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material added 11 February 2001

A circle of dominoes where no neighboring pair of dominoes shares a number.

In the above image, any two dominoes that share no numbers are connected with a line. They are arranged in a circle, with the property that no neighboring pair shares a number. Finding five-fold symmetry wasn't easy. Is it possible to make this graph with three-fold symmetry? Can 3 circles of 5 dominoes be made, so that each circle has the "neighbors don't share numbers" (NDSN) property? A more direct version of the question was sent to me by Douglas West, whose book directly inspired the drawing. His version: "Does the graph contain three pairwise-disjoint 5-cycles?" Send Answer.

Before tackling the problem above, you might want to try a simpler problem first. From the diagram above, remove all the dominoes with a 6, and remove the 1-2 domino. Can you make a nine-circle with the NDSN property? Send Answer.

A few weeks ago I asked, "Hmm, can the 24 interior blocks be distributed so that each of the 24 pieces becomes a hexomino?" Patrick Hamlyn found a brilliant little impossibility proof: "No. Refer to the attached pic. Consider the three outlined empty cells. The left two must contribute a cell each to the dark green and the ...um... dark aqua pentomino. The right-hand one must thus contribute to both the red and the purple."

Dan Hoey wrote a Dots and Boxes analyzer, and made an excellent commentary for my game against Joe. See it at my Dots and Boxes page. The winner is usually the first to make a sacrifice - I find that lovely! The next really interesting game for QDB would be the 3x5 game.

I downloaded Irfanview recently (it's free), and have made it one of my main programs. Another site allows you to make License Plates:

The class of Odette de Meulemeester has started a Pentomino Bridge competition, with €25 going to the winner.

Alex Selby has updated his Eternity page. And here's another view of the Domino graph. Can anyone find a symmetric version of this graph when the dominoes including blanks are thrown in? (No doubles, and I couldn't find one.). Can 3 circles of 7 dominoes with the NDSN property be made? Or 7 circles of 3?

material added 4 February 2001

A lively mailing list I've been following is polyforms@yahoogroups.com . Here's a solution recently found by Peter Esser:

I mentioned Mathematical Art last week. Ishihama Yoshiaki pointed me to his excellent http://www.asahi-net.or.jp/~hq8y-ishm/gpart/gp-art.html. Igor Bakshee pointed me to the excellent Graphica books.

I watched the first XFL games last night. The games were scheduled by two mathematicians (New York Times story). I liked learning that Tim Lester, the quarterback for the Chicago Enforcers, is a high school math teacher.

material added 28 January 2001

The Tetris Logic puzzle by John Gowland was popular last week. Bob Kraus decided to try making some himself, and came up with six logic tetris puzzles. Wow! Bob's Site hosts the guest Puzzle of the Week. Puzzle #3 is particularly nice.

Joseph DeVincentis beat me at 3x3 QDB.

It isn't easy to introduce hard material in an amusing way. Mathematica Animations do just that.

A nice gallery of mathematical image is at http://www.kfunigraz.ac.at/imawww/vqm/pages/colorgallery/index.html.

Here's the Game of Sprouts Association webpage.

Aram Hakobyan, Roel Huisman, Mark Thompson, Stas Soumarokov, Andrej Jakobcic, Aron Fay, Evgeni Lukin, HappyMutant, Chuck Fallon, Stephen Kloder, Joseph DeVincentis, and Michael DuFour solved Scott Kim's 4x4 Queens problem. His general case problem is still unsolved -- for an n x n board, where each queen attacks exactly k other queens, what is the most queens that can be put on the board?

