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Material added 25 December 2007 (Merry Christmas)
Church Bells and Kneser Graphs
I recently made a math demo for Kneser Graphs. These are basically pretty graphs based on dominoes, but I was long stymied on how to draw these nicely until Doug West gave me the hint "permutations". One permutation I found was 13527486, so I looked that up, and found that this permutation is heavily used in church bell ringing. For example, Matthew Sorrell's "Mathematics of Church Bell Ringing" (a fascinating paper) lists this permutation as Plain Bob. In bell ringing, eight bells are rung in pairs, with every pair represented. Same as double-7 dominoes without the doubles.
$77 Dollars for the 77-graph
One graph I've had no luck in drawing nicely is the 77-graph, also called the M22 Graph, due to connections to Mathieu Group M22. The 77 graph is linked with the Golay code, Steiner systems, and distance-regular graphs. In Mathematica, getting a set of vertices is as simple as StringJoin/@ ((Drop[#1,1]&) /@ With[ {poly = x^11+x^9+x^7+x^6+x^5+x+1}, Select[ Union[Select[ (Flatten[ Position[ CoefficientList[#1, x], 1]]&) /@ NestList[ PolynomialMod[poly*#1, x^23-1, Modulus->2]&, poly, 2047], Length[#1]==7 & ]], First[#1]==1&]]-1 /. Thread[ Range[22] -> Characters[ "abcdefghijklmnopqrstuv" ]]) , with the output {abcilu abdfrs abejop abgmnq abhktv acdghp aceqrv acfjnt ackmos ademtu adinov adjklq aefgik aehlns afhoqu aflmpv agjsuv aglort ahijmr aipqst aknpru bcdekn bcfgov bchjqs bcmprt bdgijt bdhlmo bdpquv beflqt beghru beimsv bfhinp bfjkmu bgklps bikoqr bjlnrv bnostu cdfimq cdjoru cdlstv cefpsu cegjlm cehiot cfhklr cginrs cgkqtu chmnuv cijkpv clnopq defhjv degoqs deilpr dfglnu dfkopt dgkmrv dhiksu dhnqrt djmnps efmnor egnptv ehkmpq eijnqu ejkrst eklouv fghmst fgjpqr fijlos firtuv fknqsv ghilqv ghjkno gimopu hjlptu hoprsv iklmnt jmoqtv lmqrsu}. Two vertices are connected if they share no letters. As a second contest, I'll give $56 for the first really nice drawing of the Gewirtz graph. The vertices of the Gewirtz graph are the 56 words lacking "a" (or any other letter), and the edges are again between words sharing no letters. Send pictures. Some examples of nice graph drawings are at the entry Dyck graph.
Cast Ring and Other Puzzles
The Nob Yoshigahara Puzzle Design Competition had many excellent entries. I've gotten my hands on some of them, such as Cast Loop and Duck Case.
The XKCD Problem
At there is a cartoon about nerd sniping, involving a grid of resistors. The problem is one of the 20 Google Problems that came out a few years ago, problem #10.
Cornfield Mazes
Bob Abbott writes: I just added something to my site that I think is the best writing I've done about cornfield and other large mazes. It is Mazes We Visited Summer, 2007. It starts out like a journal, but then I get into reviews (good and bad, but mostly bad) of various mazes. I explain what they do right and what they do wrong, and I give my own opinion of what a maze should be. I have a brief history of the rise and fall of wooden fence mazes, and I think I have a good explanation of why they disappeared. I also warn that cornfield mazes could suffer the same fate. Also, there is a description of an implementation of Ed Pegg's UP-DOWN multi-state maze.
Kobon Triangle Problem 17 Solved
Johannes Bader has solved the 17-line Kobon Triangle problem. The problem: What is the maximum number of triangles that can be bounded by 17 lines? Answer. More details at OEIS A006066, MathWorld Kobon, and Wikipedia Kobon.
Thermal Resistance, Christmas Tree Lane
With a piece of Mathematica code, I found the longest well-mixed transposals in Wikipedia. Without mixing, there are many cases where word order makes multiple entries. The longest well-mixed transposals are:
Patron client relationship,   Phil Spector International
Ashland County Courthouse,   Odontorhynchus aculeatus
Portuguese Marine Corps,   Singapore Supreme Court
After War Mobile Units,   Blue Martini Software
Human genetic history,   Youth Training Scheme
Attiar Hindu College,   Gautier de Chatillon
Metropolitan Anthony,   National Poetry Month
Domine Non Es Dignus,   Dungeon Dimensions
Bisoprolol fumarate,   Super Mario Football
Electron irradiation, Trilinear coordinate
One more as a puzzle. Click on the links for the answers. First phrase: "a point where a population can no longer sustain itself." Second phrase: "Senate Bill 1047, responsible for new golden dollars."
