Material added 17 December 2006
 When Chesspieces Attack
 Bernd Rennhak reminded me of Erich Friedman's Attacking Chess Pieces Math Magic of the Month. Erich has had many great investigations lately, including Polyline compatibility, building trees, polyform addition, and triangulations. Bernd also did his own analysis.
 W and H oddity Improvements
 George Sicherman: Tonight I shrank the H pentahex oddity from 59 to 29 tiles and the W pentahex oddity from 149 to 41. I cheated a littleI used a computer!

 Hofstadter Butterflies of Bilayer Graphene
 A sheet of graphene can have fascinating patterns.
 Expandible Circular Tables
 Fletcher Capstan Tables have the amazing ability to double in size with a 3 second spin. The videos are well worth a look.
 Christmas Letters
 Jed Martinez: The ten fourlettered words below contain four different
things associated with Christmas. The first three of these things can be found
by taking one letter from each fourlettered word, and reading it from left
to right. Circle one letter from each word, to spell out the first thing 
this way, you won't make the mistake of reusing said letters, in order to determine
what the other two things are. (NOTE: The first three things associated with
Christmas each consists of two or three words. It is up to you to figure out
how many letters there are in each word.)
When you have accomplished this task, there will be ten letters left (one from each word) without a circle. Rearrange these ten letters to spell out the fourth Christmasrelated thing (which is a oneword answer). Good luck... and "Merry Christmas"! 
SONS HALO DONE TAIL GRAY INCH ROIL GAIT HUED SECT
 Loop the Loop
 David Millar: I have some sudokuesque puzzles called 'Loop de Loop' that I am making for my site. I have a few posted at The Griddle and I also have them available through Zoho Sheet, which is a rather cool online spreadsheet application. I'm also branching out and trying other online spreadsheet utilities like Google Docs and Spreadsheets and EditGrid. It's quite interesting to see all of the options there are out there. [Ed  Quite fascinating.]
Material added 9 December 2006
 Rectilinear Crossing Number Project
 The Rectilinear Crossing Number Project has made a number of discoveries since 2000. They've resolved the K10 problem, then K11, and then all the way up to K17. K18 is still unresolved. They've also solved K19 and K21, shown below. Those red dots are pts = {{35, 67}, {18, 28}, {63, 50}, {27, 69}, {17, 23}, {87, 66}, {8, 79}, {18, 16}, {69, 53}, {5, 86}, {0, 0}, {94, 66}, {4, 88}, {5, 6}, {115, 69}, {9, 74}, {14, 13}, {108, 67}, {6, 85}, {2, 2}, {111, 68}}.
 Google books vs Amazon books
 For looking up info on obscure topics, I have often gone beyond Google to Amazon, which can find quotes inside books. Now, Google Books is available. Both are excellent sources for researching a topic. For "hexecontahedron", for example, Amazon gave 17 books, and Google Books 12 books.
 Polycube solutions
 Bob Harris: I've also uploaded a nice rendering of my favorite polycube puzzle the 10x10x10 filled with the 166 hexacubes (and a 2x2x1 void in the center of one face).
 World's Smartest Person Contest
 Matt Sheppeck: Thanks to you (and Ken Duisenberg) for posting that link to the 2006 World's Smartest Person Challenge. I took first place along with seven others, earning me $62.50 and a Tshirt. Maybe the WSP title gets me a discount on a cup of coffee somewhere? http://www.highiqsociety.org/wsp_highscores.php Eleven people were given a set of tiebreaking questions. When I saw that the tiebreaking questions were relatively easy, I considered submitting one wrong answer in the hopes of being the sole winner of the $200.00 second prize, rather than a small share of the $500 first prize. As it turned out, three people split the second prize, earning them $66.67 each. So who's smarter? Thanks again for your site, always a delight.
 Ken Nordine Fibonacci
 The video fibonacci numbers by Ken Nordine was nicely done. I've always been a big Ken Nordine fan, so I'm glad to see he's making videos.
 Overview of Math
 A nice overview of mathematics is given on page 2 of "Is the theory of everything merely the ultimate ensemble theory?" by Max Tegmark.
 Spidrons
 After mentioning spidrons last week, I was reminded by noone less than Daniel Erdély that I should link to the main Spidron page, spidron.hu.
