VECTOR1

VECTOR

Quantity:

In the physical world which are measurable are called quantity.such as:mass,length,weight etc.

Classification of quantity:

All physical quantities are divided into two sections:1.scalar quantity

2.vector quantity

Scalar quantity:

The quantities which are expressed only by their magnitude are called scalar quantities.such as:mass, length etc.

Vector quantity:

The quantities which need both magnitude & direction are called vector quantities.such as:weight,force etc.

Quantity

Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity. Being a fundamental term, quantity is used to refer to any type of quantitative properties or attributes of things. Some quantities are such by their inner nature (as number), while others are functioning as states (properties, dimensions, attributes) of things such as heavy and light, long and short, broad and narrow, small and great, or much and little. One form of much, muchly is used to say that something is likely to happen. A small quantity is sometimes referred to as a quantulum.

Two basic divisions of quantity, magnitude and multitude, imply the principal distinction between continuity (continuum) and discontinuity.

Under the names of multitude come what is discontinuous and discrete and divisible into indivisibles, all cases of collective nouns: army, fleet, flock, government, company, party, people, chorus, crowd, mess, and number. Under the names of magnitude come what is continuous and unified and divisible into divisibles, all cases of non-collective nouns: the universe, matter, mass, energy, liquid, material, animal, plant, tree.

Along with analyzing its nature and classification, the issues of quantity involve such closely related topics as the relation of magnitudes and multitudes, dimensionality, equality, proportion, the measurements of quantities, the units of measurements, number and numbering systems, the types of numbers and their relations to each other as numerical ratios.

Thus quantity is a property that exists in a range of magnitudes or multitudes. Mass, time, distance, heat, and angular separation are among the familiar examples of quantitative properties. Two magnitudes of a continuous quantity stand in relation to one another as a ratio, which is a real number
if you want to see bacground click here

Russia's Conquering Zeros

It may be no accident that, while some of the best American mathematical minds worked to solve one of the century's hardest problems—the Poincaré Conjecture—it was a Russian mathematician working in Russia who, early in this decade, finally triumphed.Decades before, in the Soviet Union, math placed a premium on logic and consistency in a culture that thrived on rhetoric and fear; it required highly specialized knowledge to understand; and, worst of all, mathematics lay claim to singular and knowable truths—when the regime had staked its own legitimacy on its own singular truth. All this made mathematicians suspect. Still, math escaped the purges, show trials and rule by decree that decimated other Soviet sciences.Three factors saved math. First, Russian math happened to be uncommonly strong right when it might have suffered the most, in the 1930s. Second, math proved too obscure for the sort of meddling Joseph Stalin most liked to exercise: It was simply too difficult to ignite a passionate debate about something as inaccessible as the objective nature of natural numbers (although just such a campaign was attempted). And third, at a critical moment math proved immensely useful to the state.Three weeks after Nazi Germany invaded the Soviet Union in June 1941, the Soviet air force had been bombed out of existence. The Russian military set about retrofitting civilian airplanes for use as bombers. The problem was, the civilian airplanes were much slower than the military ones, rendering moot everything the military knew about aim.What was needed was a small army of mathematicians to recalculate speeds and distances to let the air force hit its targets.The greatest Russian mathematician of the 20th century, Andrei Kolmogorov, led a classroom of students, armed with adding machines, in recalculating the Red Army's bombing and artillery tables. Then he set about creating a new system of statistical control and prediction for the Soviet military.Following the war, the Soviets invested heavily in high-tech military research, building over 40 cities where scientists and mathematicians worked in secret. The urgency of the mobilization recalled the Manhattan Project—only much bigger and lasting much longer. Estimates of the number of people engaged in the Soviet arms effort in the second half of the century range up to 12 million people, with a couple million of them employed by military-research institutions.These jobs spelled nearly total scientific isolation: For defense employees, any contact with foreigners would be considered treasonous rather than simply suspect. In addition, research towns provided comfortably cloistered social environments but no possibility for outside intellectual contact. The Soviet Union managed to hide some of its best mathematical minds away in plain sight.In the years following Stalin's death in 1953, the Iron Curtain began to open a tiny crack—not quite enough to facilitate much-needed conversation with non-Soviet mathematicians but enough to show off some of Soviet mathematics' proudest achievements.By the 1970s, a Soviet math establishment had taken shape. A totalitarian system within a totalitarian system, it provided its members not only with work and money but also with apartments, food, and transportation. It determined where they lived and when, where, and how they traveled for work or pleasure. To those in the fold, it was a controlling and strict but caring mother: Her children were undeniably privileged.Even for members of the math establishment, though, there were always too few good apartments, too many people wanting to travel to a conference. So it was a vicious, back-stabbing little world, shaped by intrigue, denunciations and unfair competition.Then there were those who could never join the establishment: those who happened to be born Jewish or female, those who had had the wrong advisers at university or those who could not force themselves to join the Party. For these people, "the most they could hope for was being able to defend their doctoral dissertation at some institute in Minsk, if they could secure connections there," says Sergei Gelfand, publisher of the American Mathematical Society—who also happens to be the son of one of Russia's top 20th-century mathematicians, Israel Gelfand, a student of Mr. Kolmogorov. Some Western mathematicians, Sergei Gelfand adds, "even came for an extended stay because they realized there were a lot of talented people. This was unofficial mathematics."One such visitor was Dusa McDuff, then a British algebraist and now a professor emerita at the State University of New York at Stony Brook. She studied with the older Mr. Gelfand for six months, and credits this experience to opening her eyes both to what mathematics really is: "It was a wonderful education... Gelfand amazed me by talking of mathematics as though it were poetry."In the mathematical counterculture, math "was almost a hobby," recalls Sergei Gelfand. "So you could spend your time doing things that would not be useful to anyone for the nearest decade." Mathematicians called it "math for math's sake." There was no material reward in this—no tenure, no money, no apartments, no foreign travel; all they stood to gain was the respect of their peers.Math not only held out the promise of intellectual work without state interference (if also without its support) but also something found nowhere else in late-Soviet society: a knowable singular truth. "If I had been free to choose any profession, I would have become a literary critic," says Georgii Shabat, a well-known Moscow mathematician. "But I wanted to work, not spend my life fighting the censors." The search for that truth could take long years—but in the late Soviet Union, time seemed to stand still.When it all collapsed, the state stopped investing in math and holding its mathematicians hostage. It's hard to say which of these two factors did more to send Russian mathematicians to the West, primarily the U.S., but leave they did, in what was probably one of the biggest outflows of brainpower the world has ever known. Even the older Mr. Gelfand moved to the U.S. and taught at Rutgers University for nearly 20 years, almost until his death in October at the age of 96. The flow is probably unstoppable by now: A promising graduate student in Moscow or St. Petersburg, unable to find a suitable academic adviser at home, is most likely to follow the trail to the U.S.But the math culture they find in America, while less back-stabbing than that of the Soviet math establishment, is far from the meritocratic ideal that Russia's unofficial math world had taught them to expect. American math culture has intellectual rigor but also suffers from allegations of favoritism, small-time competitiveness, occasional plagiarism scandals, as well as the usual tenure battles, funding pressures and administrative chores that characterize American academic life. This culture offers the kinds of opportunities for professional communication that a Soviet mathematician could hardly have dreamed of, but it doesn't foster the sort of luxurious, timeless creative work that was typical of the Soviet math counterculture.For example, the American model may not be able to produce a breakthrough like the proof of the Poincaré Conjecture, carried out by the St. Petersburg mathematician Grigory Perelman.Mr. Perelman came to the United States as a young postdoctoral student in the early 1990s and immediately decided that America was math heaven; he wrote home demanding that his mother and his younger sister, a budding mathematician, move here. But three years later, when his postdoc hiatus was over and he was faced with the pressures of securing an academic position, he returned home, disillusioned.In St. Petersburg he went on the (admittedly modest) payroll of the math research institute, where he showed up infrequently and generally kept to himself for almost seven years, one of the greatest mathematical discoveries of at least the last hundred years. It's all but impossible to imagine an American institution that could have provided Mr. Perelman with this kind of near-solitary existence, free of teaching and publishing obligations.After posting his proof on the Web, Mr. Perelman traveled to the U.S. in the spring of 2003, to lecture at a couple of East Coast universities. He was immediately showered with offers of professorial appointments and research money, and, by all accounts, he found these offers gravely insulting, as he believes the monetization of achievement is the ultimate insult to mathematics. So profound was his disappointment with the rewards he was offered that, I believe, it contributed a great deal to his subsequent decision to quit mathematics altogether, along with the people who practice it. (He now lives with his mother on the outskirts of St. Petersburg.)A child of the Soviet math counterculture, he still held a singular truth to be self-evident: Math as it ought to be practiced, math as the ultimate flight of the imagination, is something money can't buy.
This essay was adapted from Masha Gessen's latest book, "Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century," a story of Grigory Perelman and the Poincaré Conjecture. She lives in Moscow and is the author of three previous books.
Russia's Conquering Zeros

