Geometry Junkyard pages.
Daniel Tammet: Math Savant
60 Minutes has put together a page of clips and videos about Daniel Tammet, a noted math savant.
The Berlekamp-Buhler Puzzle Column
The free newsletter of MSRI (Mathematical Sciences Research Institute), The Emissary, has a regular puzzle column by Elwyn Berlekamp and Joe Buhler.
Problem-Solving book
A wonderful free problem-solving book is available at Most of the problems deal with number theory, as might be found in high-school math competitions.
Eric Weisstein talks at Cornell
And the Cornell Daily Sun wrote it up. Eric is the creator of MathWorld, of course.
3 · 23136255-1 is prime
A large Riesel prime, with 944108 digits, has been found. It's the 12th largest prime, #5 among the non-Mersenne primes, and the longest prime found so far in 2007. It could also be called a Thâbit ibn Kurrah prime.
Material added 19 February 2007
What is Good Mathematics?
Terrence Tao: Some personal thoughts and opinions on what "good quality mathematics" is, and whether one should try to define this term rigorously. As a case study, the story of Szemeredi's theorem is presented.
Oskar's Triangular wins Mobile Games award
Oskar van Deventer's Triangular game has won the top honors in the IMGA awards. Triangler is a massive collaborative geometric outdoor mobile interactive game. Two teams of 100 players play a two-hour match in a city or rural area. The object of the game is to enclose enemy players with 2000-meter equilateral triangles formed by you and your team buddies. [As a side question -- 7 people can make 6 unit triangles. 12 people can make 12 unit triangles. Are there solutions to most unit triangles with n points?]
Hexahex Cell Shifts
George Sicherman: I've put up some Hexahex Cell Shifts. I'm pretty sure that the last 2r3 can be improved, but no luck so far!
Logic Mazes in Numb3rs
Logic mazes will get a brief mention in the upcoming One Hour episode of Numb3rs. There might be an activity at weallusematheveryday. and are two places to blush up on logic mazes.
Tipover, River Crossing Column
Ivars Petersen has written a column about the difficulty of Tipover and River Crossing. Amusingly, I introduced both of these puzzles to Thinkfun. More amusingly, both of these puzzles are now available in a Spiderman version: Spiderman Tipover, and Spiderman City Crossing. Ivars also recently added new pictures of the Szilassi polyhedron.
Pentagonal Glider
Carter Bays has a page of unusual cellular automata. One of his discoveries is a slow pentagonal glider.
Computational Record for Euler's Gamma
NYU Freshman Alexander Yee managed to compute 116 million digits of Euler's constant = 0.577215665... His local paper wrote up the story. His accomplishment has been recorded at the Constant Records page.
Triple Seven Sudoku
Andrew Clarke: This one's quite a lot harder by hand. If we combine a 2x2 square, a domino and a single square we get a set of 21 pieces. The attached is based on one solution to a 7x21 rectangle. [Andrew also found a 10-clue puzzle based on a complete set.]
Burr Tools Updated
The excellent Burr Tools program has been updated.
Perplex City Solved
The Receda Cube has been found.
Eternity II and Global Warming
A sequel to the Eternity puzzle will be released on July 28, with a prize of 2 million dollars (press release). The previous winners were Alex Selby and Oliver Riordan, both visitors to mathpuzzle. I'm of a mixed mind, though, since Christopher Monckton has made himself a major global warming skeptic. Here's a link to the Global Warming summary that was recently released by the United Nations.
Material added 5 February 2007
Obliteration Game
Laszlo Kozma: Here's a simple game that I thought of, I never heared of it anywhere, but probably it is too simple not to have been invented already. If it exists already, and has a name, I'd be happy to learn about it. Two-player game, played on mxn rectangular checkered board, players alternate in putting a piece in a free square (just like in go). It is not allowed to put a piece in a square that has any of it's neighbours (out of the 8 (or 5 if on the margin)) occupied. If a player can't put a piece anywhere, he loses... I'd be interested to find out who has a winning strategy if anyone. For smaller boards it's trivial of course, but for larger boards it seems too much computation is needed to find a strategy. Puzzle: Who wins 4x4, 4x5, 4x6, 5x6, and 6x6? Send Answer.
Chessboard Attacks
Erich Friedman: Arrange 4 white knights and 4 black knights so that each knight attacks 3 pieces of the other color. This and many similar problems are at the latest Math Magic. If you can extend or improve any of these solutions, send them in to Erich.
M&M's Dark Puzzle
An interesting corporate puzzle has been used to promote M&M Dark. 50 movies are hidden in a spooky picture.
Excellent Snakes
The archive of matchstick snake results from the Al Zimmermann contest is now available. Hugo Pfoertner is maintaining a page of best zigzag paths. Here is the best known 30-degree snake that fits in a diameter 4 circle.
US Sudoku Team, UK Sudoku Qualifier
From The members of the 2007 US Sudoku Team have been announced: Grayson Holmes, Wei-Hwa Huang, Jonathan Rivet, Jim Schneider, Thomas Snyder, and Jason Zuffranieri. From Are you Britain's best Sudokulist? We're looking for team members for the World Sudoku Championship in Prague in late March, and the qualifying competition is being held on 8-10 February.