Material added 13 November 2006
 New Largest Probable Prime
 Norm((1+I)^1127239+ 1)/5, or (2^1127239+2^563620+1)/5, has 339333 digits, which puts it at the top of the Probable Primes list. Norm((1+I)^n+1)/5 is proven prime for n = 5, 6, 7, 9, 11, 13, 17, 29, 43, 53, 89, 283, 557, 563, 613, 691, 1223, 2731, 5147, 5323, 5479, 9533, 10771, 11257, 11519, and 12583. For n=23081 , 36479, 52567, 52919, 125929, 221891, 235099, 305867, 311027, 333227, 365689, and 1127239, all the probable prime tests work, but no method is known for proving primality. Many congratulations to Borys Jaworski for setting this new record.
 Hexominoku
 Andrew Clarke: Here is as a Sudoku type problem. In each 6x6 square all rows and columns contain 16 as does each hexomino. See also Numbered Polyiamonds and Numbered Polyominoes.
 The Popular Science Periodic Table
 Theo Grey's Periodic Table is now a gorgeous interactive screen at Popsci.com. If you get the latest copy of Popular Science, the Dow ad features a beautiful foldout poster of all the elements. One of these items is recently in the news  polonium210, the active ingredient in a camera brush.
 Wordplay DVD
 My longtime friend Will Shortz now has a DVD out: Wordplay. This film about intelligent puzzle people wound up being one of the best reviewed movies of the year.
 Powerful vector support
 Geometry Expressions, the most mathintensive vector drawing program, now interfaces directly with Mathematica.
 Snakes on a Plane
 The records for the matchstick snake contest are in. Vadim Trofimov is the big winner. I hope to show pictures of most of the solutions soon.
 Fractal Maze
 Martin Windischer: On www.mathpuzzle.com I´ve read about the fractal mazes, but they don´t looked very attractive for me. If you insert the original maze in each of the boxes it will be too small in very few steps. So I tried to make another fractal maze with only one limit point. Here is the result. Send Answer.
 Irfanview 3.99
 My favorite free fast art editor, Irfanview, has just come out in an improved version.
 The LobsterSnake puzzle
 George Sicherman: Here are two of the 12 hexiamonds, the Lobster and the Snake. Make two congruent shapes by adjoining the same hexiamond to both. This arose from Erich's latest Math Magic. Erich Friedman: Find a polyomino that can be joined with each of the two pictured hexominoes to get two congruent shapes. Send Answers. Colonel Sicherman also sent me a note that the T and X pentahexes are compatible.

 Nonunique Town Placements
 Given six road lengths between 4 towns, can the town placements be discerned? Turns out it's ambiguous. Can 5 points be done ambiguously? Can 4 points be set up so that all distances are integers? Send Answer.
 Bimagic Square of Primes
 Christian Boyer has made the first Bimagic square of primes. Under 701, only the primes 2, 3, 523, 641, and 677 are missing. It's a magic square that remains magic if all the terms are squared.

137 131 317 47 5 457 541 359 467 353 683
401 277 239 647 23 421 229 181 7 419 653
463 269 701 59 157 257 563 557 179 191 101
593 311 379 503 197 83 53 521 149 619 89
307 617 397 241 571 661 109 107 79 127 281
373 443 29 587 383 61 19 409 631 389 173
73 11 607 433 613 577 263 97 227 313 283
43 599 151 199 509 487 223 163 293 691 139
673 37 113 271 193 31 601 431 331 337 479
67 233 103 439 499 251 547 659 491 41 167
367 569 461 71 347 211 349 13 643 17 449  Polyspidrons at Kadon
 Jacques Ferroul's Polyspidrons are now available as a handsome set from Kadon Enterprises. Polyspidrons uses the famous Spidrons of Dániel Erdély. Ivars Petersen wrote an article about the Spidrons, Swirling Seas. I've also made Ivars a permanent link, in the upper right.
 120cell Sculpture
 Ivars also wrote about a recently dedicated 120cell scupture. Here's a picture from that event, showing the 120cell trapping John Conway's arm in the 4th dimension. It was part of a dedication for Coxeter, whose biography, King of Infinite Space, recently came out.