about Edward Nussbaum

A. Edward Nussbaum of Clayton, a theoretical mathematician and longtime professor at Washington University, died Saturday, Oct. 31 at Barnes-Jewish Hospital from complications from congestive heart failure. He was 84.Mr. Nussbaum was a Holocaust survivor whose youth was spent in the chaotic years between two world wars and whose adolescence was the stuff of movies.A serious man who scribbled his mathematical theorems and derivations on napkins and tablecloths and anything else handy, he worked with such giants of 20th-century theoretical physics and mathematics as J. Robert Oppenheimer and John von Neumann. Along the way he also rubbed shoulders with Albert Einstein. He was a devoted husband and family man, whose own parents died at Auschwitz.Mr. Nussbaum earned both a master's and Ph.D. at Columbia University in New York, which he entered with almost no formal schooling. Both shy and humble, he eschewed the title of "doctor," preferring to be addressed simply as "Mr. Nussbaum," said his wife of 52 years, Anne Nussbaum.Mr. Nussbaum was born in Rheydt, a small town in northwestern Germany. The youngest of three children, he was essentially orphaned at the age of 14, after the Nazi takeover of Germany.He and his sister, Lieselotte, survived, but were separated after both were sent on a Kinder Transport to Belgium in 1939. His father, Karl Nussbaum, a wounded veteran of World War I in which he was awarded the Iron Cross, and his mother, Franziska, died in Auschwitz. His brother, Erwin Nussbaum, a Zionist, was also captured and killed.When Belgium was invaded by Germany, a sponsor from a Jewish women's organization helped the young Ed Nussbaum escape to southern France, then under the Vichy Regime. There he lived with 100 other children in a castle known as Chateau de la Hille, which at the age of 17, he single-handedly wired for electricity.It was also here that he started his teaching career. As a teenager and one of the older occupants of the "castle on the hill," he taught mathematics to the younger children, some who were just three- years-old.After many harrowing experiences including being twice captured —and once jailed — by the Nazis, he managed to escape on foot, walking through the forest to Switzerland, where he lived with a sponsor and attended a university in Zurich, studying both mathematics and physics. Eventually, when he was in his early 20s, he was able to find sponsorship from relatives who lived in New Jersey.Shortly thereafter he moved to Manhattan and studied mathematics briefly at Brooklyn College until one day, after seeing a "room for rent," notice for Washington Heights, he announced he was going to Columbia."His friends laughed," said Anne Nussbaum, smiling. He had no degree, little formal schooling and besides, they said, "Jews can't get in there."Mr. Nussbaum got in. And he received his master of arts degree from Columbia in 1950 and his Ph.D. in 1957.During the summers while he was writing his thesis for Columbia, Mr. Nussbaum worked at the world-famous Institute for Advanced Study in Princeton with John Von Neumann, the father of the modern computer, among other things. Mr. Nussbaum's son, Karl Nussbaum, has a picture of his father standing on a ladder and working on the first computer, a monster larger than their living room.Von Neumann, used a concept called Hilbert Spaces in his development of the mathematical basis of modern computer language. Hilbert Spaces eventually became Mr. Nussbaum's area of expertise and with von Neumann, he wrote several papers. Also during this period, Mr. Nussbaum sometimes rode to work with Albert Einstein, another of the original group at the Institute for Advanced Study."He told us how Einstein would often get into the car with bare feet and Mrs. Einstein would run after him, carrying his shoes," Anne Nussbaum reported.Mr. Nussbaum's thesis was accepted with no revisions and he received his doctorate shortly after his first blind date with his cousin's sister-in-law, Anne Ebbin, whom he invited to attend the ceremony and who would soon become Mrs. Nussbaum.In the meantime he had worked at both Rensselaer Polytechnic Institute in Troy, N.Y., and, before that, at the University of Connecticut in Storrs, where he co-authored papers with Allen Devinatz, who would soon move to St. Louis to teach at Washington University.Mr. Nussbaum proposed to his wife and announced his intention to follow Devinatz practically in the same breath. "I didn't know exactly where St. Louis was, but I said 'yes,' '' Anne Nussbaum said.That was 1958. Except for their travels and two visiting professorships, the Nussbaums stayed in St. Louis. In 1962, Mr. Nussbaum was a visiting scholar at the Institute for Advanced Studies working with Robert Oppenheimer, father of the atomic bomb; in 1967-68 he was a visiting scholar at Stanford University in Palo Alto, Calif.In addition to his wife and son, Mr. Nussbaum is survived by a daughter, Franziska Nussbaum, of St. Louis.A funeral was scheduled for 1 p.m. Wednesday (Nov. 4) at United Hebrew Cemetery, North and South Road at Canton, in University City. After the service, shiva will be held at the Nussbaum home, 8050 Watkins Drive in Clayton. The family sat shiva after the service and Thursday at the Nussbaum home in Clayton.
Nussbaum was Shoah survivor, accomplished mathematician

math puzzle

Martin Gardner in New York Times Article
John Tierney: "For today’s mathematical puzzle, assume that in the year 1956 there was a children’s magazine in New York named after a giant egg, Humpty Dumpty, who purportedly served as its chief editor." See the rest of the article.
Wolfram Homework Day
Today, Wednesday Oct 21, is Wolfram|Alpha Homework Day. I'll be one of the dozens of people on hand to answer questions, from noon (CST) until the wrap-up 14 hours later. Feel free to send in any questions you like.
MathCamp Qualifying Quiz
The qualifying questions for MathCamp 2009 are a nice selection.
Golly 2.1
The cellular automata program Golly 2.1 has been released. Some extensions are also available. Tim Hutton wrote a turmites extension, and noticed that my wormtrails turmite got trapped in a cycle after 4.3 million steps, making it the best known "busy beaver" of 2-D Turing machines.

The Zen of Labyrinth
Robert Abbott: Dave Phillips wrote a new maze book called "The Zen of the Labyrinth." I reviewed it here:

http://www.logicmazes.com/reviews.html

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

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

You may retrace your path but may not make a U-turn on a
pathway. You must follow the paths in the order red, blue,
yellow and then red, blue, yellow again, as needed, changing
color on the white squares.


[Ed - I went ahead and picked up the book myself, and it's gorgeous. Every page is like a piece of art, and every one is an interesting maze-based logic puzzle, of many different varieties.]
Acute-dissected Squares and Cubes
A square can be divided into acute triangles. Can a cube be divided into acute tetrahedra? Various papers look at the problem, some with solutions with a large number of tetrahedra:Tiling space and slabs with acute tetrahedra, Acute triangulations of polyhedra and R^n, A Dihedral Acute Triangulation of the Cube, Triangulation of Simple 3D Shapes with Well-Centered Tetrahedra.
Can't Decide? Undecide!
Chaim Goodman-Strauss has written an excellent paper on undecidability for Notices of the AMS.
Material added 9-9-9
9-9-9
Lots of 9 news today. The Beatles "Revolution 9" almost never got onto the track, because the higher-ups thought it was too uncommercial. Now, it's the centerpiece of one of the biggest commercial campaigns of all time. For the Wolfram Blog, I wrote 9-9-9 about almost integers with lots of nines.
The Diabolical Box
One thing that slowed me down in recent weeks was Professor Layton and the Diabolical Box. This is a nice collection of about 150 puzzles, much like Professor Layton and the Curious Village. Many are familiar. For example, 10 of them are knight-tour and peg-jumping puzzles. But all nicely interactive, and there were a few I hadn't seen before.

Material added 7 Sep 2009
NPR Puzzle
The puzzle from NPR this week is mine. "This challenge comes with help from math puzzle expert Ed Pegg. Take the names of the first nine elements of the periodic table: hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen and fluorine. Select one letter from each of these names in order to spell a familiar nine-letter word. Hint: It's a word used in math." Send Answer.
Here's a similar puzzle that Will Shortz though was slightly too obscure: Take the names of the officially recognized planets in order, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune. Select one letter from each of these names in order to spell a familiar eight-letter name. Hint: It's a name used in math. Answer.
Don Knuth on Puzzles
I had the pleasure of seeing Don Knuth speak at the International Puzzle Party. Around his neck he had a necklace of 12 disconnected L-trominoes based on unit squares, with the centers of each end joined by strings of unit length. He asked if it was possible to make a 6x6 square with the necklace of trominoes.

After showing various cool tricks possible with polarized film on an overhead projector, he started his talk on how Boolean Decision Diagrams were great for solving puzzles. He used it to solve the Knuth Necklace problem, and then demonstrated his program for sliding block puzzles. He showed how BDD could solve Slitherlink, then introduced Skimperlink, which allows multiple loops, the goal is to find the minimum number of edges to satisfy all given constraints. Amusingly, Wei-Hwa Huang was helping with the slides, and showed a few impressive fast-solving techniques. Don announced an upcoming book, Selected Papers on Fun and Games, which will be out next year (Amazon doesn't list it yet). Speaking to Don later, he shared the quick puzzle with me: "f4e, s9, se5en, ??" I also asked what got him started, and he told me his story on how he won the Ziegler's Giant Bar contest as a boy, pretending to be sick so he could built up the winning word list - what are all the words you can make from 'Ziegler's Giant Bar'?. While he was doing it, he figured out algorithms that could save him time. For example, no reason to look through the C and D pages of the dictionary. Can you name a political party or animals that use all but 4 letters in 'Ziegler's Giant Bar'?
Oskar van Deventer Videos
I also had the pleasure of seeing Oskar van Deventer's latest creations. many of them are shown in the incredible series of videos under the name OskarPuzzle. Many of these puzzles are available for sale at the 3D printing shop Shapeways Oskarpuzzles. Some are also available at Puzzlemaster.ca, for example James Stephens mentions that "Oskar's wurmm puzzle is now available from Puzzle Masters. I am lucky enough to have one of the George Miller produced versions and think it is one of Oskar's best inventions (tied with about 20 other Oskar puzzles, of course, but that's still a pretty exclusive list for him). Oskar has also written up papers for a few of his puzzles, such as Topsy Turvy which mechanically recreates the sporadic M12 group (video). In addition to Shapeways, Oskar mentioned tools Solidworks, Meshlab (STL Repair), and Minimagics (Materialize). A favorite video of mine is the the Caution Cube, a geared puzzle that has drawn Oskar's blood.
George Miller Videos
George Miller, who runs the wonderful site puzzlepalace.com, also has a puzzle video collection under the name MrPuzzleman. The videos of the Geary cube, Fire, and People Put-together (with Oscar) are well worth a look.
Erich Friedman Puzzles
Erich Friedman: Multi-Balance Puzzles, Pyramid Puzzles, Crypto-Product Puzzles, Weight Equation Puzzles, Gold Star Puzzles, and Packing Puzzles have been added to Erich's Puzzle Palace. For example, for Weight Equations, put a digit in each box so that the equation is true. The boxes should also balance, where each digit represents the weight of that box. (His entry on Packing Problems at Math Magic this month is also very nice.)

Gary Foshee puzzle
Gary Foshee gave me this puzzle: "I have two children. One is a boy born on a Tuesday. What is the probability that both are boys?" Answer.
Nob Yoshigahara Puzzle Design Competition
The Floppy cube was the winner of the Puzzle Design Competition. My own entry, Super-Hamilton, didn't win any prizes, but seemed fairly popular. I have two copies left, available for $25+shipping. If there is enough demand, I'll ask Walter Hoppe to make up to 30 more, before I reach the 150 limit.

Tom Cutrofello Puzzle Blog
The latest Games Magazine has a great article on George Hart. Not all of Tom's columns get accepted by Games, and those go into his excellent Puzzle Blog, Gottasolveit.
New Densest Tetrahedron Packing
S. Torquato & Y. Jiao published (in Nature Vol 460, 13 August 2009) a packing method for tetrahedra with a packing density of 0.782021. Exact coordinates can be seen in their page of supplemental information.

Squares vs Cubes
From Asim Shah: Find the two smallest numbers whose difference between their squares is a cube and whose difference between their cubes is a square. As a hint and encouragement, both numbers are between 3 and 12. The next such pair is 384, 640.
Water Retention in Magic Squares
Craig Knecht has work with Walter Trump on the water retention problem, and has some nice results.