New Amazing Tilings
Joseph S. Myers: I've now added results on polymorphic tiles, including three new 10-morphic tiles and an 11-morphic tile.
Solution for 25 Squares
Richard Korf: Optimal Rectangle Packing: New Results. He solved the 25 squares packing problem. This is sequence A081287.
Hyperbolic Dominos
Margenstern Maurice: ( About the domino problem in the hyperbolic plane, a new solution.
Double Du-Sum-Oh
Bob Harris: I've posted a small batch of double-5, double-6, and double-7 on In these puzzles you have two overlapping Du-Sum-Ohs (Squiggly Sudokus).
Mental Stimulation Combats Alzheimers
A new study shows that modest mental stimulation goes a long way towards warding off Alzheimers.
Monkey Nut Puzzle
At Grand Illusions, one of the oldest puzzles is now on sale. The Monkey Puzzle Nut is a naturally occurring sphere that breaks up into 7 irregularly shaped nuts.
Puzzle Blogs
A few puzzle blogs I like are Passion for Puzzles, Indexed, and
New Taxicab Numbers
Christian Boyer: I've updated my Taxicab and Cabtaxi page. Because several persons ask me the intermediate values, the .TXT files with the full list of the upper bound values and their decompositions in sums (or differences) of two cubes are now downloadable at the end.
Material added 21 January 2007
Double-6 Sudoku
Andrew Clarke (Poly Pages): If we add two monominoes to a 2x2 square then we get a one-sided set with 12 pieces which can form a 6x12 rectangle. These can be made into sudoku puzzles. There is a fair amount of crossover between the two halves and they make reasonably tricky manual problems. Here's one example with only 11 clues and, surprisingly, half the peices have no clue in them. I have done this by hand - tricky but possible.
Octiamond Cell Shifts
Col. George Sicherman: I've added a page for Octiamond Cell Shifts. Additions and improvements to these and the smaller polyiamonds are welcome! [An earlier page dealt with Polyiamond cell shifts.]
Largest Twin Primes found
Eric Vautier: I didn't believe it when I saw something in the output file... but it was true : 2003663613*2^195000-1 is prime! 2003663613*2^195000+1 is prime! [An official announcement is at, there is also a slashdot discussion, and a discussion.]
Largest Prime Progression found
On Jan 18, 2007, Jaroslaw Wroblewski, with help with the network at the Mathematical Institute of Wroclaw, became the first person to find an AP24. For k from 0 to 23, 468395662504823 + 45872132836530k is a prime number. The Prime Arithmetic Progression site by Jens Kruse Andersen has more information.
Get Off the Earth
A gorgeous rendition of the classic Get Off the Earth puzzle has been printed by
The Homicidal Chauffer Problem
A mainstay of TV and movies, a car (high speed, low manueverabilty), tries to run over a pedestrian (low speed, high manueverability. Can the pedestrian survive? This turns out to be the Homicidal Chauffer problem. There is a history (ppt) of the problem available.
Tough Puzzles Magazine Discontinued
Nick Deller: Tough Puzzles has suffered a slump in sales over recent months, so much so that we've been making a significant loss on every issue. As a result, Puzzler Media took the hard but, I think, correct decision last week that the magazine is to cease production with immediate effect. The recently published Issue 263 will be the last one to reach the printed page. I'll be working on some brand new titles for a while - probably nothing that will especially tickle the tastebuds of the Tough aficionados, but I think after 30 months and 10 issues of Tough I've probably earned a bit of time working with the more straightforward stuff! It's a completely different challenge personally, and one that I'm looking forward to getting my teeth into.
Puzzle Auction
At, a wide variety of handmade puzzles are available for purchase or auction. There is also a page of new puzzles available.
MIT Mystery Hunt
The 2007 MIT Mystery Hunt was won by the team of Dr. Awkward. The puzzles are available online.
Material added 7 January 2007
US Sudoku Team Qualifier
The 2nd World Sudoku Championship will be held in Prague, Czech Republic, between March 28 and April 1, 2007. The US Team looks to be very strong this year, including Thomas Snyder and Wei-Hwa Huang, who placed second and third respectively in last year's WSC. If you are a US citizen and interested in joining the US Team, then go to the registration page for more information, practice, and the qualifying test. Entries must be submitted by January 15. [Lots of good Sudoku puzzles there.]
Happy 2007
Erich Friedman: Q: Using the digits 3, 4, 5, 6, 7 each once, and the usual + - * / ^ ( ) and concatenation, make the new year 2007. There are 2 solutions. Hover for Answers.
Geocaching Puzzles
Chris Lusby Taylor: Have you come across Geocaching? It's a leisure activity that uses GPS receivers to locate caches that people have hidden for this purpose. When you find a cache you write an entry in its log book and later do the same on a Web site. Many caches exist simply to challenge you to find a small container in the middle of, say, a large wood. The precise latitude and longitude will be clearly stated on the geocaching Web site But a few involve solving puzzles to get the coordinates. Some of these may be of interest to you.