 Jenn 3D
 Poor John Conway... when he tried to blow some bubbles after the dedication, they looked like the below. Actually, this figure is from Jenn3d, an excellent free program for playing around with higher polytopes  beautiful stuff.
 Lorenz and Modular Flows
 A very tubular and very beautiful set of animations is available at Lorenz and Modular Flows at ams.org, in an article by Etienne Ghys.

Material added 29 October 2006
 Interview with Martin Gardner
 Colm Mulcahy's latest Card Colm column is lengthy interview with Martin Gardner, in honor of Martin's 92nd birthday.
 Paul Halmos passes
 Paul Halmos, author of many books, including I Want to be a Mathematician, passed away on October 2 at age 90. Kirk Bresniker: He was one of the fastest walkers I'd ever seen, and could always be seen zipping around the campus at SCU. Several years ago he was walking during the winter and slipped and detached a tendon in both legs. Since he could not walk as quickly during his recuperation, he calculated the number of calories he was no longer burning and deducted that amount from his daily intake. That's discipline!
 More highlights from Games magazine
 Robert Abbott: I got my Starry Night program working on the GAMES
web site,
and I just put a notice about it on my home
page.
Serhiy Grabarchuk: Just to add to your note on the latest GAMES Magazine, I though you'd be interested to read a big article of mine among the issue's features. It's named Playing with Puzzle Classics, and contains a lot of interesting puzzle materials I've never published before. [Indeed, great article.]  Making Salt the Hard Way
 My friend Theo Gray wanted to salt some popcorn, so he filled a net with popcorn, put it over a bowl of molten sodium, then started bubbling chlorine gas through it. For awhile, everything was working fine, but then a piece of popcorn fell out from the net, starting a watersodium reaction and explosion. As more heat was generated, the net holding the popcorn started to melt, and then chaos ensued. Theo had the wherewithal to turn off the chlorine gas in the midst of it all. The video and pictures are spectacular.
Material added 21 October 2006
 Games 100
 The latest Games Magazine is
out, with the Games
100 list of top games. Robert Abbott has
a devious logic maze on the cover. I was very pleased to see that the Thinkfun
Gordian's Knot was the puzzle of the year  congrats to Frans de Vreugd
and George Miller for designing
it. Gordian's Knot recently showed up at the end of Numb3rs episode
The Mole.
Even more amazing  the HoffmanSingleton game was selected as one of the 100 top games of the year. I thought this elegant item from mathematics would make a great card game, and many playtesters agreed with me. Column about the game. 
 Hexed Chess Robots
 Erich Friedman: I've added a number of new puzzle types to Puzzle Palace: Hex turn, Chess attack, Robot mazes, Color strip puzzles, Chess mazes, Unequal length puzzles, Color mazes, and Left right mazes. (wowsers.)
 Math Pickup Lines, and N E W S
 Alan O'Donnell: I thought you might like some of these 'Math
pickup lines'  no warranty provided or implied! eg: My
love for you is a monotonically increasing unbounded function, Let's
take each other to the limit to see if we converge, and I
wish I were a derivative so I could lie tangent to your curves.
I've always noticed that American urban architects like their roads to travel N/S and E/W, but did you know they sometimes they get a bit anal about this? (An amazing road design) That image made me shake my head slowly in disbelieving astonishment  thought it might amuse you too...  Peter Hugo McClure  Math Artist
 Peter McClure: Greetings... I am independent artist and maths/geometry/puzzles have been my greatest inspiration see my website at: http://www.peterhugomcclure.com. [Ed  129 fascinating thumbnails of math art, right off the bat]
 Fractal Forum
 There are forums on many topics... one I just learned about is the Fractal Forum. What other good forums are out there?
 Pseudoku and Sudorku
 Timothy Y. Chow: I've made several new sudoku variants based on objects other than Latin Squares. The first variant is the closest to ordinary Sudoku, and is the one I like best, because it is closely related to an unproved mathematical conjecture of mine, as mentioned in the endnotes. If you have any suggestions about how I could spread the word about this variant, or encourage other puzzle creators to make other instances of it, I would be interested to hear them. [Also very cute is a recent Foxtrot comic. Another puzzle is Hard Corners, by Joseph White]
 World Puzzle Championship Blog
 The final results are in for the World Puzzle Championship. The WPF site has more info. WeiHwa Huang (link to his excellent puzzle gadgets) came in second. Thomas Snyder (4th place) wrote a WPC blog item about the event.