Triangular Clock
Jörg Pretz: I have new idea for a binary clock. You can look it it under joerg.pretz.de which has a detail PDF document.

4A = 6V
George Sicherman has shown that 4A = 6V.

Yahoo MathPuzzle Group
A link for the MathPuzzle Yahoo group is at http://tech.groups.yahoo.com/group/mathpuzzle/ .
Material added 28 Jul 2009
Droste Effect Music videos
There are two excellent music videos showing off the Droste Effect. Wild Beasts and Clap Your Brains Off.

Symmetry Festival
The Symmetry Festival 2009 takes place in Budapest, 31 July - 5 August http://symmetry.hu/. You can watch all plenary events of the Symmetry Festival 2009 on-line, Central European Time (GMT +2), Aug 1 - Aug 4.
Material added 26 Jul 2009
Mirror Array
Edmund Harriss built a mirror array using acrylic mirrors bent in just one direction. It gives some nice results.

Gravity Based Puzzles
Inventor P. C. Houlis let me know of some gravity based puzzles that he invented, along with some videos (Cubedron, Krystalledron, Icosedron, and Puzzle Ninja, ). He also has the kastellorizo youtube channel.
Yahoo MathPuzzle Group
I know I should join Twitter and various other sites, but I still rely on the Yahoo MathPuzzle Group to send out notices that I've made an update. With any luck, I'll be doing them more regularly now (though I keep saying that).
Talk to the Times
Will Shortz to a week and answered a lot of questions about crossword puzzles and his methods.
Red Green Blue Maze
Chris Lusby Taylor: I've just been asked to do something for a local school's playground. I planned to use the existing paving slabs as squares but then found that they're laid in an offset pattern, so each has six neighbours.

Enter at the top, cross the blue, green, and red bars, and keep this sequence until you exit at the bottom. Or enter at the bottom, and cross the red green and blue bars, and keep this sequence until you exist at the top.


Demonstrations Site
The Wolfram Demonstrations Project now has over 5000 entries. George Beck and Conrad Wolfram both blogged about it. Many of the flash videos have been added to YouTube.

Galvagni Figures
George Sicherman: I've posted Galvagni figures for polyenns and polydecs.
Various items at Amazon
Some of the books, games, magazines and puzzles I've ordered from Amazon in the past six months. I'm always interested in hearing about obscure recreational math related sites, books, puzzles, and games, so always feel free to write me.

Anti-virus
One puzzle game I haven't been able to find anywhere yet is Anti-virus, by James Stephens and Oskar van Deventer. Online, this is their Bulbous Blob puzzle, long one of my favorite puzzle series.
Mondrian Knight
Julian Courtland-Smith (inventor of Survive!): Please find enclosed 'Mondrian's Knight's Tour' with numeric solution. As a designer, I am obviously interested in the history of art. One of my favourite artists is Mondrian. Looking back, his work looks passe compared with today's modern art, but he did set the tone for the modern architecture of the twenties and thirties which is still enjoyed and practised today. When looking at his art, it becomes obvious Mondrian would not have simply painted a knight's tour on one canvas as this would have obliterated the obligatory white spaces so beloved by him. Therefore, I trialed a few ideas and do believe that this two canvas problem/solution matches his style. (Puzzle in ODG format).

New Packings and Coverings
I was just looking at Erich's packing page, and was amazed at some of the recent improvements. His latest Math Magic deals with Weightominoes.
8 triangles in a circle (April 2008) 8 triangles in a hexagon (May 2008)
9 triangles in a square (July 2008) 6 triangles in a triangle (August 2008)
2 squares covering a triangle (March 2009) 6 triangles covering a square (April 2009)
5 squares covering a circle (April 2009) 5 triangles covering a circle (June 2009)

China Labyrinth
There are 64 possible patterns of black and white around a hexagon. At Mindsports is an amazing solution that combines all of them.
New Elliptic Curve Cryptography Record
Joppe W. Bos, Marcelo E. Kaihara, Thorsten Kleinjung, Arjen K. Lenstra and Peter L. Montgomery have set a new record in Elliptic Curve Cryptography.
Long, Perfectly Packed Rectangles
Brian Trial: Here are some new results that Stuart Anderson was kind enough to render and display on his web site: SPSR with integer aspect ratios 13:1 up to 18:1.

Puzzle-Up Five
The fifth annual Puzzle-up has just started, a 24 problems/24 weeks competition where each week a different problem is put accross for you to think on and try to solve.
Candy Fabrication
The Candyfab 6000 is an intriguing method for printing 3D shapes in sugar.

Tetrapentos
Thérèse Eveilleau, whose Magic Maths is very nice, has put Tetrapentos online. The pieces can be moved with mouse and arrow-keys.
Poker Odds
I've been studying various variants of Poker recently, trying to figure out good sets and matching odds for things like a five-color deck. These could be used to improve various very popular Poker Odds webpages.
Casino Guide
In my study of gambling games, one site I tried with a good selection of casino games is casinoguide.com.
Capture the Cat
A game called Capture the Cat has been making the rounds. It's always possible to win, as shown by Adam Holers.
Material added 21 Jun 2009
Holey Megaminx
A hollow but functional Rubik's cube won a puzzle design competition recently. The high-end of rubik-type puzzles has been the dodecahedral Megaminx. Designer Lee Tutt has made a Holey Megaminx, and it is being made as a limited release.
DodekPuzzle
If you put magnets in small plastic capsules so that they can move in a restrained way, then glue those into polyhedra, they will attach together in a very nice manner. The Dodek Puzzle is based on this, a matching puzzle based on the dodecahedron, with extremely high quality magnetic pieces. These can be crushed and reassembled in about 5 seconds, which makes for an excellent figidity toy. The two puzzles are also excellent. In addition, this is the first mass-produced toy entirely made in the US that I've seen in awhile. A bit larger and heftier than a Rubik's cube. Highly recommended.

Latin Hexagon
Wei-Hwa Huang posted a nice Latin Hexagon on his site.
New Al Zimmermann Contest and Site
At Al Zimmermann's Programming Contests, a new contest has started, Son of Darts.
Harvey Heinz's Magic Squares Site
Harvey Heinz's excellent site on magic squares, magic stars, and other objects, had an uncertain future at the soon-to-die Geocities. A copy of his site is now at Recmath.org.
Anthill Substructure
A youtube video, several tons of cement, and lots of digging reveals an ant colony structure.
Conan Boron Rant
Back in February, Conan went on a rant against Boron. Boron has 4 forms, not three.
Magic tricks with Math
Peter McOwan has made various videos linking magic tricks with math.
The Problemist
A few thousand chess problems are collected in the Problemist Collections.
New Pattern found in Prime Numbers
Benford's law is a well known feature of statistics. A similar phenomenon has been found in prime numbers.
Material added 14 Jun 2009
A Collection of Algebraic Identities
Tito Piezas: Could provide a link to A Collection of Algebraic Identities? After all, solving Diophantine equations is a form of a puzzle too. [An encyclopedia's worth of work -- very nice]
New Mersenne Prime
A new Mersenne Prime has been discovered: 2^42643801 - 1. It's not the largest. MathWorld has the story.
World Puzzle Championship US Qualifier
Signup for the World Puzzle Championship 2009 US Qualifier is now open. There is also a practice test. The qualifier, put together by Nick Baxter, always has about ten pages of great puzzles.
Math Magic
Erich Friedman: the smallest square (not divisible by 5, 7, or 8) that can be tiled with squares of sides 5, 7, and 8 was found by Brian Trial at this month's Math Magic. [Ed- Other news from Erich: 7, 10, 11, the largest circle coverable by five unit squares, and 15 points in a Heilbronn square. He's also added 3 new puzzle types at Erich's Puzzle Page.]

Configurations of Points and Lines
Branko Grünbaum latest book, Configurations of Points and Lines, is a gorgeous gem of a book. collecting all the known information about configurations. In a 4-configuration, for example, there are four lines through every point, and four points on every line. In an extended Euclidean geometry, an 18-point 4-configuration is possible. The figures below all all work as 4-configurations without points at infinity. Amazingly, the first geometric 4-configuration was found in 1990, the second one below.

The first 5-configuration was found in 2007 by Leah Berman. 5 lines through each point, 5 points on each line.

Incidently, Branko's classic Tilings and Patterns is being reissued in paperback at the bargain price of $27.
Simon Tatham's Portable Puzzle Collection
One of the best sites I've seen for puzzles is Simon Tatham's Portable Puzzle Collection. I've seen it before, but didn't have the time at that moment to try it. Recently, I noticed they were all available as a batch install for Ubuntu Linux, and tried all of them. This is a great collection of puzzle games, with Black Box, Bridges, Cube, Dominosa, Fifteen, Filling, Flip, Galaxies, Guess, Inertia, Light Up, Loopy, Map, Mines, Net, Netslide, Pattern, Pegs, Rectangles, Same Game, Sixteen, Slant, Solo, Tents, Twiddle, Unequal, and Untangle.
More on the Klein Quartic
On a whim, I mapped the 24 points of the Klein graph onto a heptagonal tiling (PDF).

Material added 15 May 2009
Burr Puzzles and Numb3rs
Bill Cutler and burr puzzles get a mention in tonight's season finale of Numb3rs. For many links, see my write-up below, or the current cbs.com/puzzle/.
Tiling Pentagons
I recently added Tiling Pentagons to the Wolfram Demonstrations Site. I give exact solutions for all 14 families. A must program to try for anyone that likes neat tilings.
Wolfram|Alpha
The new computational knowledge engine Wolfram|Alpha launches tonight.
Material added 3 May 2009
CRC Encyclopedia of Mathematics, 3rd Edition
The third book that kept me busy: Eric Weisstein's CRC Encyclopedia of Mathematics, 3rd Edition. It's a huge, three volume encyclopedia, all of it available at Wolfram MathWorld. I assisted with the update, compiling the comments and suggestions of thousands of MathWorld visitors, allowing for just as many additions and corrections.

Similar Polyominoes
I've been playing around with polyforms a lot recently. One good paper is Michael Reid's Tiling With Similar Polyominoes, which was expanded some with the October 2002 Math Magic. I used Burr Tools to try out some of the problems at Torsten Sillke's packing site, and at Puzzles will be Played. One puzzle example I made -- all the 2-7 square polyominoes with rotational symmetry can be fit into a 10x13 rectangle. One solution is below, with the center of rotational symmetry given for each of the pieces. You can also look at the Steady State cube from microcubology.