Joseph DeVincentis, Michael DuFour, Koshi Arai, and Brett Champion solved the 11x11 rectangle problem, divided into areas in the teens. Solutions.

material added 24 January 2001

Dots and Boxes starts by drawing a square grid of boxes. After that, players alternate connecting dots (no diagonal lines). Whenever a square is completed, the player that drew the final line claims that box with their initials, and moves again. When all boxes have been claimed, the person with the most boxes wins. My only gripe against Dots and Boxes (notation here) is relatively slow game opening. I tinkered with the rules, looking for a fix. Quick Dots & Boxes (QDB) is played in the same way, but each player draws two lines per turn. The instant that a player draws a third line on any box, their turn ends, and play goes back to normal Dots and Boxes. QDB is a fairly deep game. I *think* the second player can always force a win *on the 3x3 board*. Let me know. When I posted this two days ago, I forgot to mention that it was the 3x3 board I was looking at. Joseph DeVincentis did an analysis of the 2x2 board. More on Dots and Boxes.The book was recently reviewed in Scientific American.

Winning move in QDB: A3— . Are there others?

Let me point you to Karl Scherer's website. Karl has produced about a hundred great games for the Zillions engine (the best thing in recreational gaming, ever). I'm still trying a lot of them out. Also, I've been seeing his name a lot in the copies of the Journal of Recreation Mathematics I've been going through. I'm quite impressed by all Karl's done. Why, just today, he has new things available at the Zillions site.

material added 21 January 2001

Now that I have a copy of ONAG2, I see the cover is by puzzlemaster Scott Kim. Neat! Here's a nice puzzle by him: Put 6 queens on a 4x4 board so that each queen attacks exactly 2 others. Send answer. This problem can be expanded, of course.

Dwight Kidder solved John Gowland's Double Squares, and said "Incidentally, as an aside, note 72^2_27^2 = 2277^2. (5184_729 = 5184729)" Okay, let _ be the concatenation equation representation. Are there integers a, b, and k such that (a^k_b^k)^(1/k) is an integer, for k>2? Send answer. If you can scribble any results or proofs in a margin, write to me. I pondered trying to fit the Wiles proof into the margin of a handout on Diophantus, but my printer resolution wasn't strong enough. I also took a look at 14 proofs that Zeta[2] = Pi^2/6.

I mangled Erich Friedman's lovely problem last week -- divide an 11x11 rectangle into rectangles with areas in the teens. What is the highest number of different rectangles that can be used? Send answer. He goes on-- "Another (unsolved) question similar to your fill-agree one: take a 2x3 rectangle, and cut holes in the individual squares in every possible way. There are 24 of these possible - arrange them in a 12x12 square so that all the holes are touching.

I'm still loving the Kites and Bricks problem. Koshi Arai asked if the 7x7 could be built with 7 1-2 kites, 7 1-3 kites, and 7 dominos. I looked at extending that to nxn, where the third piece could be a shape of your choice. The 8x8 problem was easy. Is the 9x9 solvable?

I've moved Michael Reid's fantastic series to the Similar Dissection Page.

I caught up on movies, and saw Castaway, Crouching Tiger Hidden Dragon, and The Emperor's New Groove. I liked them all, but liked the last one the most. It was a tremendous amount of fun. I asked if the sequel could be loosely based on The Emperor's New Mind by Roger Penrose. I got a reply back from Disney within ten minutes -- 10:52PM on a Saturday -- "Thank you for your letter. Unfortunately, there are no plans at this time for a sequel to this film." Not the answer I wanted to hear, but at least it was extremely speedy! I wonder if they publish any math journals.

Puzzle Palace (www.puzzle.gr.jp/index_e.html) has puzzles similar to those found in Mensa Math & Logic Puzzles .

Here's an entertaining maze applet by Sami Silvennoinen.

I recently asked for differing ways of making Pascal's triangle with Mathematica.

material added 14 January 2001

I like perusing college bookstores. Usually, I can count on finding at least ten great books. I now have in my hands Winning Ways, 2nd Edition, Volume 1. A few seconds after I touched it another math student said to me, "I can't believe it's finally out. I've looked everywhere." Anyways, I compared my first edition to the second edition (Volume Spade -- This book is 1/4 of the full book.). New preface. Modernized format. The "Extras" are expanded. Amazons is mentioned. The "References and Further Reading" sections are expanded. A new section on Blockbusting. Various minor corrections and added explanations. I'm highly pleased with it. I planned to put a Winning Ways type problem here, involving Amazons, so I tried to find a site for the game. I ran across Abstract Game Magazine (why did no-one tell me?)! Then I found Amazon Rules, written by me, oddly enough. And Amazon links, completely me-free this time. I finally found Berlekamp's article on Amazons.