 Repeated squares, and the Smartest Person Challenge
 Ken Duisenberg's latest Puzzle of the Week, Unique 2x2 Squares, is quite nice. He has a link to the 2006 World's Smartest Person Challenge, put on by the High IQ Society. A nice set of puzzles.
Material added 11 October 2006
 Solving Techniques
 If some of the puzzles at the WPC seem difficult, Cihan Altay offers an essay of various solving techniques (PDF).
 Magnetic Tetris
 If you'd like to cover your refrigerator with Tetris pieces, artlebedev.com has them. Just 278 rubles per set.
 Patterns in Ramanujan Tau
 Simon Plouffe's homepage has hundreds of fascinating patterns. The lastest patterns explore the Ramanujan Tau function.
 Wpentahex Oddity
 Col. George Sicherman: I finally found a fullsymmetry oddity for the W pentahex!
 Emma Lehmer's 100th birthday
 Emma Lehmer, a famous mathematician, will soon be celebrating her 100th birthday. People are invited to send best wishes to her mailbox, 1180 Miller Avenue, Berkeley CA 94708.
 Magic Square of Cubes
 Christian Boyer: Nobody knows a 4x4 magic square of cubes, using distinct
positive integers. But very interesting step with the first known 4x4 semimagic
squares of cubes (semimagic means nonmagic diagonals), by Lee Morgenstern,
USA. Who will construct a 4x4 magic square of cubes, with 2 magic diagonals? [Much
more news is given at multimagie.com]
16^3 20^3 18^3 192^3
180^3 81^3 90^3 15^3
108^3 135^3 150^3 9^3
2^3 160^3 144^3 24^3  Halloween Themed Squiggly Sudoku
 Bob Harris: I've added a new batch 43 puzzles with halloween related clues. Some are pretty easy (the first five might be nice for a children's halloween party). The ones at the bottom of the page are probably hard.
 Color Mazes
 Erich Friedman: A new type of puzzle for you: Color mazes. Find a path from Start to Finish (moving only horizontally and vertically and never passing through a square more than once) so that you pass through each (nonwhite) color an equal number of times.
 The Tangent Circle Problem
 Dick Hess: I ran across this one recently in the Pi Mu Epsilon Journal and wondered if you'd seen it before. Four planar circles are pairwise externally tangent. Three of them are also tangent to a line, L. If the fourth circle has unit radius what is the distance of its's center from the line? It's amazing to me the distance in question doesn't depend on the relative sizes of the other three circles. Send Answer.
 Me and Numb3rs
 The local GazetteTelegraph wrote an article about Wolfram Research and Numb3rs. The Numb3rs season 2 DVD ($38) just came out, and it's loaded with great stuff. Near the start of episode Dark Matter, Andy Black and Cheryl Heuton graciously mention a story about me on the commentary track. You can still get Numb3rs Season 1 ($40), which curiously has fewer episodes at a higher price. If you prefer digital versions, Numb3rs Amazon Digital offers individual episodes for $2 each.
Material added 30 September 2006
 Asymmetrical Looney Gear
 M. Oskar van Deventer: A few months ago I challenged people to design four gears fitting inside a fifth gear. Andreas Röver took up the challenge. The sketch below and this gear animation shows some of Andreas' results. Andreas realised quickly that it would be hard or even impossible to find a solution that would result in an exact fit. In an exact solutions, the gears would fit perfectly and mesh perfectly. Instead, Andreas developped an algorithm that searches for approximate solution. Andreas found several criteria which a solution would satisfy, like a maximum mismesh of x%, gears not having common denominators and gears fitting "nicely" together. Finally, Andreas performed a quasirandom search for goodenough solutions. The resulting gear arrangements look quite nice. The Looney Gear animation demonstrates how they can rotate as a set of planetary gears, albeit quite asymmetrical. Two questions remain. 1) Do exact solutions exist, or only appromiate ones? 2) Do these Looney Gears have any useful applications? [Ed  The animation is fascinating. Other gears can be found at the Kinematic Models for Design library]
 Pentagon Rule broken
 A buckyball molecule has 12 pentagons and some number of hexagons. This can be proven with Euler's formula, V+FE = 2 (vertices, faces, edges). Another buckyball rule has been that the pentagons don't touch, but a new buckyball built around triterbium nitride violates this rule.