Void Cube and other Variants
The 2007 winner of the Nob Yoshigahara Puzzle Design Competition was the Void Cube (youtube), by Katsuhiko Okamoto. These are now available at gentosha-edu.co.jp. Easier to order are some of the exotics now available at mefferts.com. The mirror block (yousaytoo) is another variant.
Mad Science
In addition to introducing the Bacon lance, Theo Gray's book Mad Science is finally out. Glorious pictures and wonderful write-ups walk you through the wonderful experiments that Theo has tried. I've helped him with a few of them, and suggested others, some of which later wound up on Numb3rs. Our Sodium party wound up getting a write-up in Playboy magazine. (When I was younger, I never imagined I could get into Playboy by doing science experiments). Over at Amazon, try a random sample from Click Inside. More is at his site periodictable.com.

Lasercut Binary Addition
M. Oskar van Deventer: I made a minimalistic binary adding machine. It has two laser cut plates and steel balls running between them. That is all. Here is the YouTube video. The object is a mechanical puzzle aimed at 6-10 year olds. [Ed - Another fantastic Oskar invention. To see many more, check out the May 2009 College Mathematics Journal. It's a Puzzle issue, with lots of great columns by Oskar, Martin Gardner, and Stewart Coffin.]
World Sudoku Championship
Vladimir Zahoransky: I visited World Sudoku Championship held in Slovakia in Zilina. It was fantastic event. Snyder, Kusui, Bertrand, Novotny and Ondrousek all made mistakes in the semi-final. The block was 45 minutes for 4 puzzles, but these 4 puzzles were very, very hard. I used my binoculars to watch the progress of all the contestants. Snyder solved only two puzzles, so his chances at the final were very theoretical. Bertrand had troubles too, only two puzzles. Novoty and Ondrousek solved 3 puzzles. Final part was crazy. Organizer made one mistake and all the contestants struggled with different methods for solving a superhard puzzle. At the end, the Slovakia team scored the golden medal, the Czech team claimed second and Hungarian came in third. Individual part ? polish solver presented best concentration. I have a lot of photos from WSC. I got Thomas Snyder's sign as a souvenir. The puzzles can be seen at szhk.sk, with the English version of puzzles about 2/3rd down the page under "competitions & results". One of the puzzles came from Steve Schaefer, who runs mathrec.org.
Puzzle Design Competition
The 2008 Puzzle Design Competition results have been up for awhile. If you have an idea for an entry for the 2009 competition, you have until June 30 to enter.
Games Collection
At my local gameshop, I recently found examples of The Games Collection, all for under $20. These are excellently made wooden games. I've been trying out Creeper, Megalith, and Fire&Ice.
Game Playing
Do you know how to play Lines of Action, Amazons, and Go? If not, sites like Boardgamegeek can help you to catch up. some of the best of these games are available for play at iggamecenter and gamerz.net. Three new games I was unaware of are Dragons, Attangle, and Yavalath.
Rick's Tricky Six
The paper Rick's Tricky Six by Alex Fink and Richard K. Guy is a fantastic linkage of the 15 puzzle, Moebius transforms, edge colorings, projective planes, icosahedra, the Hoffman-Singleton graph, Steiner systems, and the Golay code.
The Griddle
David Millar: I've added a comments feature on puzzle pages at The Griddle (http://www.thegriddle.net). Hopefully it will help me get good feedback on the kind of puzzles people like to solve. I'll also be releasing my 350th puzzle page soon, and perhaps something else big on my 21st birthday, like some puzzles with a "21" theme. (21 is a triangular number - brilliant! I'm already thinking of some kakuro and sum sudoku.)
18 Black Squares
Jean-Charles Meyrignac: A new record for fewest blocks in a crossword, by Kevin G. Der: xwordinfo.com. Also well worth a look are the main site, and the grid art section.
Tierney Lab
At the New York Times, I should soon have a puzzle in TierneyLab, with a Hamilton-path based puzzle.
The Cube
Jerry Slocum points to a recent video of a person paging through his book The Cube, which is also available at Amazon. Published by the same company that also published mad Science, above.
Wymondham College Math Links
Graham Colman sent a link to the Wymondham College website, and I spent a while checking out the very interesting links and items.
Fetch
I recently attended EbertFest, and saw Sita Sings the Blues, by Nina Paley. Then, she dropped by my office, as a friend of Theo Gray, they both went to the same school. After seeing some of my puzzles, she pointed me to her short film Fetch, which is loaded with dozens of perspective tricks and impossible objects.
Bridged Polyforms
Bernd Karl Rennhak has made some beautifully curved figures that he calls bridged tritans.
New Polyform Oddities
George Sicherman: This full oddity for the Z pentomino is considerably smaller than the previous one. It has 73 tiles. [George has also found a new Galvagni figure.]

Curly Cube
A new metal puzzle at puzzlemaster: Curly Cube. Also looking very interesting are Metroville and The Ball Puzzle.
Jack Good Obituary
Mathematician Jack Good, a colleague of Alan Turing, recently died at age 92.
Foxtrot Puzzle
Bill Amend recent put a puzzle in Foxtrot.
Mathematics of Mirrors
A Philadelphia Inquirer article discusses the mathematical mirrors of Andrew Hicks.
Dodecamorph
Terry Stickels: Here's something from my friend Robert Webb, an Australian buddy who has worked with me on several projects: Dodecamorph.
Recent demonstrations
Recent Wolfram Demonstrations of note include Cayley tables, Finite Field tables, Look and Say Vectorgrams, Solar System Mandalas, Packing Squares with side 1/n, Coin Flips, and Fibonacci Number Interpretations.
Math Reference Sheets
Cody Miller: We just released our new free math reference sheets and this resource maybe valuable to your readers. These free reference sheets cover algebra, geometry, trig, and calculus. There are 6 sheets in all. Our goal at ecalc is to provide good free math resources to students and professionals.
80 Vertex Polytope
Someone was just asking about this, and I could remember where I'd seen it. From Math in the Media by Tony Philips: Eric Altschuler and Antonio Pérez-Garrido published an article in Physical Review last year (E 76 016705 (2007)) in which they described "a four-dimensional polytope, new to our knowledge, with a high degree of symmetry in terms of the lengths of the sides." They found the configuration "by looking at the ... problem of finding the minimum energy configuration of 80 charges on the surface of the hypersphere S3 in four dimensions" with the energy function Σ(1/rij) where rij is the distance between the i-th and j-th points, and the sum is taken over all pairs of distinct points. (They remark that they cannot prove this is actually a global minimum, but add that "even good local minima can be interesting or important configurations.") The other N for which they found symmetric configurations are 5, 8, 24 and 120; corresponding to the 4-simplex, the dual of the 4-cube, the 24-cell and the 600-cell. The authors give a method for visualizing their 80-vertex polytope in terms of the Hopf map S3 --> S2. They triangulate S2 with 16 equal equilateral triangles: 4 abutting the North Pole, 4 the South, and a band of 8 around the Equator. This polyhedron has 10 vertices. Each of these vertices corresponds to a circle of the Hopf fibration, along which they describe explicitly how to place 8 of the polytope's vertices. Another description of the 80-vertex polytope was published by Johannes Roth later in the same journal (E 76 047702 (2007)).
Optimal Packing of 6 Circles
A student project led to a great paper: Optimal packing of 6 circles in a flat torus.
Invisible Car
An impressive illusion by artist Sara Watson resulted in an invisible car.
Replica Narwhal Tusks
If you would like to get a replica of nature's most amazing spirals, Bone Clones has narwhal tusks.
Langton's Ant video
A great video by aldoaldoz discusses many varieties of Langton's ant.
Games and Puzzles Miniconference
Matthew Kolokoff: Ed! Why aren't you at the Games and Puzzles Mini-Conference, right now? Ok, I think it's in Israel, but that's no excuse. [Ed - looks like it was a great event.]
Material added 9 Mar 2009
Mathematica Home Edition
For years, recreationalists have wanted a less expensive version of Mathematica. Mathematica Home Edition is now available for $295.00. It's pretty much designed for at-home users, without some of the advanced capabilities more attuned to commercial usage.
My Second Gardner Tribute Book
Mathematical Wizardry for a Gardner, edited by Ed Pegg Jr, Alan Schoen, and Tom Rodgers, is now available for pre-order at Amazon.com. Articles were contributed by Gary Chartrand, Jeremiah Farrell, Stanley Eigen, David Lister, Istvan Orosz, George I. Bell, Bob Harris, Derek Kisman, Richard Guy , Alex Fink, Rodolfo Kurchan, Peter Gabor Szabo, Matthew H. Baker, Aviezri Fraenkel, Thane Plambeck, Dick Hess, Mogens Esrom Larsen, Istvan Lenart, Colm Mulcahy, David Rhee and Jerry Lo, Robert Bosch, Stanley Eigen, Chaim Goodman-Strauss, George W. Hart, Akio Hizume, Robert Barrington Leigh, Ed Leonard, Ted Lewis, Andy Liu, George Tokarsky, Karl Schaffer, and Lajos Szilassi.
Puzzles on cbs.com
Another thing keeping me busy has been weekly puzzles on cbs.com. I wrote a blog item about the puzzles so far.

Wolfram|Alpha
Stephen Wolfram has announced Wolfram|Alpha, another project I've spent some time on.
MathWorld Updates
And another biggie, I've been working with Eric Weisstein to update Wolfram|MathWorld. Long lists of updates for January, February, and March. Sorry for the long delay in an update here, I'll try to get to all the material that's been sent in soon.
Material added 12 Jan 2009
Happy 1 * 2 - (3 - 4 - 5) * 6 * 7 * 8 - 9
Denis Borris notes the above, made with only multiplication and subtraction. I noted that 2010 made all but four letters of "counting down the days," and Will Shortz used it. This is a really late update for me. The December ice storms caused me to lose about 3 days of vacation, due to a lot of very large branches on my fence, house, and around my yard. I worked on two Numb3rs episodes, and caught up on my columns for Japan Airlines. I did a lot of reading of mathematical books and papers that have been accumulating. And I finished off my second Gardner tribute book. Apologies for the delay.
My First Gardner Tribute Book
Homage to a Pied Puzzler, edited by Ed Pegg Jr, Alan Schoen, and Tom Rodgers, is now available for pre-order at Amazon. Articles were contributed by Robert Cotner, David Meyers, Jerry Slocum, sarah-marie belcastro, Carolyn Yackel, Peter Hilton, Jean Pedersen, Byron Walden, Sandor Kabai, Louis Kauffman, Michael Longuet-Higgins, NJA Sloane, Peter Gabor Szabo, Zsofia Ruttkay, Oskar van Deventer, David Dillon, Jeremiah Farrell, Yossi Elran, Robert Friedhoffer, Judith Morrel, Robert Fathauer, Adrian Fisher, Markus Gotz, Serhiy Grabarchuk, Thomas Hull, Kate Jones, Rodolfo Kurchan, Mogens Esrom Larsen, Earnest Hammingway, Ann Schwartz, Jeff Rutzky, Norton Starr, James Stephens, and Robert Wainwright.
Mathematica 7 Reader launches
Jeff Bryant blogs about the new Mathematica 7 Reader, and a couple hundred new math demonstrations (now 4406). Some notable new demos include Manipulating Graphs, Irrational Tiling, Alternating Subtriangles, Truel World, Lattice Circles, Earth's Second Moon, Isotope Browser, and Gambler's Ruin. Another recent blog item concerns the Yellowstone Earthquakes.

