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Math Games
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Material added 13 May 06
Set on an Affine Plane
An excellent paper on the mathematics of the card game Set is available from Benjamin Lent Davis And Diane Maclagan.
Numb3rs wins Carl Sagan Science award
The Numb3rs TV show, for which I am a math & science advisor, has won the Carl Sagan Award for the Public Understanding of Science. Cheryl Heuton posted a recap of the event.
Sudoku in the New York Times
I got a nice mention in the New York Times in the article "In Sudoku, Nine Little Numbers Add up to a Big Challenge". Also mentioned are Wei-Hwa Huang and Gordon Royle. Next week, Scientific American will take on Sudoku, with puzzles by me and Bob Harris.
Loop Sudoku
Cihan Altay: Solve each one of the four "Consecutive Sudoku" puzzles, where all digits from 1 to 6 appear in each row, column and region in a grid. All neighbouring cell pairs with consecutive digits have a border in between. Copy the digit on a shaded cell into the corresponding cell of the next grid in the loop. [UPDATE: Cihan's grid had a trick -- a mirror was necessary to solve 3 of the grids. Here is a flipped version, in which a mirror is needed to solve one of the grids (lower left). Joseph Devincentis solved the original puzzle. Solution.]
Typo in Kryptos
Wired reports that the Kryptos sculpture has a typo.
Oreo-powered Rocket
Theo Gray's chemistry column has remained popular in Popular Science. His latest column talks about how to mix stump remover (salt peter, or potassium nitrate) and oreo filling to make dangerously explosive rocket fuel. Other candy rockets can be seen Candy Propellant Experiments, and at Homemade Fireworks.
Crossing State Lines
The July 2006 Games has an interesting contest. Build the smallest rectangular word search puzzle which contains all 50 states. They offer a $500 prize to the winner.
Polyform Combinations
Erich Friedman: The May Math Magic is about tiling triangles, pyramids, and diamonds with pairs of polyominoes.
Alphametric Challenge
Burr Tools updated
Ronald Kint-Bruynseels: The new version of BurrTools became available: The amount of changes and improvements made it worth waiting such a long time (we hope)... Although the project is far from finished and we still welcome your suggestions and bug reports.
Dead Reckoning
Kai Gauer: K7/8/2k5/8/8/8/8/8, black is capitals, and the question is to determine who moved last, and more importantly, the right question that gives a reply to the question of "why?" will give the answer to the question. This is known as "dead reckoning." Other interesting chess pages include Open Chess Diary, The 110 Most Fantastic Moves Ever Played, Tim Krabbe's Chess Curiousities, Ultimate Blunder, and Check!
Equal Area Split
Eduard Baumann: See my updated Homepage concerning "Equal Area Split" Basically, divide a triangle, square, or circle into n equal pieces using the least cutting.
Interactive Symbolic Geometry
Saltire Software has launched the ultimate geometry program, Geometry Expressions. I give a list of 10 geometry programs (some free) in my Vector vs Raster column, but this is better than all of those (but not free). Geometry Expressions offers the best combination of symbolic algebraic expressions and interactive geometry that I've ever seen.
Virtual Street Geometry
The task of putting 3D anamorphosis artwork on streets is explored at Virtual Street Reality.
Regularizing polygons
Steve Gray: You might be interested in a puzzle that seems to be a combination of math and game strategy. Here's a geometry problem with no known answer. It's Problem 60 in The Open Problems Project (TOPP). I thought it up about a year ago. As one plays with it, preferably using a dynamic geometry program, it's not at all clear whether it's solvable. If it is, one wants a method or algorithm and the number of moves required. It's possible that it's solvable only for certain values of n. I've played with it for quadrilaterals (n=4) and have not been able to make a square. I'm planning to write a paper about it but it has to wait until I finish (if I ever do) another paper about combinatorial geometry. I don't mind if someone solves it but if they do I'd like to be contacted. Feel free to add this to your math games list.
Always 100
Serge at offers the math game Always 100. You must add math operators to a series of numbers to obtain exactly 100. A very nicely done challenge.
Material added 29 Apr 06
Site Outage
MathPuzzle was down for over a day due to some weird glitch at Yahoo, which hosts the site. I plan to move the hosting to for better stability.