The Branko Grunbaum Lectures on Configurations are very interesting. One example of a configuration is below, 54 lines, each through 4 points, and 54 points, each coincident with 4 lines. (Powerpoint files can be viewed with OpenOffice)
Configuration 54_4
World Clock
Dick Saunders Jr.: You might like Peter Russell's World Clock. Some other news items from the year: 307-digit number factored and the E8 structure.
Christmas Wreathes
Erich Friedman: Some Christmas wreaths for you, made from equal 9-gons.
Xmas Sudoku
Andrew Clarke: I thought you might like this one. The conditions are Green diagonals contain numbers 1 to 8 Red diagonals contain numbers 1 to 7 Adjoining squares do not contain the same number.
xmas sudoku
2008 Puzzle
The number 2008 can be expressed as the sum of 3 positive cubes in exactly 2 different ways. One way is 23 + 103 + 103 = 2008. What is the other way of expressing 2008 as the sum of 3 positive cubes?
Nauru graph
David Eppstein: You once suggested that F24 needs a name. I've decided that it should be called the "Nauru graph," with reasoning explained in my recent post.
Material added 18 November 2007
Martin Gardner Interview
Donald Simanek (who has an excellent science site) interviewed Martin Gardner in the latest issue of Make Magazine. Among other things, Martin levitates the King of Hearts.
Various nice programs
Some programs I've recently updated: Winamp 5.5 (music program), Irfanview 4.10 (image processing), Yahoo Messenger 9, Crossword Compiler 8, OpenOffice 2.3, Lavasoft Ad-Aware (spyware detector),7-Zip (compression), Adobe CS3, Firefox 2 (browser), Daedalus 2.1 (maze generation).
Fore and Aft
Yang Chao: I recently wrote a little program "Toads and Frogs Puzzle", which is a generalization of Sam Loyd's classic puzzle "fore and aft". With this little tool, it is convenient to explore puzzles of this type. The "fore and aft" type puzzle resembles the sliding blocks puzzle with extra permission that a block can jump over another, so it is interesting to play with.
Bryce Herdt: After seeing the hexagonal Black Box on your site, I decided to push my hexagonal Magnets-like puzzle, called Nucleus. The groups of three circles are either protons or neutrons, the black circle is a gluon, and the uncolored circles are quarks. Quarks are either red, green, or blue, and though in neutrons they cannot be distinguished, same-colored quarks never touch among protons. Of course, each proton consists of one red, one green, and one blue quark. Given the numbers of distinguishable quarks in some lines, determine the placements of all the protons.
Rube Goldberg Shopping Site
The funniest Rube Goldberg device I've ever seen is at the Hema shopping site.
Times Square Ball
The new Times Square ball that will be dropped for the new years has a very mathematical shape. The video showing the half-ton ball in action is well worth a watch.
Times Square Ball
The Rolling Ball Web
A compendium of rolling ball sculptures and clocks is available at the Rolling Ball Web. It seems to need an update.
Sums of Three Cubes
The list of unsolved values x under 500 (not of the form 9n±4) for x=a3+b3+c3 is down to 33 42 74 114 165 390. Results are at the bottom of Joerg Jahnel's Research page. Some history is at Daniel Bernstein's page, and in MathWorld's Cubic Number entry. For example, for x=52, one answer for a,b,c is 60702901317, 23961292454, and -61922712865.
Sums of 4 Quartics
More solutions to a4=b4+c4+d4 are known. A full list is at the bottom of One example is 8738221214 = 7693212804 + 6067108714 + 5584244404. Recent discoveries found with Robert Gerbicz's program.
Forty years of LOGO
Slashdot had a discussion of the 40 year Logo anniversity.
Morpion Solitaire - Update 2
Posted earlier: In Morpion, starting with a 36-point cross shape, you get 1 point for each additional 5-in-a-row. A score of 79 points in Morpion was recently acheived. UPDATE: Much higher scores are listed at UPDATE 2, from Michael Quist: You recently posted results for Morpion Solitaire. Actually, the lower and higher records are for two slightly different variants of Morpion Solitaire: in one variant ("disjoint"), two lines in the same direction may not share an endpoint; in the other ("touching"), they may. (The lower score, of course, is for the disjoint variant.) Demaine et al. wrote a Morpion paper in which they define these and other variants and prove upper and lower bounds for record scores.