Another excellent book I found at the bookstore was Introduction to Graph Theory by Douglas West. He's one of the coauthors of another of my favorite books, Mathematical Thinking. I wish all textbooks could be this good.

Dick Hess asked "3 Pythagorean Triangles have the same hypotenuse, and areas A, B, and C. Can A = B + C?" John Robertson informed me that this is equivalent to the unsolved Magic Square of Squares problem. $100 from Martin Gardner, if you can solve it.

A similar problem is at the site of Junichi Yananose - Holey Rectangle. Rearrange the pieces below to get a 6x8 rectangle with 16 circular holes. There are many other puzzles at his site, and some stellations.

Another site with spectacular displays is by Vladimir Bulatov. Take a look at his beautiful Stellation applet.

HORSELESS CARRIAGE and GREGORIAN CALENDAR are two phrases that can be said without moving the lips. What 22 letter, three word phrase has the same property? It's something you can order at a restaurant. Send answer.

Math news, re the Euler Brick -- There are no perfect integer cuboids with the smallest edge <= 2^31. An exhaustive computer search found 13,401 body cuboids, 7,992 edge cuboids, and 13,044 face cuboids for a total of 34,437 in this range.

material added 7 January 2001

Gearing up for the rerelease of Winning Ways and On Numbers and Games, I've recently been reading two excellent books on game strategy. You can get all of these books at www.akpeters.com. Other sites devoted to game strategy: http://www.abstractboardgames.com/, http://www.gamerz.net/, http://www.zillions-of-games.com/.

Hex Strategy by Cameron Browne. Mathematical proofs are best introduced by purely visual means. I believe my own first proofs involved tictactoe. Hex Strategy is filled with game analysis, commentary, and puzzles. It comprehensively lists related games. Many of the strategies given were new to me. Another section has blank game boards of many sizes for easy copying and play. Hexy is mentioned. Beautifully made book.

As usual, I've moved a lot to my Solutions and Commentary page. Many thanks to all who sent solutions.

Harvey Heinz has published a book on Magic Squares.

Erich Friedman asks for number suggestions.

Dean Howard informed me that The Flanders Panel is a mystery with a retrograde chess problem. This reminded me of a problem I made in 1988. "Things are looking bad for White. He has a king on G3, and a bishop on E8. Black still has all 16 pieces. With a bishop sacrifice, White can force a stalemate in 4 moves. Can you construct Black's position?" John W. C. McNabb sent me this answer. My intended answer is here.

Cluster Rooks has been moved here.

material added 28 December

I've been looking more at Rock, Paper, Scissors lately. Andrzej Nagorko very graciously sent me his prize winning code Greenberg.c , and has allowed me to post it here. You can see some of the competition's code here, at the Roshambo site. One paragraph from the comments in Phasenbott intrigues me - "Phasenbott's metric would be more appropriate in a non-zero sum Rock-Paper-Scissors game where one simply tallied points for wins. This game is more interesting from the theoretical standpoint, as there is now incentive for cooperation and no longer a single optimal strategy. Random scores an expected 1/3, but cooperating players could do better by alternating wins, for 1/2. A player wanting to do better than 1/2 would try to exploit the other player, but not enough that the other player detects that it's worthwhile to switch into Random mode. The weak player scoring say 2/5 could know that it's being exploited by the stronger, but still go along with it as if it refused (by going Random) its score would drop to 1/3. This in my mind makes for a much more interesting Rock-Paper-Scissors game to study than "Roshambo". Maybe the next Rock-Paper-Scissors programming contest will feature such a non-zero sum game. [Hint, hint. :) ]"
I'd score this Win = 2, Tie = Loss = -1. Random scores zero! I'm considering my first Programming Competition -- 1000 games against all other programs, highest score wins. I'll likely make a few simple programs myself. For example, always play Rock, until the score drops a certain amount, then play randomly. Let me know if you'd be interested in entering.