New Cubic Puzzles
Eric Fuller: After a long break between updates, we reward your patience with many new puzzles! From John Devost we have several new packing puzzles, including "Anti-Slide" and "Just Fit" by William Strijbos, as well as Dean Hoffman's excellent "Hoffman Packing Puzzle". Eric has finished several interlocking puzzles as well, including two new puzzles by Tom Jolly (Double Bar Cube and H Cube), Oskar Van Deventer (Two in One), Sheffield Steel 6BB by Ronald Kint-Bruynseels. Also, I am pleased to annouce an excellent puzzle (Gymnasium) by a heretofore unknown designer, Duane Enfield. Additionally, there are very limited re-editions of the excellent "Two Piece Oddity" as well as "Oskar's Matchbox Puzzle".
Dance Like an Idiot
I have a favorite new music CD -- Hip to the Javabean by Lemon Demon. I first heard of him via the Dr. Demento show, where Ultimate Showdown went to #1. So, I ordered the CD, which had 54 songs on it, most of which I liked. Usually, I feel lucky if a CD has 2 or 3 songs I like.
Scientific American Puzzles
Fulfilling a lifelong dream, many of the puzzles in the next issue of Scientific American are by me. It should be on the news stands around May 20th. Puzzles by Bob Harris will alos be featured.
Deep Note
The story of the program that made the THX deep note is given at Music Thing and Slashdot.
Tiling space with fun shapes
I got a chance to play with rhombic dodecahedra and truncated octahedra in a display I helped make for the MSI Chicago DaVinci exhibit. Exploring 2-cell growth rules was Stephen Wolfram's idea, but I had fun implementing it. Everything was printed on a ZCorp printer.
A Sangaku Construction
George Hart: This will be a large geometric sculpture -- a sphere 6.5 feet in diameter --assembled from ten thousand eight hundred small plastic components.
Chess Sudoku
Matthew Skala: I've gotten interested in other ways of combining chess and Sudoku. Two variants for which I've already generated puzzles are where instead of the number 9, you use chess knights, with the condition either that no two knights can attack each other, or that *every* knight must attack at least one other. An easy example of one of those is is at Matt's Puzzle Corner.
Maxwell Motor added to Magnet Man site
Rick Hoadley, AKA the Magnet Man, has added Maxwell's Motor to his site of cool magnet experiments. He timed the magnet spinning at 2000 rpm in this simple experiment.
Exponential decay in 1.4 Minutes
Liquid Metal has the property that a bearing will continue to bounce for minutes. There's a neat movie illustrating this. The sound of bearing bouncing goes through an incredible speed up towards the end of the demo.
Octiamond Similar holes
Patrick Hamlyn posted various solutions to putting similar holes inside of hexagons with the full set of octiamonds.
Material added 17 Apr 06
Gathering for Gardner 7
My latest Math Games column, about Gathering for Gardner 7, is now at Of particular note is the Maxwell Motor, the most simple+amazing science demo I've seen in years.
Google tries a Puzzle Contest
Google and Sony have put out a puzzle contest for the movie, The DaVinci Code. The person behind the contest is none other than Wei-Hwa Huang, puzzle supergenius. He's been working on the puzzles since last November, so they should be great. Concerning the set of 12358 puzzles he created, Wei-Hwa recently posted to the Google blog. More coverage is on
Material added 16 Apr 06
Fractal Stamps
Rodolfo Kurchan: Here are the latest stamps I've added to my puzzle colection, they are from Macau, China.
Nested Games
Mark Steere introduces the concept of nested connection games.
The puzzle blog,, is excellent. He even has a write-up for Puzzles and Wine, which I was just about to write up myself. Josh: I run a site called and I have a new puzzle that you might be interested. It's not really a math puzzle; more of a logic puzzle. I'm calling it "wordstream" and it's based on nurikabe or "islands in the stream" puzzles. You can find my first puzzle here: Wordstream Wednesday.
Jay, on the other hand, reviews Flash puzzle games at Jay is Games. Another good site for the many puzzle games out there, many of which seem to be new to me. It takes a dedicated expert to wade past all the clones.