Under my alter ego of Mr Tumnus, I have created a number of puzzle caches, one involving a modified Sudoku ( ) where the latitude and longitude were hidden in the grid, and another a puzzle of the "Who owns the zebra" style. This one has proved rather tricky to solve. To extract the purely mathematical from this puzzle, and distill it further, try this:

The only cities in Pentland are, from North to South, Naples, Otranto, Pisa, Rome and Sienna. All are on different longitudes and each has a direct road to the other four. A new salesman set off from home four weeks ago. He works Monday to Friday in a different city each day, travelling in the evenings. On Monday evenings he has always travelled eastwards (that's not due east, but definitely easterly as opposed to westerly). Similarly on Tuesday he's gone northwards, on Wednesday westwards and finally on Thursday southwards. He doesn't travel any more until the next Monday evening. By now, he's driven all ten roads that link the five cities.
It is Monday. He's spent each of the last four weekends in a different city, miles from home. Where is home?
Cake Cutting, part 2
Last week, we saw that a 6x6 cake with corner missing could be divided into 7 equal pieces with 3 cuts. Below, a 10x10 cake with a corner missing is divided into 11 pieces with 4 cuts (solution by Chris Lusby Taylor, also solved by Warren Phillips). Can you do it with a 9x9 cake with 4 corners missing? Serhiy Grabarchuk was the first solver of this problem. None of the cuts cross themselves, and each crosses the other cuts exactly once.
Happy 2007
Marek Penszko: Happy 2 + 7 + 27 + 72 + 207 + 270 + 702 + 720.
Pi and e on a blind date
Lyman Hurd: "Just in case you've wanted an icosahedral pecan pie," Now where else would I ever find a website with a lead in like that :-). The world clearly divides into those of us who think this is a cool idea and those other people! I meant to pass this link along. My daughter forwarded it to me... Pi and e on a blind date. Happy New Year. By the way, I got the Gordian Knot puzzle for Christmas based on your recommendation and my daughter and I have both been enjoying playing with it.
Spreadsheet competition
Dave Millar: I'm holding a competition to create the best page design and maze generator in a spreadsheet application. There are many methods of doing this and they all have varying results. Maybe you can enter and come up with a new one! Details can be found at The Griddle or specifically at Maze Contest. The deadline is January 31st. I hope you all will give it a try!
Mathophobia Leads to Stabbing
Chicago Sun-Times: A 51-year-old Malcolm X College instructor who was demonstrating a math problem on her blackboard Tuesday was stabbed in the back by a student who apparently became frustrated with the exercise, authorities said. Full Story.
Material added 2 January 2007
Oskar's Nutcase
A limited edition Hamayana Cast puzzle by Oskar van Deventer is available - Cast Nutcase ( Oskar has also recently won an award for his 100-player team game Triangler, where you and two teammates capture as many opponents as possible in a triangle.
Daedalus Maze Program on Numb3rs
The excellent maze program Daedalus was recently featured on Numb3rs. Walter Pullen,the programmer, did a great write-up of his network debut.
Cake Cutting
A cake with a corner missing can be cut into 7 unequally sized pieces with 3 cuts, following the gridlines. None of the cuts cross themselves, and each crosses the other cuts exactly once. Following these rules, cut the cake into 7 equally sized pieces with 3 cuts. Answers and Solvers. There are two solutions, so try to solve it before looking at the solution. Will Shortz mentioned "Beautiful puzzle. I've never seen anything like it before."
Pecan Pie-cosahedron
Just in case you've wanted an icosahedral pecan pie, full instructions are given at
Xmas Trees from Serhiy
Serhiy Grabarchuk: We wish you a Nice Holiday Season and a Happy and Peaceful New Year! Attached please find my Holiday Puzzle Greetings. Happy Puzzling!
Square+Two Dominoes Sudoku
Andrew Clarke has been working on a sudoku puzzle based on the 40 shapes obtainable with a square and 2 dominoes.
BBC MindGames
For Christmas, I got a copy of BBC MindGames Magazine. It's excellent. Currently, it's tricky to subscribe to -- I got it only by giving myself a gift subscription, then listing a fake UK billing address. After that, I could finally put in my credit card info. It's a lot of hoops, and the subscription website shouldn't be so broken, but the magazine is top-notch.
Using 1-9
Erich Friedman: What is the only positive integer n with the property that together 4n and 5n use each digit 1-9 exactly once? Too easy to solve with a computer, so try to solve it by hand!
Happy 2007 puzzle
2007 is divisible by 9. If a 1 is added onto the end, for 20071, the number is prime. What can be added to the end of 20071, to obtain another prime? What delights can be found beyond? Send Answer.
Piano-hinged dissections
Greg Frederickson: I am excited to announce the publication of my new book, "Piano-Hinged Dissections: Time to Fold!", published by the firm of A K Peters. The book explores geometric dissections in which the pieces are connected by long, narrow hinges that run along shared edges---like the hinge on a grand piano which connects the lid to the sound box. Such hinges allow a type of folding motion similar to that of origami, the art of paper folding.
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