I did read both The Planiverse by A K Dewdney, and The Wonder of Numbers by Clifford Pickover. I enjoyed them both. The NPR Puzzle of the Week was mine. STATEHOOD UNWON = TWO THOUSAND ONE. Paul Strauss, United States Senator for the District of Columbia, wrote to thank me for discovering this.

material added 3 January 2001

Michael Kleber reminded me of an old poem on seeing Marek Penszko's comment, so I penned the following:

As I was going to St Ives
I met a man with seven wives
Every wife had seven sacks
Every sack had seven cats
Every cat had seven kits
We traded bits
Each cat, sack, wife, and he
Took a kit. The rest for me.
So now I have a kit supply.
How many kits did I just buy?

I posted the poem to the National Puzzler's League list. Dean Howard (shrdlu) sent a reply.

The kits in this fine piece of lore
Are seven to the power four.
Each cat takes one, maternally,
Or seven to the power three.
The sacks, as must be clear to you,
Hold seven to the power two.
The wives, to have a bit of fun,
Pet seven to the power one.
And last, our multi-mated hero
Has seven to the power zero.
When added up, the number shared
Becomes precisely twenty squared.
So after the subtraction's done
You still retain two thousand one.
And so St. Ives turns out to be
The start of one more odyssey.

material added 20 December

The most important books in Recreational Mathematics have just been reprinted. Winning Ways for Your Mathematical Plays (Berlekamp, Conway, Guy) and On Numbers And Games, 2nd Edition (Conway).

If you know anything about the X-Files, you'll probably enjoy the launch of the Octium IV chip.

material added 19 December

The new demo page of webMathematica is well worth a look.

material added 17 December

John Rausch -- The Puzzle Art of Stewart Coffin is now online.
Lew Baxter -- R(86453) = (10^86453-1)/9 is a Probable Prime Repunit.
Craig Kasper -- The lastest Putnam competition has been posted.
Mike Henkes -- I've created a new idea for sliding block puzzles. [very nice]
Bill Ritchie -- FlipIt, by Nob Yoshigahara, is now available. [good puzzle set]
Martin Demaine -- I have been working on folding problems. [fascinating]
Nick Baxter -- I've posted rules for the International Puzzle Design Competition.
Livio Zucca -- I've solved your DSP problem:

material added November 24 MSOworld has just added Brain Power Magazine. Scads of good things at that site.

C M Shearer has created a page about the master of tiling, Marjorie Rice.

I've gotten some excellent puzzles from Bob Kraus and Patrick Hamlyn. I'm having some system problems at the moment, so please forgive me as I present them as Ascii Puzzles. Bob did some Balloon Balance problems, while Patrick has made a wonderful puzzle with 10 octominoes. I also include Michael Reid's list of unresolved rectifiable polyominoes.

Quite a few people were interested in the Forbes article on Stephen Wolfram. He's recently built a scrapbook page. Page two features a cryptography challenge with some sort of prize. I have no idea what that prize might be. For more Cellular Automata, you can visit my old page. If you have any links I should add that page, mail me and tell me about them. Mirek's Cellabration is something I should add, for example.

The exchanges of the G4G4 convention are well worth a look.

material added november 17th This website could save your life! It turns out heavy thinking is good for your immune system, according to a recent Washington Post article (Is it in the cards?). So, next time you need a health boost, try a puzzle. (including crosswords? Will Shortz -- "Absolutely!") You can also try a game. After all, the Games 100 has just been announced.