The Griddle is taking puzzle requests
David Millar wants to make 18 pages of puzzles for his birthday, on June 8. Visit The Griddle, and email him if you have a request for any grid-type puzzle.
Puzzle Monster Easter Egg Contest has an online contest to find all the hidden Easter Eggs on the site.
As long as I'm mentioning blog sites, I may as well mention I helped to add John Forster's song Helium to list, a very funny song about the effects of helium.
Clock Number puzzle
Rodolfo Kurchan: Number cards 1 to 12, and arrange them in a circle counterclockwise. To move, choose a card, count forward clockwise the number on the card, and exchange the card with the card that finishes the count. For example, if we choose card 4, and finish on card 12, then exchange card 4 with card 12. GOAL: Move the cards to the normal clock position. Answer. You can also play like solitaire (with cards from 1 to N), starting in a random position. Can the cards always be placed in clockwise order? Prove it. The puzzle is by Jesus Sanz from Spain.
A Pad of Paper
T Roberts: I bought a pad of paper the other day. The number of sheets in the pad was interesting - it was the smallest possible number such that I couldn't change it into a prime number by changing one of its digits. How many sheets were in the pad? Answer.
No three in a row problem
Benjamin Chaffin: How many points can you place on an NxN grid so that no three of them are in a straight line? This means any line, not just the orthogonal grid lines. Well, obviously no row or column can have more than two points in it, so the answer is never more than 2N. This upper bound is achievable for small grids; but it is conjectured that there are a finite number of solutions with 2N points. I heard about the problem from Ed Pegg’s Math Games column on chessboard tasks. Achim Flammenkamp has extensive notes on this problem, and has computed all solutions for N up to 16, and the number of solutions in certain symmetry classes for much larger N. He also has the largest known solution, for N=52. Together these two sources give much better history and references on the problem than I’ll attempt here. The number of unique solutions for each N is given in Sloane’s sequence A000769. [And Ben has extended the known results to 17x17 and 18x18 boards.]
Road Sign Math
If you know of a road sign with lots of numbers, you might want to enter it in Road Sign Math.
New Chess record
Guy Haworth: On 10th March 2006, Marc Bourzutschky announced that Yakov Konoval's program had computed the DTC/Z endgame table (EGT) for KQBNkqb and found maxDTZ/C = 330 moves:
    maxDTZ position = 1k6/1b5q/N7/8/8/1Q6/8/B1K5 (black to move, diagram)
DTC = Depth to Conversion, i.e., change of force and/or mate
DTZ = Depth to (move-count) Zeroing (move), i.e. P-push and/or Conversion

This depth leaves all chess records of this kind well behind:
193m = the longest decisive game in classical chess: Stepak-Mashian (1980)
199m = longest (rapid) decisive chess game: Petrosian-Milanovic (2005)
262m = the greatest known EGT maxDTM(ate), in KRNKNN
269m = longest (drawn) chess game: Nikolic-Arsovic (1989),
290m = the deepest known Chess Problem - by O.T.Blathy
290m = the previous maxDTC/Z record - in KRRNKRR

Generation and verification of the EGT required 3.5 weeks of a 3.6GHz processor. The first two attempts to generate this EGT were frustrated by interrupted power supplies.
Bimagic squares, multiplicative cubes
Christian Boyer has made a large update for his magic squares website, including a 6x6 bimagic square, and an order 4 multiplicative cube.
Material added 30 Mar 06
Scrambled phone cords, eggshells, and mirrorred spheres
If you've wondered how phone cords can get tangled, the paper "Tendril Perversion in Intrinsically Curved Rods" by McMillen and Goriely will help you. For a study of egg breaking, consider "Fragmentation of shells" by Wittel, Kun, Herrmann, and Kroplin. "Wada Basin Fractals" explores what happens when reflective spheres touch each other.
Sum-diff Configurations
David Clark sent me the following configuration of consectutive integers. Each number is the sum or difference of two neighbors. For example, 50=23+27. He wonders if anyone can beat this, with numbers 1-64, or perhaps even more. Answer and Solvers. Itamar Faybish sent a solver.