Plane Boarding
Dick Saunders Jr: John Paulos is always coming up with something interesting! He shows plane boarding can be cut to 1/6 the time.
Circles of Descartes, Mod 12
Playing around with my Circles of Descartes program, I noticed that any integer solution, mod 12, had only 4 different values, either 0149, 0589, 367A, or 236B (where A=10 and B=11). I wondered about the minimal set of circles that would cover all integers, but didn't find it. Likely, there are other moduli that are also important. Click on any image for a much larger visualization.

Melbourne Museum
Kiki Tanousis: Thanks for plugging our city. You might want to include the cube attached to the Melbourne Museum.
Z Oddity
George Sicherman: This oddity for the Z pentomino has 125 tiles and full symmetry.

Late Christmas Tree
Serhiy Grabarchuk: Here is a Strimko inspired Christmas tree.

La Ora Stelo
Jacques Ferroul: I added some pages : flowers, witch's hats, pentagona series. [Ed- A gorgeous series of pages.]
#1 Job: Mathematician
According to the Wall Street Journal, the #1 Job is Mathematician.
The Unitarity Triangle
In the latest Particle Physics Booklet (free), one new section is about the Unitarity Triangle, based on the CKM Matrix, which describes the difference between matter and antimatter. In order for the Standard Model to work, the Unitarity Triangle has to be perfect.

The Tiling Listserver
Brian Wichmann has added a series of improvements to the Tiling Database.
Tesla Coil Music and Lenz Forces
Lots of interesting music made with huge Tesla coils has been posted to Youtube, including Sugarplum, Nintendo Theme, Tocatta and Fugue, Creepy circus. The site arcattack.com has more. Did you know that near an MRI, a block of aluminum will fall slowly due to Lenz forces?

Fractals with Apophysis
The article 40 Amazing Fractals, using the program Apophysis, shows many gorgeous images.

Penrose Sudoku
Wei-Hwa Huang has posted a Penrose-base Sudoku on his blog. With Slocum, Singmaster, Gebhardt, and Hellings, he's also written the book The Cube, about the Rubik's cube (page 5). The same publisher will put out Theo Gray's Mad Science (page 8). Both books will come out in the spring.
Erich Friedman's Xmas Puzzles
Erich Friedman made five great X-mas themed puzzles. For example, Cut the ornament into 24 equal shapes. Four of the shapes have already been cut to start you off (see his link for the answer). His Math Magic this month combines polyominoes and chess pieces.

Paterson's Worms Update
Benjamin Chaffin: Hope all's well with you. I haven't had much time for math fun lately, but I did manage to update my page on Paterson's worms. I now have pictures of every worm, including close-ups around the origin so you can see the individual line segments. It's fun to just scroll through and look at all the different shapes.
Golly 2.0 Released
For explorations of Conway's Game of Life and similar automata, Golly 2.0 is now available. Golly now supports multiple algorithms, and universes with more than 2 cell states. Tom Rokicki has extended Gosper's hashlife algorithm to allow up to 256 states, and that means Golly can handle many new types of CA. Andrew Trevorrow has added many more improvements.
Material added 30 Nov 2008
Mathematica 7 launches
Mathematica 7 has launched, as noted in Stephen Wolfram's blog post. Among the new features are huge equation typesetting, transcendental roots, and discrete calculus. Looking back at the version 6 discussion, it's perhaps inevitable that comparisons will be made to CAR, CGsuite, GAP, Geogebra, Geometer's Sketchpad, Geometry Expressions, Geonext, LaTeX, Magma, Maple, Matlab, nauty, noneuclid, Pari, Sage, or SeifertView. In other news, the Wolfram Demonstrations project now has over 4000 interactive math demos.

CAs on XKCD
And about the same time, cellular automate were used in webcomic XKCD.
More Demonstrations
Some of the newer demos are Complex Newton's Map, Wire and String Puzzles, and Social Golfer Problem.

La Ora Stelo
Irrational tiling systems have the property that for a sufficiently large room, it can be tiled almost perfectly without any of the tiles needing to be cut. It's very tricky to make a nice puzzle out of this, because they quickly become human-insolvable. For example, I consider that one of my own worst puzzles is the 14 Tridrafters, due to the rarity and nonintuitiveness of the solutions. To my surprise, it turns out that the Golden Triangles are "nice" for human solvers.

Jacques Ferroul seems to be the first to make a polyform set out of the golden triangle and golden gnomon, which has 2 shapes at order 1, 8 shapes at order 2, and 22 shapes at order 3. Add 5 more triangles to increase solvability, and a perfect pentagon is possible. The solving area is etched with 8 more perfect pentagons of different areas to solve. Jacques calls them the Polyore, and it impressed Kate Jones enough that it is now available for sale at Kadon Enterprise. There, an extra page on polyore is available. Jacques has put together another 8 pages of material. In addition, he is offering a pair of $150 prizes, with no purchase necessary. Recall I mentioned irrational tiling systems? Jacques has identified 148 possible trapeziums that might be solvable with the basic or extended set, and will award a prize to whoever solves the most of them. I'm not sure how well computers will do with these, since there is a fractal nature to how the shapes behave. I bought a set, and it's my favorite puzzle purchase of the year. In addition to all the nice math behind it, it's gorgeous, too. Also at gamepuzzle, large solutions.

Mathematical Coloring Book
Alexander Soifer, a former professor of mine, my reason for having Erdos number 2, and the editor of Geombinatorics, has finished his long-time work The Mathematical Coloring Book. The book covers many aspects of mathematical coloring. For example, what is the chromatic number of the plane? In the book, I show that 1/302th of the plane can be removed, and a unit six coloring is possible. All the thick bars have unit length. The x value is the first real root of 1 - 40x + 448 x2 - 720x3 - 11288x4 + 38048x5 + 88576x6 - 491328x7 + 391824x8 +1082624x9 - 2217984x10 + 231424x11 + 3368960x12 - 4374528x13 + 2490368x14 - 655360x15 + 65536x16.

Periodic Table Element Cards
Theo Gray, of Popular Science, Mathematica, and periodictable.com fame, has made the ultimate element card deck. He's also made an element jigsaw puzzle. They are large enough to cover a wall, or an innocent passerby.

New Puzzles by Erich Friedman
Erich has published a number of great new puzzles, including: 23maze, plustimes, letterorder, trios, duplicate, insert, and anagram. For his December Math Magic, Erich is looking at graphs with numbered vertices, where each vertex is the sum of digits in adjacent vertices. The Math Magic Archives are looking increasingly spectacular.
Pictures of Mathematicians
The Dubner Library has collected several hundred pictures of famous mathematicians for maa.org.
FBI 100th Anniversery
For the 100th anniversary of the FBI, Dylan Bruno of Numb3rs gave a congratulatory message.
Surf
Surf is a nice program for algebraic surfaces.
Math Humor on the Komplex Plane
Travis has collected various pieces of math humor for The Komplex Plane.
A Cube, in Phonecam Magic
The tricks behind a Phone Cam Magic video does nice trickery with a white cube.
Musical Road
By using grooves to induce sound waves, a musical road has been made.
Puzzle Design Competition and Puzzle Palace
The results of 2008 and the rules for 2009 for the Nob Yoshigahara Puzzle Design Competition are available. One of the winners is Vesa Timonen's Tangerine puzzle. George Miller has put several of these puzzles on his site: Ringworld (Oskar), TriGears (Oskar), Rainbones (Knuth), and Perfect Packing (Knuth).
New Cast Puzzle
A new Cast Puzzle is available: the Cast Equa. Another superb design by Oskar van Deventer.

23 Mathematical Challenges
DARPA released a list of 23 Mathematical Challenges that they will provide major funding for. CNN did the article DARPA Mathematical Challenges, and they used a graphic of mine for the Riemann Hypothesis (challenge 19).
Slashdot math Articles
Slashdot has had several nice mathematical items. First, an AMS article on formal proofs (Science News and Slashdot). Second, a Science News article on Knot Theory (and Slashdot). Third, a Science News article on the card shuffling of Persi Diaconis.
More on Theseus and other iTunes Puzzles
Jason Fieldman has put Theseus and the Minotaur on the iPhone, as mentioned at logicmazes.com. There is also an iPhone Puzzle blog, now, by Michael Cysouw. Subway Shuffle, by Bob Hearn, is another nice app. (But I don't actually have an iPhone, yet).
Stocks Update
Several asked me how my venture into the stock market is doing. I mostly went into electrical utilities with good dividends, good cash flow, and no debt. After a great week, I'm down 5% two months after getting in. I've made novice mistakes, so I'm practicing more with a no-real-money account on fool.com.
Automating a series of 3D figure in PovRay
Bob Harris: I've recently posted a simple example of how I automate the drawing of polycube packing solutions, including a couple python programs I wrote to control povray (povray does the actual rendering).
A Lifetime of Puzzles
A new book honoring Martin Gardner is available: A Lifetime of Puzzles. Various fans of Martin contributed articles, including Colm Mulcahy, Persi Diaconis, Ron Graham, Jerry Slocum, David Singmaster, Roger Penrose, Oskar van Deventer, Rik van Grol, Peter Winkler, Stewart Coffin, Frans de Vreugd, David Klarner, Ken Knowlton, Raymond Smullyan, Jeremiah Farrell, James Randi, Solomon Golomb, Dick Hess, Bill Gosper, David Wolfe, me, and Martin Gardner himself.
Optimal 25-mark Ruler
The 25-mark Golomb Ruler has been proven by distributed.net. It proves the 1984 result by Atkinson and Hassenklover (my related column). (Slashdot entry)
Twisted Grid
Here's some very twisted graph paper.
Extreme Rock Paper Scissors
I haven't worked out the full graph, but the 25 possibilities can each defeat 12 others in Extreme Rock Paper Scissors.
Scientist Behind Nobel Prize now a Courtesy Shuttle Driver
Douglas Prasher laid the groundwork for major research, when his funding ran out. So he passed it on to interested colleagues. They won the Nobel Prize in Chemistry.
Rotational Pentahex Oddity
Making a rotationally symmetric figure with a number of X pentahexes relatively prime to 6 has proven quite tricky. George Sicherman has managed to do it. He's added it to his Polyform Oddities page. He has also recently been exploring Baiocchi Figures for Polycubes.