Randomness, games, and brain power. If you've seen the movie The Princess Bride (complete script), you know about Iocaine Powder -- the most dreadful poison. A snippet...
Man in black: [turning his back, and adding the poison to one of the goblets] Alright, where is the poison? The battle of wits has begun. It ends when you decide and we both drink - and find out who is right, and who is dead.
Vizzini: But it's so simple. All I have to do is divine it from what I know of you. Are you the sort of man who would put the poison into his own goblet or his enemies? Now, a clever man would put the poison into his own goblet because he would know that only a great fool would reach for what he was given. I am not a great fool so I can clearly not choose the wine in front of you...But you must have known I was not a great fool; you would have counted on it, so I can clearly not choose the wine in front of me.
Man in black: You've made your decision then?
Vizzini: [happily] Not remotely! Because Iocaine comes from Australia....
Wei-Hwa Huang told me about the Year 2000 Rock Paper Scissors competition writeup at Mindsports Olympiad. The winner of the 1999 Competition was a program called Iocaine Powder. I recently tried playing a thousand rounds against Iocaine -- and got trounced. It's squirmingly creepy to have your random behavior predicted by a short program.

material added november 11th

Here are more of his math quickies. Similar stuff:
Add two points to make this true:      (18 + 12) (18 - 12) = 18
Add one point to make this true:          = = 11                   (Ali Muniz, silly)
Use matches and one penny (the dot on the 'i') to form the equation:   S i X = 3 1 Move one object to make the equation true. (Daniel Scher)
Carlos Penedo of Neuquen sent me two pages of creative takes on the 71 puzzle. Page 1, Page 2.

I've finally added Mensa Math & Logic Puzzles by Dave Tuller & Michael Rios ($8) to my Books page. Similar puzzles can by seen on my World Puzzle Championship page.

My little word square puzzle is still topical (December 28 -- and probably always will be):
ACROSS 1. The person who won the election 2. Smallest buffalo 3. Voter turnout, e.g. 4. Outside inside France
DOWN 1. Strike sharply 2. Preposition 3. Griffins do this 4. Cappelletti, to a kid

I've moved Kites and Bricks to their own page. Here is a hard puzzle (as of 28 December, it's still unsolved). Build a 5.8 x 6.4 frame, where 1 is the unit side length. Put 10 short kites, 4 long kites, and 2 dominos into this frame.

For a nice 3-D maze, try Oskar's Cube. material added november 5th I've started working for Wolfram Research. My dream job. Down the street is Altgeld Hall, which has the third largest math library in the US. Stephen Wolfram has given me larger peeks at his book (it's incredible). Michael Trott and others are working on a Special Functions site & posters. Lots of stuff happening here. One of the main things I'll be doing is sorting through gigabytes of WRI developed material, and building a new site out of it for WRI. My site will remain a separate entity, completely under my control.

material added october 26th Eternity solved! See my Eternity page. material added october 20th Today, I'm at the <math>ml conference. Someday soon, you'll be able to see 1/2 as a nice fraction. Stephen Wolfram talked about the history of mathematical notation. I learned that Diophantus represented x³ + y³ = z³ in an entirely different form. Mathematica supports this ancient notation (!), and I got to see Stephen putting Mathematica through its paces on the fly. Among many other things, he also showed us 2³² in Roman numerals, which was very scary looking. It made me appreciate the effort of mathematicians in the past to make things easy for those of us who are alive today. After his talk, I ganged up with Eric Weisstein (Mathworld), Steven Finch (Constants), and Dave Rusin (Atlas) at a dinner hosted by IBM's techexplorer ($30, I'll wait). We discussed math websites. material added october 19th I've put together a huge page on the World Puzzle Championship 2000. material added october 8th Double Labyrinths have been added to the Space Visualization Test. These mazes by Izidor Hafner are generated by a computer program. Each one involves an unfolded net of a polyhedra.

In Russia, Paint by Numbers ( ) is known as the Japanese Puzzle, or Japanese Crosswords. There are several russian newspapers devoted entirely to such puzzles, there. Gunnavy Dennis, from the Ukraine, has a website for these puzzles.

material added october 2nd Pictures of some nice puzzles are at this japanese site.

My Pythagoras page has been updated. Wei-Hwa Huang's challenge is now at my Solutions page.

material added october 1st The Sunday Times made an announcement on the Eternity Puzzle. Christopher Monckton has offered his 200-acre Crimonmogate estate to the solver of his puzzle. material added september 29th I've added puzzleman.com to my list of links. Last Move is an interesting retroanalysis page (Q: What is the most economical position of type A where the last two moves were captures?) Slime Mold is capable of solving a maze.