Numb3rs and Chain Factor
You can see various math write-ups for the Numb3rs TV show at One recent episode, Primacy, had an alternate reality game as a subplot. Mentioned in the course of the episode was Chain Factor, which is an alternate reality game, as well as a very nice puzzle game. There is a Chain Factor Wiki. An odd Chain Factor ad is on you-tube. More exploration is at
Lens sequences
The patterns of some of the circles seen in circle geometry are seen in Lens Sequences by Jerzy Kocik.
Tom Snyder wins Sudoku Championship
A write-up of the big sudoku match is at A nice sudoku column at is also available.
Four Queens and Two Bishops
Peter Grabarchuk: I was inspired by puzzle The Four Queens by Martin Gardner and have made a related puzzle. Arrange 4 queens and 2 bishops on a 10x10 board so that every square is either attacked or occupied. Also, I'm happy to present you my personal website, launched past week.
Jagged Square Sudoku
Andrew Clarke: I've created some jagged square sudoku.
Perfect Squared Rectangle, Ratio 5
Brian Trial: Enclosed is an order 60 SPSR 705x3525 with an integer aspect ratio of 5. [Many similar results are at] Picture.
Material added 3 November 2007
Hexagonal Black Box
Eric Solomon: Franjos released BLACK BOX + at Essen. This contains the original game and the new hexagonal version which is more demanding. The set also contains a book of puzzles with solutions. The game is obtainable in the USA from I attach one difficult puzzle. The solution is, of course, unique.
Periodic Table Releaunched
Theo Gray has made the ultimate Periodic Table website, again. Some of the new features are element picture galleries and decay chains.
Eleusis Express
In the June 1959 Scientific American, Martin Gardner presented Eleusis, the card game that uses inductive reasoning. Later, in October 1977, he presented an improved and expanded version of the game. Now there is a third version—called Eleusis Express. It is smaller and faster than the full version of Eleusis, and it has the possibility of being a fun, social game. You can read about it at
Neat Demonstrations
Many of the recently added Mathematica demonstrations are worth a look. Some of my recent favorites are Permafrost, Recursive Sequence, Moving a Couch, Box Packing, and Lines on a Cubic Surface. As a vaguely related item, what is this picture? (hint)
where is this
Levitating Lamps
Crealev is a company that makes such items as levitating lamps and Buddhas.
Martin Gardner Letter to Santa, and other Youtube movies
Dana Richards talk: Martin Gardner: The Tulsa Years is on Youtube. Unrelated article: dumping 10 tons of sodium in a lake. The yahoo video 100 Movies, 100 Quotes, 100 Numbers provides clips and movie quotes for all the numbers 100 to 1. Another movie is 3D Game of Life (there is also a program).
Seventeen or Bust Scores Again
17orBust: 33661•2^7031232+1 is prime! The double checking effort uncovered this new prime showing once again why it is so important to conduct these re-testing efforts. Most re-tests conclusively verify the original result but if the first test had even a single memory error during the computation, there's a chance a prime could have been missed. That's what likely happened here. The discoverer, Sturle Sunde is a giant in the prime searching world. He is the #2 overall contributor to SB and also the #4 all-time contributor to GIMPS! [Now the 10th largest known prime.]
Why So Serious?
Batman's nemesis, The Joker, has launched various puzzle-related sites. Why So Serious is a US-wide scavenger hunt (status page). It leads to Rory's Death Kiss.
Rubik's Grid
Toby Gottfried: I may not be the first to have had this idea. Rubik's Grid. 5x5 grid of numbers 1-5 in 5 colors Object: make each line read 1 2 3 4 5 in same color (or each column, or one of each color in each line, or ....) Available moves: swapping two adjacent pairs of numbers.
Ancient grid pattern
Discovery Channel: Deep in the heart of northern Syria, close to the banks of the Euphrates River, archaeologists have uncovered a series of startling 11,000-year-old wall paintings and artifacts. [Square grid, with brown, black, and white colored squares. Related puzzle. What word relating to squares has the letters of SYRIA, in order?]