Peter Grabarchuk Book, and Strimko
The Grabarchuk family has launched Strimko, a sudoku-related puzzle. Also, Modern Classic Puzzles is now out, by Peter Grabarchuk. I picked up a copy -- a very nice collection of 200 new puzzles. He's also made a new online puzzle, Untouchable 11. Put the 11 nets that fold into a cube into a 12x12 square so that no two nets touch each other.
Mobius Game
Mark Steere: This the first known game (at least by me) for a one-sided strip: Mobius. A filled board always produces exactly one winner. [Ed-Nice idea]

Material added 16 Nov 2008
Will Shortz on the Simpsons
My friend for three decades Will Shortz will be a guest voice on the Simpsons tonight. It seems Lisa Simpson will become a big fan of crossword puzzles. Crossword composing master Merl Reagle will also lend his voice.
4000 Demonstrations
Now with 4000 math demos, the Education Portal, and new demonstrations on complex polynomials, drilling a hexagonal hole, powers of complex points, and exit times of Brownian motion.

PBS on Mandelbrot
Dick Saunders Jr: This is a good video on Mandelbrot fractals, etc. (North America only, sorry).
Viewmonster
I've been a fan of Lemon Demon for years now. In terms of favorites in my own playlist, he's the only one that beats Bach. Neil's latest album, Viewmonster, has been my favorite now for over a month now, bearing well even through my own harsh overplaying. I've been listening to music a lot lately.
Virginia Pegg (1944-2008)
After a long illness, my mom died in her sleep on Sunday, November 1. She will be missed.
Material added 23 Oct 2008
Buy Low, Sell High
Sorry about the recent lack of updates. First, there was a lot of support work for Numb3rs. There was a convention at Miami U. Then I started studying the stock market. Today, I'll use Scottrade for a few purchases, after using Yahoo Finance and Motley Fool for research. Some of the lessons I've learned... 1. There is never a rush to get in. 2. Have a watch list of companies you want to buy. 3. Be patient. Doing all the mathematical study has been perhaps a bit too fascinating.
Numb3rs
I just finished some work on the 11th episode. Our numb3rs.wolfram.com site has been expanded, and I'm doing a weekly math puzzle for CBS, at cbs.com/puzzle.
Demonstrations
In addition to the new Education Portal, Wolfram has been publishing lots of new Demonstrations, including some nice ones on the Golay Code, Voter Model, Nowhere Neat Squaring, Tetrads, 57-cell, Water-pouring Problem, Irreptiles, Galactohedra, 2-(64,8,1) Design, and Waterman Polyhedra. I've particularly been interested in the 57-cell. I believe it is the key for the 57-regular Moore Graph problem.

Tendry's Tales
I'm a huge fan of DROD, and they've just released their fourth major release, Tendry's Tales. I like it so far, but I'm not sure I like it more than Journey to Rooted Hold or The City Beneath, yet. Those two are my favorite games of all time.
Improved Pancake Sorting
You've got a stack of n pancakes of various sizes. How many flips with a spatula are needed to sort them? Thirty years ago, Bill Gates put down a bound for an answer. He's now been beaten, as explained in an article by Ivars Petersen, Improved Pancake Sorting.
4D Sudoku
I sent a puzzle email to the MathPuzzle Mailing List about the 4D Sudoku puzzle. Nyles Heise tried out the site. Nyles: "They have an on-line version of the puzzle as well as a handheld. Fortunately, I was able to be the first to solve the on-line version and was sent a complimentary hand-held version as the first solver. It is a very cool, very well designed gadget."
Adobe CS4
I did a long study of vector software, and finally decided on Adobe Illustrator and Wolfram Mathematica for my own purposes. I just got Adobe's latest upgrade. Downside: I had to clear away 20GB of space to install CS4. Yikes. Most of those were temp files I could then remove. So far, though, I'm liking CS4 a lot.

Material added 16 Sep 2008
New Mersenne Primes
The next Mersenne exponents are 43,112,609 and 37,156,667. A Mersenne prime press release is available. And the MathWorld page is freshly updated.
Material added 7 Sep 2008
Martin Gardner's New Mathematical Library
With help from Donald J. Albers, Gerald L. Alexanderson, John H. Conway, Richard K. Guy, Donald E. Knuth, and Peter L. Renz, Martin Gardner is releasing updated versions of his Mathematical Games columns. The New Martin Gardner Mathematical Library will soon be available from Cambridge. Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi and Origami, Eleusis, and the Soma Cube are available for preorder at Amazon. Some copies are being given away free at the Cambridge Blog. Just solve the puzzle for a chance to win the book.
Will Shortz's KenKen Puzzle
Will Shortz has launched a new puzzle series called KenKen. KenKen 1, KenKen 2, KenKen 3 and a KenKen giftbook are available for October preorder at Amazon. Will made a video to introduce KenKen. Two more videos with Will Shortz were done by Forbes and Oprah. Some online puzzles are at the KenKen site. The original creator is Tetsuya Miyamoto.

Nested Klein Bottles
The photo of nested klein bottles at sciencemuseum.org.uk is worth a look.
Two Alphametics
Narasimhan Eswaran: Corals are made up of polyps and polyps make a coral. The first has two solutions, the second has a unique solution. POLYP CORAL
OLYP ORAL
LYP RAL
YP AL
P L
CORAL POLYP
New Demonstrations
There are many new Wolfram Demonstrations to peruse. The Houses and Utilities Crossing Problem, Half-Distance Rules with High Resolution, L'Hospital's Rule for 0/0 Forms, A Triangle Model of Criminality, Dice Probabilities, Spectral Realizations of Polyhedral Skeleta, Simulating Harmonographs, Passing a Cube through a Cube of the Same Size, and Reduce-Replicate-Rebuild are worth a look.

Rubik's Cube vs Octopus
Octopi like Rubik's cubes. Here's a story and picture.
Rubik's Cube vs Tiger
Tigers like Rubik's cubes. Here's a video. (I posted Spiderman vs Rubik's cube a few weeks ago).
Rubik's Cube vs Will it Blend?
"I'm going to press the solution button." (Thanks, Kara)
Forced Magic Square
It's easy to make a square with numbers 1-16 in order. 1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
9 4





Add a second square, so that for any pair of numbers 1 to 16, the chosen pair will be in a row, column, or main diagonal in exactly one of the two squares. The first row starts 9, then 4. What is this square? Hint: it's a magic square. Send Answer.
Puzzle-Up Competition
Emrehan Halici has started a new series of puzzles at puzzleup.com.
Two Tiny Polyform puzzles.
Puzzles by George Sicherman and myself. 1. Arrange the 4 pentiamonds to make 2 identical shapes. 2. Arrange the 4 tritans to make 2 identical shapes (in red, below, from the Tan Tricks set). Both solutions are unique. Send Answer. I'll also offer $25 for an unsolved problem: Arrange the 25 pentapents into 5 identical shapes, each with 5 pentapents. Could be impossible.

45th and 46th Mersenne Primes Found
Verification has started for two new Mersenne primes. Sketchy details are at mersenne.org. A forum discussion is at mersenneforum.org.
SIGGRAPH Winners
The animation Mauvais Role won the Jury award at SIGGRAPH. Two other winners are Our Wonderful Nature and Oktapodi.
Cast Vortex
I just got a copy of the beautiful Cast Vortex. I haven't solved it, and I can't fathom how it got designed.

Henri Cartan Dies at age 104
Henri Cartan passed away on August 13. Science News and the New York Times had articles about him. The American Mathematical Society interviewed Cartan in 1999.
Seeing in 4 Dimensions
A full movie series about the 4th dimension has been posted at dimensions-math.org. Julie Rehmeyer has the story about it, Seeing in 4 Dimensions.
Arctic Becomes an Island
For the first time in human history, the Arctic is now an island (New York Times). Noaa.gov has an animation.
Non-rigid Polyforms
Alexandre Owen Muniz: I have a new web page for non-rigid polyforms. Also, a new section for pentomino chains on my misc. polyomino exploration page.
X and Z Pentacubes
George Sicherman: This is the smallest solution I've found for the X and Z pentacubes. It has 20 tiles with 4-rotary symmetry. I've also posted some new Galvagni figures for pentacubes.

Material added 5 Sep 2008
Topsy Turvy puzzle
M. Oskar van Deventer: Here is a YouTube video of the Topsy Turvy puzzle, which I just have successfully prototyped with the help of Peter Knoppers and George Miller. This puzzle is an implementation of the M12 puzzle, published in the July 2008 issue of Scientific American by Prof. Igor Kriz. The M12 group is a so-called "simple sporadic group" of permutations of twelve tokens. Prof. Kriz used the permutations "invert" and "merge" to construct the M12 group. My tokens are twelve disks, numbered 1-12. By cranking the handle either left or right, the tokens are entered into the mechanism that rearranges the tokens. Although the permutations "left" and "right" are slightly different from those used by Professor Kriz, they construct the same M12 permutation group. Or phrased differently, they make same fiendishly difficult puzzle.

Material added 4 Sep 2008
New Wolfram.com Front Page
Hotly following our new Demonstrations page change (now with 3636 math demos), we now have a new look for our main wolfram.com page. I've got many more updates planned for the weekend. Click the link to see the spiffy new animation.

Material added 19 Aug 2008
Rubik's Cube: 22 Moves Suffices
Tomas Rokicki: Twenty-Two Moves Suffice.

With a total of 1.28 million cosets solved, we have shown that every position of Rubik's cube can be solved in 22 or fewer face turns.

This required approximately 50 core-years of CPU time contributed by John Welborn and Sony Pictures Imageworks.

No distance 21 positions were found in this search, despite solving a total of more than twenty-five million billion cube positions.

There is a short article in New Scientist (August 9th edition) on this problem and this result.

The same techniques for the proof of twenty-five moves were used, just on many more computers.

I have found 310 cosets with an upper bound of 18, and about 82,000 with an upper bound of 19 (or less); all the rest have an upper bound of 20 or less.

My most profound thanks to John Welborn, Sony Pictures Imageworks, Herbert Kociemba, and Silviu Radu, and any others who have helped me over the past couple of years.
Material added 17 Aug 2008
Square Hole Drill and Other Demos
A slew of new demos at Wolfram Demonstrations are worth a look, especially the Square Hole Drill by Stan Wagon. A few more new demos include Triangle Interior, Prufer Codes, Dissections by Izidor Hafner, Line Shadows In Every Direction, The Disappearing Square, Projections Of The 16 Cell, and Albrecht Durer's Pentagon.