At my prize page, I've added a $100,000 prime puzzle, and $50 for a solution to Livio Zucca's Big Pizza Puzzle.

I've also built a page of unsolved puzzles. Actually, I have at least one solution to each of these, but I wonder if anyone else can solve them.

The 12345 Maze had many solvers. I've posted them all at my Solutions page.

material added september 22nd

is up! One of the top puzzle designers of the world is Serhiy Grabarchuk. Binary Arts gave him control www.puzzles.com, and his work just got posted. It's fabulous. I'm eager to see how frequently it gets updated.

The 1-2-3 maze was moved to my Solutions page.

material added september 13th The Eternity puzzle has been solved! You can see the posting here. According to the official rules, the solution will be evaluated on September 30th. Ertl will publish the results in the New York Times and London Times. material added september 7th 966^⁸+539^⁸+81^⁸-954^⁸-725^{^8}-481^{^8}-310^⁸-158^{^8}=0. The site http://euler.free.fr/ is devoted to these discoveries. A wrinkle in bifurcation diagrams is illustrated at http://www2.gvsu.edu/~sorensej/cmj.html. David Gale discusses ants in his book Tracking the Automatic Ant. Wei-Hwa Huang has written an applet that shows the path of an ant independently discovered by Dr. Kotani. The ant moves one cell each turn, following two rules: (Flag: Remove the flag, and turn left. No Flag: Plant a flag, and turn right).

The task of making two identical rectangles with a set of dominoes was solved by Juha Saukkola, Michael Reid, Joe Logic, Joseph DeVincentis, and Dan Hoey. Here are the interesting write-ups.

material added september 2nd The World Puzzle Championship will be held next month. Here is the qualifying tournament for the Argentine Team.

Cleverwood expanded. One designer they added is Eric Kelsic, a teenager who has designed several new mechanisms.

Entropy has been moved to my Solutions page.

material added august 30th G P Jelliss edits The Games and Puzzles Journal. Quite good material, so I was delighted to hear he has a site now. Here it is. In particular, the Knight's Tour Notes are extraordinary, and contains much information I did not know.

Sliced Tetrominoes. There are 14 ways to remove a 45^o triangle from the tetrominoes so that a connected shape is left. These 14 pieces make a perfect 7x7 square. Can you find it? Next, make two 5x5 squares with a triangle missing at the same location. Many thanks to Roel Huisman for showing this to me.

If you like the ambigrams of Scott Kim, you'll like this cover of the book Angels & Demons. It's by John Landon, the author of Wordplay.

Laser Tank is a nice puzzle game.

material added august 13th Information about the recent math conference is at the L A Times. But it doesn't say much. Summation symbols can't be shown in the newspaper, apparently. If anyone at the conference has a new list of problems, I'd like to hear them. Until then, I will point to the list at claymath.org. Mathworld has an excellent writeup on the Riemann Zeta Function.

Patrick Farvacque showed me some beautiful puzzles. One puzzle is a Tower of Hanoi variant. Get 3 pairs of differently sized coins, and draw three squares. Put one of each coin in two of the squares, with smaller coins stacked on larger coins. One stack is Heads, the other is Tails. Now then, moving one coin at a time, and never putting a larger coin on a smaller coin, swap the stacks. How many moves does this take? Jeffery Gosselin solved this, it takes 25 moves. Stephen Kloder has found that the general number of moves required is (7/3)*2^⁽ⁿ⁺¹⁾ - (1/6)*(-1)^ⁿ - 3n - 7/2. You can see another Hanoi variant by Junk Kato here.

David Singmaster had several nice problems to share with me. One is Polyform Towers. You have an unlimited set of all the cubic polyominoes (if you don't know what they are, visit Andrew Clarke's page). Select three of them, and make the highest possible tower, stacking them. David Singmaster conjectured that most of the time, stacking them flat by their longest length gives the highest tower. I challenged him, showing a tower with the pieces stacked at slants. The diagonals were longer, but gravity worked against me. I did find three octominoes that provide a counterexample, though. Can someone find them, or provide a simpler counterexample? Write me.

material added august 12th A Mathematical Model of Zombie Infestations Lon Miller has written an excellent page on Zombies. When he saw my page on the 1918 Superflu, he asked if he could see the program I had written, so he could make a mathematical model of zombie epidemics. Well, here's my code, and it seems to have problems. I'll see if I can fix it as a java applet.