Material added 24 October 2007
Alex Smith Proves the 2,3 Turing Machine is Universal
As reported at New Scientist, Nature, and at WolframScience, 20-year-old student Alex Smith has proven that a particular 2,3 Turing machine is a universal computer, as first conjectured by Stephen Wolfram. For his impressive proof, Alex collects a $25,000 prize.
Material added 21 October 2007
Euphoric Pentahexes
Col. George Sicherman: A euphoric polyform is compatible with all polyforms of some order in the same class. The Five Euphoric Pentahexes are each compatible with all 82 hexahexes. [Wow. Just about all the careful discoveries at Polyform Curiousities are incredible.]
XYZ Graphs
David Eppstein wrote a paper about xyz graphs. He found that the Dyck graph fits in the side-4 cube. Also, he found excellent embeddings of other Foster graphs.
foster graphs
The excellent paper Overhang by Mike Paterson and Uri Zwick describes the optimal way to place books to overhang from an edge.
Puzzles for sale
If you're looking for place to get puzzles, has an excellent selection. In addition to the Cast Puzzle line, they just added a line of puzzle houses. Kadon Enterprises has a wide selection of beautiful puzzles. Bits and Pieces also has an excellent selection, with such items as Doug Engel's Catch of the Day and Fred Szatkowski' Elegant Map.
Elegant Cast Map
George Miller article
Oskar van Deventer pointed me to a great article about George Miller's puzzle prototyping. He has a few new items at
Hour Maze
Mike Reilly: We just put up our interactive site: . [Ed - Fairly nice logic puzzles.]
What is Game Theory?
A great slideshow presentation, Everything You Always Wanted to Know About Game Theory, by Dan Garcia, David Ginat, and Peter Henderson, covers the Combinatorial, Computational, and Economic aspects of game theory.
Aggregation Pictures
Andy Lomas has many beautiful pictures of million particle aggregations.
Three-colored cubes
Peter Esser: With three colors you get 59 different cubes. Discarding the three cubes with only one color gives 54 cubes allowing for a 3x3x6 box with same colors at opposite faces. [Peter's Polyform page is excellent.]
three color cubes
Order 3 Projective Plane
Bob Harris: Here's my attempt at drawing the projective plane.  It doesn't quite have the symmetry that your drawing does.  Might look more appealing if the central 3x3 square were rotated 22.5 deg ccw or 67.5 deg cw.  And/or the 3C64 line could be C643 to balance C17B (ditto for 0547 relative to 5618). [Bob runs the excellent logic puzzle site]
Projective Plane 3
Material added 22 September 2007
Numb3rs Site and Trip
I'll be at the Numb3rs Season Premiere on Monday. The broadcast premiere in the US is Friday. First time I've ever been to anything like this. I helped with the new site, particularly the page of MathPlayer demonstrations. There's also a link at
Word Search
Place as many words as possible into a 15x15 grid for the Words Search Al Zimmermann contest. A total of $400 in prizes.
77 Moves Enough for Order-4 Rubik's Cube
Jean-Charles Meyrignac: That's the new benchmark. Brusce Norskog has the analysis.
Projective Plane
I recently made a cool picture of an order-3 projective plane. I'm still trying to figure out the best way to draw it - the current usage of 6 is a flaw.
George Miller wins prize for puzzle-making video
From, George Miller won an award for his video how "3D printing revolutionized his puzzle business" ( George explains: "In one occasion, my friend Oskar from Holland emailed me a design, which my Santa Claus machine printed overnight, so I could ship it to his customer in New York the next morning". George and Oskar have several new designs to be amazed by.
Material added 16 September 2007
Flatland: The Competing Versions
There are two versions of Edwin Abbott's Flatland: The Book coming out soon. The first is a 95-minute version, Flatland: The Film, put out by Ladd Ehlinger, Jr. I bought a copy ($22 at Amazon) and watched it, and will give it 3 stars. Very faithful to the original book, with excellent visuals and good math. The voice acting was excellent, even though most of the actors are unknowns. Looking down on the 2-D creatures, their heartbeat and actual thoughts can be seen. On the downside, at the beginning, there is frequent "silent film" style title narration that tries to help explain things. Various reviews are at imdb and amazon.
Then there is the 30-minute Flatland: The Movie. It stars Martin Sheen and Kirsten Bell, and cannot yet be purchased ($30). The whole world seems heavily influenced by fractals. I haven't seen the film yet, but I have watched the trailer. This production obviously had a bigger budget. One review is at imdb.