   50 33 43 26 40 44
38 23 27 10 12 14 30
46 15  8 19  2 16 32
39 31  7  1  3 18 37
41 24  6  5  4 21 47
52 17 11 25  9 13 34
45 28 36 20 29 22 35
      48 49 42 51   
Big Prime Milestone
There are now over 2000 known primes with more than 100000 digits. But still none known with more than 10000000 digits.
Oddly hexagonified polyhexes
Col. George Sicherman:
Hexomino, Heptomino covers
Balakrishnan V: Using a computer program, I have found covers for the hexominoes and heptominoes. [[Okay, these seem to work. All 35 hexominoes fit in the first figure. Can anyone find smaller coverings for these polyforms?]] [[UPDATE: Muniz has lowered hexominoes to 12 squares.]]
Gathering for Gardner write-up
Erik Hermanssun was one of the attendees of G4G7, and he wrote up a report. I'm still working on mine, but here's one random factoid from my 20 pages of notes: is now selling the collected 21 volumes of Hugard's Magic Monthly.
Material added 14 Mar 06 (Happy Pi Day)
World Sudoku Championship
A story about the championshipis at the Times of London. Be sure to look over all of their coverage (one, two, three). More news is here, as well as results . More information is on the US championship website. Frequent contributor and behind-the-scenes architect for my Sudoku column, Wei-Hwa Huang finished third in the competition. Placing first was Jana Tylova from the Czech republic.
The rather dull number 1729
I was helping Eric with a MathWorld entry for the number 1729, when he remarked to me "other than this taxicab-Ramanujan story, this is a pretty dull number." I instantly replied "Actually, it's also the smallest multiplication-reversal product that's one away from a higher power! 19×91=1729, or 123+1. The next one is actually perfect, 2178×8712 = 18974736 = 664. And then there's the amazing pair: 266556×655662 = 374664×466473 = 55913+1. Yes, the same number is a reversal multiplication pair in two different ways. The cube of 5321 also works if you add one, and after that is 2576816×6186752 = 251683. But it all starts with 1729." Actually, this conversation never took place. Sloane sequence A062917 has numbers that lead to squares, but I'm mainly interested in higher powers. Can anyone beat 251683? Send Answer. Update: Justin LeBeau and Denis Borris (instantly) replied with 1334633301 × 1033364331 = and 1225535211 × 1125355221 = 11131113. Some of these numbers are in sequence A035124.
Prime Polynomial Contest
The next Al Zimmermann Programming contest, for Prime Generating Polynomials, has started! Current standings are available, as well as a contest description. The below are the current known records, which might already be shattered. If you can find the most prime-evil polynomials, you could win anywhere from $10 to $250. I can't wait to see the results of all this.
100308707032367 + 156722·23#·n23n=0..22Frind
36n2 - 810n + 275345n=0..44Ruby
3 n3 - 183 n2 + 3318n - 1875743n=0..46Ruiz
n4 -104n3 + 4096n2 -72027n + 475093 35n=0..34Beyleveld
Numb3rs Preorders Available
One of my various projects is to add as much good math as I can to Numb3rs. I'm pleased to announce that you can now pre-order the first season Numb3rs DVD.
M. Oskar van Deventer: Recently, I laser-cut a whole bunch of fractal pieces for Jan Grashuis of Arabesk. The pieces can be put together in many intriguing ways, allowing one to explore the properties of this particular fractal. The pieces can be bought through the website. (Note, the Arabesk website has the annoying property that I cannot link to the appropriate page or item directly. This means that the readers will have to browse to --> English --> Catalogue (TOC on the left) --> Puzzles (square at x,y=3,-2) --> Jig saw puzzles (square at x,y=4,-1) --> Fractal Large / Fractal Small (sixth and seveth items from above, item numbers A336.0010 and A336.00200) to find and perhaps buy the fractal pieces). [Nic found a direct link.]
Negative Number MP3
The BBC has made an audiocast about the Negative Numbers.
Snevetz's Last Theorem
Snevetz's Last Theorem concerns A = 5x4 - 10x3 + 20x2 - 15x + 11.
For any integer 'x', the value 'A' will have exclusively as prime factors integers that end in ONE.
example: for x = 815,  A = 2200574091661 = 11 * 11 * 41 * 71 * 631 * 9901.
example: for x = 1004, A = 5070380945911 = 151*401*4871*17191.