The Dot Maze has been solved by Joseph DeVincentis.

One unusual puzzle I've gotten recently is Danlock.

I found out about the International String Figure Association. I innocently asked its president if he knew how to do cat's cradle, and he showed me some amazing patterns.

material added august 9th Robert Abbott asked me what was familiar about a recent Survivor task - Squared Off. "The game board is made of 100 2' x 2' pieces of plywood. Castaways may move one step at a time, flipping over the piece of wood on which they had previously been standing as they go. Castaways cannot step onto a piece that has been flipped over. Last castaway able to move from one piece to another wins." This is similar to the game of Amazons. I'll see if I can make a puzzle based on this.

Adam Dewbery found a solution to my threecolor puzzle. Basically, build a rectangle so that no two pieces of the same color touch each other. Adam sent me a 5x14 solution. Can you find it? No-one but Patrick Hamlyn has found the 7x10 solution, so here is a hint -- 8 pieces touch the X piece. No-one has solved Hamlyn's Challenge, either.

Hamlyn's Challenge -- make a 12x18 rectangle so that no two pieces of the same color touch each other. material added august 3rd I've added difficult crosswords by Dave Tuller and Craig Kasper to my crosswords page.

The Space Visualization Olympiad contains unfolded polyhedra nets which must be solved as a maze. Very nicely done. Can you become the world champion of 3d visualization?

material added july 31th I've revamped my octiamond page, and added new solutions and problems there. Andrea Gilbert just recently wrote me about solving all six colored packing problems. Also, she mentioned that clickmazes.com has a new look. The Maze of Life editor version 2 is available there, with full undo capability.

material added july 30th Andrea Gilbert has made a Maze of Life editor, see it here. If you make any nice problems with this, please let me know.

material added july 10th A new rectifiable 14-omino has been discovered by Michael Reid. More at his rectifiable polyomino page.

In a recent letter from Wolfram Research: Sarah Flannery, the 16-year-old Irish Young Scientist of the Year who used Mathematica to devise a highly innovative, fast, and secure system of encoding data on the internet, has written about her experience in a recently published book, "In Code"... more here.

material added july 6th I've been visiting with Adrian Fisher in London for the past two weeks. You can read some of what happened in the Posts area. Among other things, www.mitretile.com was launched. Much more will be added to it in coming months.

For my Puzzle of the Week, I'll concentrate on the works of Andrea Gilbert, another person I met in London. Robert Abbott has added to his Things That Roll page, and has added a very nice maze by Andrea to it. The paper versions are interesting to analyze -- all of the people I've heard from so far solve the maze on paper.

Another fabulous new invention is her Plank Puzzles. There is a lot of depth to this new type of maze, I enjoyed solving all of them.

material added june 2nd I'm working on more Zome problems. If you have any, let me see them. Many thanks to George Hart, Eric Weisstein, and Henry Picciotto for their help so far. Thanks to Luc Kumps for giving me the correct link tofor my biggermaze page. I plan to use both Mathematica and LiveGraphics3D in my project for Zome Systems. You can see the start of a Zome Applet at my applets page.

Significant discoveries have recently been made with the Heesch Tiling problem. A configuration with a surround number of 5 can be seen at the Geometry Junkyard. Mark Thompson also discusses it.

Ignacio Ruiz de Conejo solved Steve Stadnicki's problem of dissecting a [4 5 6] triangle to make a [3 8 10].

Roger Phillips and Dylan Thurston have enumerated 62 order-6 Prime Triangles (partitions without subpartitions). See my Triangle page. Also, William Watson and Timothy Firman have solved my Integer Triangle problem. Miroslav Vicher has found all of the order seven prime triangle partitions.