Toblerone hidden animal
What animal is hidden within the mountain on Toblerone chocolates? The answer is here.
Inverted Pendulum
This You-tube video illustrates that a robot can be programmed to balance a rod.
2007 Nob Yoshigahara Puzzle Design Competition
This year's batch of beautiful puzzles for the yearly international competition are now available at 2007 Puzzle Design Competition Entries.
Nob Yoshigahara puzzle competition
The Grand Vizier
A puzzle from 2002 was The Grand Vizier, by Pavel Curtis, based on Penrose tiles. A very pretty puzzle. He has a stash of copies left, if anyone would like to buy one.
grand vizier
Largest Consecutive Factorizations
Can you completely factor 447295839 · 27061 − 3, and the next four numbers? Donovan Johnson managed it, setting the record for 5 completely factored consecutive numbers. Jens Kruse Andersen is maintaining a Consecutive Factorizations page, which has a lot of clever ideas. Virtually all of the records are from the past 2 months.
Material added 19 August 2007
Disdyakis - A Mathematical Tungsten Carbide Ring
I've lately been fascinated with Tungsten Carbide rings. They are as heavy as gold, almost indestructible, almost unscratchable, and inexpensive. One of the best sources is Trueman Jewelry. I bought 30 different tungsten carbide rings from them for around $600. I was very pleased with their quality. Now, I'm making a custom order, based on the Disdyakis Triacontahedron. I've recoved caps, so that each ring has 60 triangles. If you'd like to buy one, I'll need your ring size, address, and $20 (cost of shipping included. Add $5 for overseas shipping). You can pay me via the Paypal link to the right. The money can wait, but I'll need your ring size by September 5th. Any jeweler can help you find your ring size. Sometime in November, I'll get the 80 or so Disdyakis rings, and ship them all out. Interested? Send me your ring size.
Circle Coverings
I've added a number of puzzle-related MathPlayer demoes to the Wolfram Demonstrations site. In particular, Angles in a Cube, The Circle Covering Puzzle, and Sudoku Game. Of more general recreational math interest are Pascal's Mystic Hexagon, Halving a Triangle, Multiple Reflections of a Superball, The Eye-Pentagon Construction, and The Arbelos. And thousands of other math demos.
Social Golfers
I've written a column about the Social Golfer Problem. I even include a puzzle this time around. A less obvious puzzle is the minimum number of clues to give a unique answer.
  Sixteen social golfers (A to P) play in foursomes over five days. After the first day, they pick out the tee-times on days where their schedules are tight. Fill out the rest so the each golfer plays once each day, and plays exactly once with every other golfer.
     day1 day2 day3 day4 day5
9am  ABCD GIP  M    IH   G
1pm  EFGH N    FOD  EJ   JOB
5pm  MNOP DK   NK   B    CF
7-stacked Movie Crossword
At Roger Ebert's site, there is a nice 7-stacked (7 15-letter entries) movie-themed crossword.
John Conway's M13 Puzzle
John Conway developed a beautiful sliding puzzle a few years back. Consider 13 lines going throught 13 points: {{0,1,3,9}, {1,2,4,10}, {2,3,5,11}, {3,4,6,12}, {4,5,7,0}, {5,6,8,1}, {6,7,9,2}, {7,8,10,3}, {8,9,11,4}, {9,10,12,5}, {10,11,0,6}, {11,12,1,7}, {12,0,2,8}}. Put numbered counters on 1-12. Now, shift any digit to the blank spot, and swap the other two digits on that line. This simple process underlies deep group theory. An M13 applet is available, for trying the puzzle. This is basically a puzzle on the ({0,1,3,9}+n mod 13) switching system. The {1,2,5,15,17}-21 might make a similarly nice puzzle, with 20 counters. Move one to the empty spot, then rotate the other three.
Multiples of single digits
The number 24 is the product of single digits, in two different ways: 4×6 or 3×8. 3256 has consecutive pairs 12, 24, 45, and each is the product of single digits (4×8, 5×5, and 7×8). Arrange the digits of 1-9 so that every consecutive pair is the product of single digits.
iPhone Blending
Is it possible to blend an iPhone? The people at find out.
Maximum Overhang
A classic problem asks for the maximum overhang of dominoes over the edge of a table. The paper Maximum Overhang gives a number of new solutions.