Fractal Behavior in the Josephus Problem
Student Daisuke Minematsu and his classmates have noticed that the Josephus problem has fractal behavior.

Gauss Code Loops
Since I was 6 or so, I've doodled with closed, self-intersecting loops. Jaime Rangel-Mondragon wrote a simple demo called Self Intersections In A Polygon, and that reminded me of Gauss codes, which are useful for knots. You may remember them from Martin Gardner's New Mathematical Diversions, in the chapter Victor Eigen: Mathemagician. As an example, draw a simple closed loop that crosses itself 3 times, and put an arrow on it. Following the path, the loop will cross itself 6 times. Label the odd crossings (the 1st, 3rd, and 5th) with numbers 1, 2, and 3. The even crossings (2nd, 4th, 6th) will be a permutation. Your drawing will look like one of the following loops:

Note that each of the order 3 permutations can be represented as a loop. I then wrote a demonstration for exploring Gauss code loops. Every closed loop corresponds with a permutation, but not vice-versa. For example, (34512) requires a sixth crossing due to nonplanarity. What rule describes the permutations which can't be drawn as loops? Turns out that By Laszló Lovasz And Morris L. Marx solved this problem (Bull of the AMS, Jan 1976, p. 121-122) with a brilliant short paper: A Forbidden Substructure Characterization Of Gauss Codes. Puzzle: find a simple closed loop with 9 crossings that becomes a simple quartic graph when crossings are changed to nodes.
New Yorker Article on Puzzles: The Eureka Hunt
The article The Eureka Hunt by Jonah Lehrer in the New Yorker discusses insight and puzzle solving.
Prime Sums Contest
Hugo Pfoertner: We are now running a new round of the Al Zimmermann's Programming Contests on "Prime Sums". Jean-Charles will "retire" as a contest organizer and programmer of the contest webpage after the current contest, which will run until 10 Nov 2008. After 3 contest days we already have 78 participants, and the usual suspects like the extraordinary Vadim Trofimov from St. Petersburg in Russia already have taken the lead.

Trofimov has already has won previous contests. One of the most fascinating contests producing incredible patterns was the snake folding contest running until end of 2006, with Vadim as winner. In the meantime a small group of German mathematicians has continued to search for improved folded snakes. Their work is documented in two webpages at enginemonitoring.net and rwro.de. Two examples are the colored zigzag snake and the colored mid-snake. There is also a link to special closed snakes, like the one below. [Ed- A previous Zimmermann contest winner, Tomas Rokicki, recently proved that any arbitrary Rubik's Cube position can be solved in 23 moves or less. He solved it with the help of the Spiderman 3 renderfarm.]


Oskar's Interlocking Spirals
Oskar van Deventer: My artical on Interlocking Spirals was published in Puzzlers' Tribute, A Feast for the Mind. Here is a gif animation illustrating the geometry of the spiraling Interlocking Spirals. Does there exist a useful application of this geometry, other than puzzles? [Ed: any ideas? Oskar can reached at planet.nl, by using his name m.o.vandeventer]

The Politics and Polls of 538 Delegates
Some of the sites I've found interesting for the statistical analysis of the upcoming US election are fivethirtyeight.com and pollster.com. There are dozens of sites you can check (Google "electoral map"), and the predictions are literally all over the map. A different map of recent interest: The Arctic Map.
Photos from the Bridges Conference
Some photos of the 2008 Bridges conference are at Flickr. Below is a 3D printing of George Hart's Toroidal Helical Sweep.

Computer Beats Go Pro
From Slashdot: Bob Hearn writes "I was in attendance at the US Go Congress match yesterday where history was made: the go program MoGo, running on an 800-core supercomputer, beat 8-dan professional go player Myungwan Kim in a 9-stone handicap game. Most in the audience were shocked at the computer's performance; it was naturally assumed that the computer would be slaughtered, as usual. Go is often seen as the last bastion of human superiority over computers in the domain of board games. But if Moore's law continues to hold up, today's result suggests that the days of human superiority may be numbered." [Ed - Bob Hearn is frequently mentioned here. Bob Hearn's website has many spectacular articles.]
Large Hadron Collider and Rap
Incredible pictures of the Large Hadron Collider are available at boston.com. The official LHC site seems tame by comparison. There is also the Large Hadron Rap, a music video which sums up many aspects of the project in five minutes.
Domino Logic
Another video, by Neil Fraser, shows domino logic gates.
Colorful Sea Slugs
Nudibranchs, or sea slugs, are some of the most beautifully colored creatures around.
Places to buy puzzles
The comprehensive online puzzle shops seem to be brilliantpuzzles.com, seriouspuzzles.com, and puzzlemaster.ca.
Whotsits
From James Dalgety (puzzlemuseum.com): Some Wotsits can be found at BBC News: Midweek Quiz: Inventions.
Upcoming Convention Appearances
In case you'd like to see me at a convention, I'll be going to two in the near future. On Sep 26-27, in Oxford OH, I'll be an invited speaker at the Recreational Mathematics conference. On October 23-25, in Champaign IL, I'll give a talk at the Mathematica Users Conference.
Oskar's 4 Bit Mazes
Todd Neller: Back in 2001, you mentioned M. Oskar van Deventer’s 4-bit maze at clickmaze.com. I especially liked the non-progressive 4-bit maze variation, and it struck me as an excellent beginner electronics project for my students. I was inspired write a simple generator for such mazes at cs.gettysburg.edu.

This applet’s mazes are generated by a simple stochastic local optimization that respects some graph constraints in making graph changes, while meeting other constraints through the iterative improvement process. What are the best sources for maze generation algorithms? I’m aware of Pullen’s online list of standard maze generation algorithms, but in the case of 4-bit mazes, one is seeking to generate random directed graphs with given edge constraints. Are you aware of resources along these lines relevant to directed graph maze generation? [Ed: Any ideas? At gettysburg.edu, Todd can be reached at tneller. Oskar van Deventer: "Wow, your implementation is fantastic! Well done!"]
Costas Arrays
In Rulers, Arrays, and Gracefulness article, I mention Costas Arrays. 2,4,8,5,10,9,7,3,6,1 is one such array. On each row of the difference table, values are distinct. The site costasarrays.org is now dedicated to these objects. No arrays are known for orders 32 and 33.

ABC Conjecture
A page by Bart de Smit devoted to the ABC Conjecture is also worth a look. One nice new triple found by Ismael Jiménez Calvo: 238374 + 2283711419361·127·1732 = 1817443248172.
Cold Boot Attacks
Dick Saunders Jr.: Here is a link including an interesting video of an Encryption Cold Boot Attack. [Ed - Fascinating]
Pentaking Oddities
George Sicherman: I finally found a bilateral oddity for the last pentaking! It has 109 tiles.
A Problem Solving Competition
From SlashDot: "Today, the CADE ATP System Competition will pit about 20 of the worlds most powerful mechanical mathematicians against each other — and for the first time they can win not only honour, but a monetary prize. The systems will reason against the clock on tasks ranging from undergraduate math problems and Cluedo-like puzzles to figuring out the possible responsibility for terrorist attacks from giant knowledge bases. If you think that is not impressive enough, they are doing it at a rate of 12 problems per hour, all day long. The competition starts at 10 a.m. in Sydney, Australia, which is midnight UTC. Live results will be available at the competition page. For added geek appeal, most of the contenders are available under open source licenses, so if you are weak in logic you can hack up your own brain extension and run it on an iPhone."
Material added 27 Jul 2008
Lyons + Mankiewicz = Monica Lewinsky + Z
The replacements of Ebert & Roeper are Lyons & Mankiewicz, which has an interesting anagram. Starting with that, I wrote a Wolfram Blog item about anagrams and transposals.
Erich Friedman's House, Arrow, and Zigzag
Erich Friedman: Connect the houses in pairs so that only 2 different distances are formed. It's harder than it looks! answer. This is an example of a House puzzle. I've also added more new puzzles to Erich's Puzzle Palace. Namely, Binary Product, Arrow, Zigzag, and Lightbulb.

2D Mastermind
Chris Innanen: Last night I threw together a game idea I had and today was passing it out for playtesting to some of my friends through IMs. One of them suggested I contact you for your opinion. So here it is: Mastermind Squared. [Ed - interesting. In a 2D field, move colored squares around until the across and down clues are all perfect.]
Tilting Sliding Block Puzzles
Alex Polonsky: There is a new puzzle game at puzzle4u.com, a tilting puzzle game called Spin-In. It's like a mechanical puzzle, but there is no way to built this game in the reality.
Bob Henderson: I hope you can look at SLED Gravity Blocks, a collection of 40 new virtual slide puzzles at Nick Baxter's site. [Ed - two very nice sets of sliding block puzzles based on tilting.]
Polyhex Compatibility
George Sicherman: I've posted a page of Mixed-Order Polyhex Compatibilities. Comments are welcome.
Equivalent Perimeter and Area
Denis Borris: I found these 2 right triangles for which 3 Heronian triangles have same Perimeter and Area: 204 - 560 - 596 (right), 200 - 578 - 582, 260 - 476 - 624, 296 - 435 - 629 all with P = 1360 and A = 57120. Second: 528 - 630 - 822 (right), 462 - 738 - 780, 500 - 666 - 814, 549 - 606 - 825 all with P = 1980 and A = 166320 These are the 2 lowest primitives (unless I goofed and missed some).
Multimagic Squares
Christian Boyer has posted new updates to multimagie.com. Part of it is a Coxeter 1941 problem, of a magic square of triangular numbers.
Spore Prototypes
Derrick Schneider: I'm now a programmer at Maxis, the company making the videogame Spore, and I thought you might be intrigued by the Biome cellular automata program we released. We've been releasing dev prototypes for our users to play with. Here's the link: spore.com/comm/prototypes. [Ed - Interesting programs. For cellular automata exploration, I prefer Mathematica, Demonstrations, NKS, and Golly.]
50 Thousand Tornados
The Tornado History Project has lots of data, videos, photographs and maps of 50 thousand tornados. For example, Here are the locations of the 51 Fujita-5 tornados since 1950.