 Sudoku Variations
 Uwe Wiedemann: Because it was your page where I found at first a collection of sudoku variants I will point you to my own sudoku variant page: http://www.sachsentext.de/en. There are well known variants and less known, and also some which I've created. Most of the puzzles aren't easy. [An excellent collection of variants]
 Numb3rs Puzzle
 Texas Instruments is continuing their excellent activities for the Numb3rs TV show, with season 2 and season 3 now available. One of them is mine, the missing city exercise. From the last update, I mentioned Colby, Kansas and Milford, Utah  most of the cities in the route have huge crop circles visible in their overhead maps, a feature spotted only by Walter Hoppe.
 Math Factor on iTunes
 Chaim GoodmanStrauss: I am writing to advertise the Math Factor, a short weekly segment that airs on our local NPR affiliate, KUAF 91.3, Fayetteville Ark., and then is podcast around the world. We've been having a great time last week we had Jeff Weeks explain the Poincaré conjecture! We've discussed cardinality, encryption, paradoxes, puzzles, rates of change and much more. For a show about math, it is surprisingly well received by our general audience. To find it, simply search Math Factor on iTunes, or the podcast directory of your choice, or enter the Math Factor url into your podcast browser.
 Perfect Sequential Rectangles
 Brian Trial: Your prizes page lists a $100 bounty for the first perfect rectangle consisting of sequentially sized squares 1..n. For now the money is quite safe, but how close can one get? For a given n, what is the highest percentage of the squares 1..n one can use to make a perfect rectangle? The smallest perfect rectangle, 33x32, uses 9 squares in the 1..18 range, or 50%. Squaring.net lists a 60x84 rectangle that uses 17 out of 1..33, or 51.5%. It appears that rectangles that do better than 50% are uncommon, and I've only found 5 that do better than 60%, for n=30,32,33,36, and 41. My best so far, 66.6% and 65.9%, are attached. Pascal Huybers has independently found the 80x89 66.6% solution. For larger values of n, would the percentages increase, or do they plateau at some value of n? [Ed  Is the rectangle below the best possible?]
Material added 17 September 2006
 Ultimate Periodic Table
 A longterm local project is the ultimate periodic table by Theodore Gray, which I've mentioned here many times. At considerable expense, Theo has now made a spectacular illustrated periodic table poster, along with photographs of every element. Many sizes are available at reasonable prices. The large scale views are amazing.
 New Mersenne Prime
 A new biggest prime exists. 2^{32,582,657}  1. See the story on MathWorld.
 Coxeter: The Man Who Saved Geometry
 A delightful book has just been released by Siobhan Roberts: The King of Infinite Space: Donald Coxeter: the Man Who Saved Geometry. In my latest maa.org column, I mention the love of geometry that Washington and Jefferson had. At the turn of the century, geometry was on it's way out. Largely by himself, Coxeter revived the entire field. A great book, with lots of wonderful math along the way.
 Lightforce Games
 JeanCharles Meyrignac: I just discovered Lightforce. There are a lot of nice puzzles on this site.
 Numb3rs Season Premiere
 The first episode of the third season starts Friday, 22 September. Among other things, I was given the task of picking out data points across the United States as a part of the plot. Here are two of them: Colby, Kansas and Milford, Utah. Can you figure out what trait many of the data points have in common? Lots of cool stuff is coming up in the next few episodes.
 Replacement Puzzles
 Erich Friedman: I've made a number of replacement puzzles. For example, Rule #1: {2,1,2}>{1,1}, Rule #2: {2}>{1,2,2}, Rule #3: {1,1}>{2} QUESTION Using only these three replacement rules, one at a time, on some consecutive substring, get from {2,2,2} to {1,2,1,1,1} in 13 moves. You never need a string longer than 6 digits.