UPDATE: Proven true by David Broudhurst with Quartic Reciprocity. He used a paper by Lemmermeyer, along with A = -25, B = 2, C = 11, m = 5.
Material added 04 Mar 06
The Occasional Front Page Hack
Every once in a while, I hack down the front page so it won't be excessively long, and store the older material. You can see them in the Archived Pages under the Math Games columns: Nov-Dec, Jul-Oct, Mar-Jun. I've recently posted various answers to older puzzles. Richard Sabey extends Erich Friedman's 2006 puzzler (Answers) with 2006 = ((.1 ^ -2) + .3) * 4 * 5.
Octiamond Oddities
George Sicherman: I've posted a page of Octiamond Oddities. Additions and improvements are welcome!
Polydrafter update
Bernd Karl Rennhak: Experimenting with drafter based polyforms led me to some new extended tile sets. I started from the polydrafter notes I found on your pages related to the Eternity Puzzle. There only grid conform polydrafters are counted. The idea is to extend the grid conform polydrafter with all others, which can be cut out of polydrafter based solutions. This way you get a closure of the tile set. These tiles are marked "rejected" in your notes, but I found them very useful and interesting. See the attached example of the onesided extended didrafter set. These tiles create many grid shifts in the solutions. The different grid orientations are marked with colors in the left version to make them more visible. I managed to find all solutions of all convex forms with this particular tile set. As the solutions numbers are very low, the forms seem rather difficult to solve by hand. More details you can find at and the following pages. For the SVG fan club there are some SVG powered grafics included.
Sudoku World Championship
Jason Dyer: The official instruction booklet for the World Sudoku Championship is up. In the booklet, Frame, Outside, and Star are variants not mentioned in your article. [Ed - He also mentioned an issue, now fixed. In addition, the WSC has added several new variants.]
Polyomino covers
I've recently read some articles about Polyomino Covers. Alexandre Muñiz page has a good introduction to the subject. What is the minimal cover of the hexominoes, heptominoes, and heptiamonds? Send Answers.
Bimagic Square
Christian Boyer: "The first known 6x6 bimagic square using distinct integers found by Jaroslaw Wroblewski, University of Wroclaw, Poland." In a bimagic square, it's a normal magic square, which remains a magic square if all the terms are squared. Christian will premeire the new discovery at his bimagic square page. Jaroslaw's solution has largest entry 135. A 5x5 solution remains unknown.
Penny stacking
Justin: I was sent this page about penny stacking earlier today. Kind of cool, some math/physics principles in there somewhere
Integer Square Tiling
Erich Friedman: Some orange squares have already been placed in a rectangle. place one more square so that the remaining shape can be tiled with integer sided squares in exactly 2006 ways. Answer and Solvers. Picture. Bigger picture (by Patrick Hamlyn).
Optimized Dungeon Robbery
Joshua Taylor: A while ago I thought up this puzzle. I was wondering what you think about it. Inside a dungeon you find a room with a square are in the center walled off. On each side of the square are 3 doors. On each door is a number and a slot for coins. Putting that many coins in the slot opens the door and closes all others. (Doors don't close otherwise.) Inside the doors is a 3x3 grid of rooms each with a few coins on the floor. Each of the cells in connected to its neighbors (orthogonally) by a similar door. The puzzle is to see how much money you can gain. Answer and Solvers.
Hitchhiker's Guide to the Galaxy
I'm always on the lookout for great games and puzzles, old or new. One particularly nice game is Infocom's Hitchhiker's Guide to the Galaxy, now presented in two wonderful versions by the BBC. If you'd like to learn more about interactive fiction, there is XYZZY News, The Brass Lantern, Spider and Web (java), Baf's Guide, the IF Guide, Emily Short's Recommendation list, and the Underdog Ratings.
Site Goals
Martin Gardner celebrates math puzzles and Mathematical Recreations. This site aims to do the same. If you've made a good, new math puzzle, send it to My mail address is Ed Pegg Jr, 1607 Park Haven, Champaign, IL 61820. You can join my moderated recreational mathematics email list at