Irfanview 4.2
My favorite imageviewer, Irfanview, just got an upgrade. If any of my Adobe programs could launch instantly, I'd use them more, but most of the time I prefer the instant results of Irfanview.
Rotary
David J Bush: In Christian Freeling's chess variant "Rotary," the board is a 9×9 square grid. The kings are circular disks with pointers in four equally spaced directions, oriented in one of two ways: like an × or like a +. With just the two kings on the board, each move consists of either switching the orientation of your king from + to × or vice versa without moving it, or moving it one space in one if its indicated directions followed by optionally switching its orientation. You may not pass. The object is to deliver checkmate. Stalemate is impossible. Under what conditions in this two piece endgame is it possible to force checkmate, as opposed to a draw due to insufficient material? A discussion is at boardgamegeek.com.
Abundant numbers
An abundant number is one where the sum of divisors other than itself is greater than the number. The smallest pair is 5775, 5776. The smallest triplet is 171078830, 171078831, 171078832. Bruno Mishutka found that 141363708067871564084949719820472453374 is the start of a quadruplet, as noted at Can You Find.
28 cuboids
Can you put 28 3×4×5 cuboids into a size-12 box? There are 3 solutions. This problem by Don Knuth was originally solve by George Miller. The problem of 27 cuboids is in Winning Ways, p. 914. An example of 27 cuboids is shown at box packing.
Jean-Charles Meyrignac, Crossword Champion
Usually, Jean-Charles is often noted here for incredible programmatic results. But he's also now the fastest French crossword solver.
Material added 16 Jul 2008
Spacetime Arcade
Spacetime 3 is math program for portable devices. The designer, Chris DeSalvo, has also put together the Spacetime Arcade, a collection of flash-puzzle games, all with attributions and permissions from the original designers.
RAFAEL + NADAL = TENNIS
Rodolfo Kurchan: I have made this (base 10) alphametic: RAFAEL + NADAL = TENNIS. The solution is unique.
KrazyDad Puzzles
The KrazyDad Puzzle blog has a huge number of puzzles. He's recently added Penrose Slitherlink and Altair Slitherlink.
Oskar Online
Oskar van Deventer has various puzzle games online. In Threesome (Java), three colored dots must work together to escape. He also sent a recommendation for Zeparate (shockwave), you must pull out the colors you own before your computer opponent.
Sudoku Variations
Nrich.maths.org has 42 sudoku variations at the moment.
Go Problems
The site goproblems.com has thousands of well-organized go problems, searchable in many varieties and skill levels, with a built in player.
2008 US Puzzle Championship
I missed the online 14 June US Puzzle Championship. The excellent set of 20 puzzles (password gc9yj2) is still available for your testing.
Repton
Luke Pebody: I, like you, love playing DROD. Have you ever played the "Repton" series of Games from Superior Interactive? I have been playing them (on and off) since I was about 6. They are well-designed level-based games like DROD. Unlike DROD the decisions take place in real time. It is fairly similar to the classic game "Boulder Dash", but more puzzle-based.
L and X Pentominos
George Sicherman: The attached compatibility figure for the L and X pentominoes has 44 tiles. This improves on the famous 80-tile solution of "Polyomino Number Theory."

Commensurable Triangles
The paper Commensurable Triangles (pdf) by Richard Parris studies the problem of a triangle where one angle is a multiple of another.
Steve Sigur Passes
Steve Sigur, the author of the pending Triangle Book with John Conway, has passed on. The sites legacy.com, huffingtonpost.com, edublogs.org, and ajc.com have articles about him. His webpage on triangle geometry has many of his beautiful findings. With help from Colm Mulcahy, he delivered a final version of his book to publisher A K Peters shortly before passing.

Material added 6 Jul 2008
Valentine's Day Maze on Games Magazine cover
The cover of the latest Games uses Robert Abbott's excellent Valentine's Day maze. You can also take a look at the latest version of his Theseus and the Minotaur.
25 Primes in Arithmetic Progression
Raanan Chermoni & Jaroslaw Wroblewski: 6171054912832631 + 366384×23#*n, for n=0 to 24. New longest known arithmetic progression of primes! (May 17 2008). [Ed - A paper with Wroblewski's method is available.]
Length 17 Cunningham Chain
Jaroslaw Wroblewski found x1=2759832934171386593519, the start of a length 17 Cunningham chain. With xn+1 = 2xn+1, the xn are prime numbers up to x17. He found a total of four record setting length-17 Cunningham Chains.
Plouffe Invertor
Simon Plouffe posted a message about 2.5 billion mathematical constants at sci.math.symbolic.
Watering a Magic Square
Craig Knecht has put together a page about water retention in topographical magic squares. His other magic square models are also very clever.
23 Moves is Enough
Tomas Rokicki has proven that any arbitrary Rubik's Cube position can be solved in 23 moves or less. It was solved on the Spiderman 3 renderfarm at Imageworks.
4D Megaminx Puzzle
Roice Nelson: I recently published a 120 cell permutation puzzle (which could be considered the 4D analogue of Megaminx), and I wanted to let you know in case you'd like to share it with the mathpuzzle.com readers. [Ed - Just in case Rubik's cube is now too simple.]
The Digit Puzzle
Alex Polonsky: I think you would be interested in my new puzzle-game called Digit. It can be found at www.puzzle-4u.com. All levels of this puzzle-game were created by computer program. [Ed - An incredible series of puzzle miniatures. For each move, you may pick up and move a single piece. To win, the treasure chest must be visible with all pieces placed.]

Bozzball's Puzzling World
Luke Pebody: I have released over 600 logic puzzles at bozzball.blogspot.com, with more appearing daily. [Ed - A large variety of logic puzzles is there.]
PennyDell Puzzles Site
Another site with daily puzzles: pennydellpuzzles.com. A new site from the largest publisher of puzzle magazines.
Conceptis Relaunch
Conceptis Puzzles also has daily logic puzzles, and just got relaunched.
Puzzle Picnic
For even more puzzles, Puzzle Picnic has 600 logic puzzles and counting.
Power Problem
Erich Friedman: everyone knows that 24 = 42. But hardly anyone knows 25 + 27 + 29 + 53 + 54 = 52 + 72 + 92 + 35 + 45. Are there examples of this type with fewer terms? (Also see his recent wonderful Math Magic findings, including Frame Tilings, Powers (183425228501 + 438841438125 = 622266666626, 1834252285012 + 4388414381252 = 226226622266262266222626), Polyforms in Parts, and Square Packing. Also take a look at his lovely powerpoint presentation Rep-tiles.)
Journal of Number Theory on Youtube
The Journal of Number Theory is now on YouTube.
Simple Groups at Play
At the Scientific American site, some java puzzles based on Mathieu groups have been made available. Ridiculously hard, but worth a look.
Four Cubes Puzzle
Peter Grabarchuk (peterpuzzle.com): You have four identical color cubes (1x1x1) which form a shape shown in the illustration; yellow cube lies on the other three. The object is to determine the distance which corner A of the yellow cube passes when the cube rotates counter-clockwise for 60 degrees from Start to Finish (see both Top Views). Note that while rotating, the yellow cube remains in the continuous contact with the other three ones which do not move. (solution) [ See also his Simple Book of Not-So-Simple Puzzles.]

Total Gadha
Sanjeev Singh: I am a math teacher from India who runs his own Math and English website titled totalgadha.com. I write math chapters for students preparing for competitive MBA exams. If you think they are useful, can you mention our website on your blog? [Very nice, so yes.]
Gardner Article
John Gowland: Saw this article in London (formerly Manchester) Guardian Weekend supplement. It talks about Gathering for Gardner, and gives a puzzle by your friend Wei-Hwa Huang. I was one of those in late 50s who discovered that it was OK to enjoy math! I don't seem to find time to make any crossnumbers since I retired (never been so busy), but I enjoy teaching extra High School Grade 11 and 12 math twice a week.
Slanty Sliding Block Puzzles
Relatively new at puzzlebeast.com are Slanty Sliding Block Puzzles.
Povray Short Code Contest
The results of the Povray Short Code contest are stunning.
Computational Geometry
The Computational Geometry Algorithms Library is a great resource for code and explanations involving this topic.
Lightning in a Block
Theo Gray explains Lichtenberg figures -- lightning trapped in plastic. Another neat popsci link is self-repairing rubber.
Cabtaxi(10) = 933528127886302221000
Christian Boyer: After his recent work on Taxicab(6) confirming the number found as an upper bound by Randall Rathbun in 2002, Uwe Hollerbach (USA) confirmed this week that my upper bound constructed in Dec 2006 is really Cabtaxi(10). See his announcement.
933528127886302221000
= 83877303 + 70028403 (1) = 84443453 + 69200953 (2)
= 97733303 - 845603 (3) = 97813173 - 13183173 (4)
= 98771403 - 31094703 (5) = 100600503 - 43898403 (6)
= 108526603 - 70115503 (7) = 184216503 - 174548403 (8)
= 413376603 - 411547503 (9) = 774801303 - 774282603 (10)
See also http://cboyer.club.fr/Taxicab.htm, with updated tables of Taxicab and Cabtaxi numbers. You can also freely access to my paper published in Journal of Integer Sequences, with explanations on how this number was constructed, before to be proved the real Cabtaxi(10) number. Reminder:
-Taxicab(n) is the smallest number expressible as a sum of two cubes in n different ways.
-Cabtaxi(n) is the smallest number expressible as a sum or difference of two cubes in n different ways.
Ammann Chair
The Ammann Chair is one of many demonstrations recently added at the Wolfram Demonstrations site. Other recent additions include Conformal Mapping, Irregular Tilings, Intrinsically Knotted Graphs, Fifteen Great Circles, Game of Hecks, and the Four Runner Problem.

Morpion Solitaire Site
Christian Boyer: First update of morpionsolitaire.com: thanks to Michael Quist, the 4T and 4D games are now solved! But 5T and 5D still open... Who will improve the current records? An easy game, only paper and pencil needed: 5T Morpion Solitaire (the original version of Morpion Solitaire) is one of the rare games still having its best scores produced by hand... and more than 30 years ago! Computers greatly helped on 4T/4D/5D, but seem fully unable on 5T.
Fibonacci Seed Hearts
Some gorgeous pictures of Fibonacci Numbers and Nature are available at a page maintained by Ron Knott.
Eric Harshbarger's 7th Puzzle Party
Eric Harshbarger: Thought you might like to read the write-up I've done about my latest puzzle party, which took place the week after the Gathering for Gardner.
Polyhedra Stellations and Sculptures
I first mentioned Vladimir Bulatov 7 years ago. I'd mentioned his gorgeous stellations applet. He is now offering beautiful metal polyhedra sculptures.

CalcZilla
A bloody cartoon about integration: Calczilla.
Crossword Compiler
One puzzle program I use a lot is Crossword Compiler 8.1. If you'd like computer assistance for constructing a crossword puzzle, this is the program to get.
source:www.math puzzle.com