Self-Referential Phone Numbers
376-9767 is an interesting phone number. If you add pairs in sequence, 376, 9767, 10143, 19910, 30053, 49963, 80016, 129979, 209995, 339974, 549969, 889943, 1439912, 2329855, 3769767 -- you eventually get the phone number back. There are 3 other 7-digit phone numbers with this property.
Self-Referential Sentences
A lot of self-referential sentences are at This sentence contains three a's, three c's, two d's, twenty seven e's, four f's, two g's, ten h's, eight i's, thirteen n's, six o's, ten r's, twenty five s's, twenty three t's, three u's, three v's, six w's, three x's, and four y's. Many others are listed.
Missing Number Sudoku
Andrew Clarke, master polyformist, has put together a number of Polyform Sudoku and Missing Number Sudoku puzzles.
3 Million Visitors
Dick Saunders Jr.: What date will you turn over 3 Million Visitors? I will guess July 4, 2007. [Ed - Hmmm... about 2993900 right now. And I'm back from a week long vacation. Jean-Charles Meyrignac: As of 8 August, you had 3,004,441 visitors.]
Material added 29 July 2007
New Rolling Cube Puzzle
Robert Abbott: There have been some new developments in Rolling Cube mazes and I thought you'd want to write about them in I added a description of these developments on my rolling cube page. At an up-coming conference, there will be a paper (which can be downloaded from my site) on the computational complexity of rolling cube puzzles. This paper also includes a revolutionary new rolling cube maze, and this maze is also on my site. [Bob's Sliding Door Maze has also been reposted.]
Eternity II Puzzle
The 2 million dollar Eternity II puzzle has been released. The Yahoo Eternity II Group has lots of mathematical discussion about it. It is essentially an edge-matching puzzle, long championed by Kadon Enterprises. Unlike a Kadon creation, though, the Eternity II puzzle was designed to be fantastically difficult to solve. The previous Eternity puzzle was solved by readers of this website -- but they had to create new solving methods to conquer it. At, a distributed solving program by Dave Clark is available.
Moon and Sixpence
Colonel Sicherman has added his excellent cardgame Moon and Sixpence to his site. Also, to his Polyform Curiousities page, he has added Pentapent Oddities. He gives one as a puzzle (solution on his site) -- make a symmetric figure from the 3 pieces below.
Humans Beat Computers at Poker. Checkers a Draw.
The results of the Man-Machine Poker Championship are in. In the story write-up (NYT, Herald Tribune), humans win. In related news, the Chinook system, under lead programmer Jonathan Schaeffer, has finished a complete analysis of Checkers. An earlier version of Chinook was beaten by Dr Marion Tinsley, considered the world's greatest checkers player.
Ultimate Search for Bourne
Like the DaVinci code last summer, Google is assisting with a puzzle hunt for a movie. This year, it's The Ultimate Search for Bourne. Another Google Puzzle Hunt is the Google Conglomerate Board of Directors. More info on that at Wei-Hwa's journal.
Sam Loyd site
Tony Fatseas has put together a beautiful site devoted to Sam Loyd. The Encyclopedia of Puzzles is there, and high-quality reprints of some of Sam's best-known puzzles are there. Elsewhere, you can also now buy a reprint of Loyd's Encyclopedia, and Jerry Slocum's analysis of the true history of both the 15 Puzzle and Tangrams.
Puzzleup 2007
Emrehan Halici's puzzle competition at will begin on August 1.
New Wooden Puzzles
Tom Lensch, one of the best puzzle craftsmen, and who recently released a book on puzzle crafting, has now started his own website, There are also some new puzzles available at Vin&Co Puzzles is another new wooden puzzle site.
1111111 ..... 111111 (270343 1's) is a Probable Prime
Maksym Voznyy and Anton Budnyy report (on NMBRTHRY) the probable prime repunit number R(270343) (consisting of 270343 1s, base 10). Known repunit primes are R(2), R(19), R(23), R(317), and R(1031). Known probable prime repunits are R(49081), R(86453), and R(109297).
Curlicue Fractal, Unilluminable Room, and other Demos
I've added demoes for the Curlicue Fractal and Penrose's Unilluminable Room to the Wolfram Demonstration Project.
The Truchet Game
Dave Dyer: I think you might like Cameron Browne's new game, Truchet.   I'm in the process of adding it to, so it will be playable online sometime soon.
3 Million Visitors
Dick Saunders Jr.: What date will you turn over 3 Million Visitors? I will guess July 4, 2007. [Ed - Hmmm... about 2993900 right now. And I'm back from a week long vacation.]
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.]
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