 Mathematical Equivoque
 Ken Suman: I have seen on various sites that you are interested in crosswords and wordplay as well as mathematics. So am I. I have been building a collection of mathematical wordplays that I hope you might find interesting.
 Coordinates of the Harborth Graph
 Eberhard Gerbracht: I have prepared a much deeper analysis of the Harborth Graph. I put some more thought to the problem and finally (with the help of MATHEMATICA) was able to produce minimal polynomials of degree 22 which completely describe the coordinates of the vertices of the Harborth graph. Thus now the problem is not horrifying anymore, but has become quite nice (at least in my opinion). Thus I found it worthy of a more thorough exposition.
 Noncrossing knight tour
 Alexander Fischer: Hello dear friends of mathematical recreation. Here is another improvement concerning the longest noncrossing leaper tour on a 14*14 chess board, it's of 135 steps length. By board extension some other records can possibly be improved. [Alexander also found 163 moves on the 16x16.]
 Melbourne, City of Math
 My latest maa.org column is about the spectacular math architecture in Melbourne. Christian Boyer pointed out some other unusual buildings. Also, ARM has more math buildings in the works.
 Rolling Block Ramp
 Cihan Altay: A red block, with a length of 39 units, is standing next to another block which supports a ramp that doesn't move. Roll the red block around the board, without exceeding the rectangular border, so that it ends up standing upright on the supporting block. A move is to roll the red block using one of its edges (touching the ground) as the axis of rotation. There is a chasm on the board on which the red block can not stand upright, but it may lie down. What is the minimum number of moves to achieve the goal, following these rules? [A simple solution is flop the block S, then to roll W a lot, N at the proper spot.... but that is not the shortest path.]
Material added 27 August 2006
 New Mersenne Prime
 Robert Bosch: This summer, I finally had the time to put together a page on my "TSP Art". It has samples of my recent pieces, a link to a second page describing how I do what I do, and links to related pages by Craig Kaplan and Mo. [The below is a simple loop, not a knot.]
 Anisohedral Tiling Database
 Joseph S. Myers has compiled a tiling database of interesting tilings possible with polyominoes, polyiamonds, and polyhexes.
 PolyAddition
 Erich Friedman: I've made a page of Polyomino Addition Problems. The first two are surprising! They might make good puzzles for your readers.
 Sudoku Variations
 A large variety of new sudoku variations is on display at hexapuzzle.com.
 New Hanayama Puzzles
 Various new metal puzzles have been minted by Hanayama, and are available at Puzzle Master. All of them are exquisitely made, and feature only 2 to 4 pieces. Some of the newer puzzles are Oskar's Cuby puzzle, and Serhiy's Coaster puzzle.
 Survo Puzzles
 Seppo Mustonen: During the past 45 years I have made statistical software, one of them being the SURVO MM (Survo) package, which is a general environment for statistical computing and related areas. As an application of some special computational features (especially those related to combinatorics) of Survo I got an idea of cross sum puzzles having something of the flavour of Kakuro but with unique and mathematically challenging features of their own. I call them Survo cross sum puzzles or Survo puzzles (link to PDF). As an example, arrange the numbers 1 to 12 in the grid below so that the rows and columns sum to the given numbers (problem 10 on page 24). [The survo website has been further updated.]
 Poincare Conjecture Proved
 Back in 2003, Perelman proved the Poincare conjecture. After several years of study, his proof has been accepted. An excellent report on the full story is given in The New Yorker story, Manifold Destiny. Another Fields medal winner is Terence Tao.
 Clickmazes Update
 There are new logical mazes available at Andrea Gilbert's clickmazes.com. Oskar: When writing the challenge generator for the Active Maze, I discovered that I could not use a genetic algortithm, as even changinging the color of only one square would change the entire maze. I wonder whether there would be any intelligent approach to such generator, other than bruteforce search.
 Combinatorial Object Server
 Many combinatorial objects are explained at the Combinatorial Object Server.
 Davis Megamaze
 The Davis Megamaze (in Sterling, Mass.) is a huge cornfield maze designed by Adrian Fisher. A feature of the maze, in addition to the many bridges, is a series of gates which allow for 24 different mazes. The honor system prevents a person from passing through various gates. Oskar sent a photo. Aerial shot.
21  10  18  29  

24  
15  
39 