MathPuzzle.com

A Circle Packing Puzzle: Bill Gosper: For the last several years I've sought to make challenging puzzles based on packing a given set of disks into a given cavity. Unique solutions are nicer and presumably harder to find, so no two disks want to be close in size. On the other hand, if the sizes are widely disparate, the smallest disks fit between the largest, and are simply redundant. These conflicting criteria become nearly impossible to meet as the number of disks reaches twelve, where the sheer number of configurations also works against uniqueness. To make matters worse, it appears to be infeasible to check for uniqueness computationally, or even solve these puzzles at all without simplifying assumptions.
: For circular cavities, the best I have done is eleven disks (The Huddle), with various attempts at twelve (Twubblesome Twelve, TTII, ...) cooked by expert solvers. Perversely, the unintended solutions have generally been *looser* than the apparently close-packed "mathematical" solutions, which probably *could* be found by a sufficiently clever program.

Noncircular cavities enormously complicate things for both the designer and the solver. E.g., the designer no longer has a family of cavity-preserving Moebius transformations on the disk sizes, and the solver (e.g., a program) is faced with a continuum of distinguishable places to start. And by precluding rotations and reflections, an asymmetrical cavity cuts the solution space by another factor of 4. Perhaps best of all, given the size constraints on the disks, it seems possible to fill a slightly greater percentage of a noncircular cavity, although the computations are formidable. Greater coverage leaves fewer solutions.

Experts again cooked my early attempts (Octave, Arnold Laidanegger, ...) but for Arnold Dozenegger, I spent months repeatedly solving systems of 33 polynomials, many with 3367 terms, and 36 unknowns. It very probably falls short of optimal coverage, but so far, no one has found even the intended solution, let alone a bogosity.

[Ed - In addition to the demo above, a picture is at gosper.org. If you are intrigued enough to get a copy of the latest version after years of analysis, even after hearing the price is $300, Bill can be contacted through yahoo.com with username rwmgosper.]
Anagram: Every few months, someone forwards me a letter about anagrams. A comprehensive list of anagrams that have been published in The Enigma is at puzzlers.org.
Animator vs Animation: Two works by Alan Becker, Animator vs Animation and its sequel, make good fun of Flash and the Windows Desktop.
Sperner's Triangle Game: Play one of three colors. Don't make a small triangle with all three colors. You can play The Sperner Game online. Then you can read the Sperner Game paper to see how difficult it is.
Baiocchio Figures: What is the most symmetrical figure you can make with 12 T pentominoes? Colonel Sicherman records everything up to heptominoes in his new Baiocchio Figures page.

The Random Chord Paradox: I added the Random Chord Paradox to the Wolfram Demonstrations Project. What are the odds a random chord measures more than 1.732, the square root of three (and Washington's birthyear)? If the height is chosen randomly, 1/2. If two points on the rim are chosen randomly, 1/3. If a random point inside is used as the midpoint, 1/4. A new method of randomness occurred to me. Two random points inside the unit circle define a chord. What are the odds that this chord is longer than the square root of three? Send Answer. I made a blog post about Demonstration Puzzles for Puzzle Day.

MIT Puzzle Hunt: Steve Nadis wrote up the MIT Mystery Hunt. The Little Black Book Puzzles from the hunt are now online.
Sliced Menger Cube: What does a sliced Menger Cube look like? Answer.
The Darkest Material: BBC writes up an array of carbon nanotubes that makes the darkest material ever made, developed by a team led by Pulickel Ajayan.
Abe Lincoln Must Die: Cartoon duo Sam and Max have done the impossible: episodic computer games, delivered on time. In addition to their unique humor, the series has a number of good puzzles. One of their episodes from last season, Abe Lincoln Must Die, is now available for free.
Self-Affine Tilings: Kenyan and Solomyak have written an interesting paper on self-affine tilings. Another semirecent paper is George Bell's Diamond Solitaire.
Happy 70th Birthday, Donald Knuth: Jeffrey Shallit's Recursion blog celebrates Knuth's 70th birthday.
Benoit Mandelbrot Judges Fractal Art: The Fractal Art Contest 2007 had many stunning images, and was judged by Benoit Mandelbrot. Enjoy the pictures.
Bell Kites: Alexander Graham Bell, in addition to inventing the telephone, was a constructor of octahedral truss kites. Some kite-builders have built some huge examples, as seen on the site.
What song is this?: A very impressive youtube song. Lots of cute effects, with no tricks but memorization.
Spinning Girl Illusion: Wei-Hwa Huang hacks the Spinning Girl Illusion.

Theseus and the Minotaur: Robert Abbott: I finally got Theseus and the Minotaur published as a pretty interesting download. The publisher is Kristanix Games, a company run by a couple of bright Norwegians. Toby Nelson and I will actually get royalties (5%) for the game. I really hope this new version gets popular. I have a write-up about it on my home page. We only have 85 levels, but I'm working on more -- they are all good.
Crayon Physics: I like the game Crayon Physics a lot. A deluxe verse is rumored to be coming out soon.
Luke Pebody Puzzle Blog: Luke Pebody: I have started a puzzle blog at bozzball.blogspot.com. Currently there are only 2 sudoku's and 1 "sudoku X" but more puzzle types will be coming over the upcoming weeks, including: * British-style Cryptic Crosswords * Battleships * Kakuro and more...
A blank and a blank: Rearrange the letters of ABROGATION to get an ending for a sentence that starts "A blank and a blank ...." You'll need to fill in the blanks yourself.
Cubic Dissections Puzzle Marketplace: cubicdissections.com now has a marketplace for high-quality, craftman-made puzzles. Also some one-of-a-kind pieces, antique puzzles, and experiments.
Point Flexagons: Scott Sherman: I noticed that a couple years ago you posted the discovery of the dodecaflexagon, a flexagon-variant with 12 triangles per face. This joins the flexagons Martin Gardner originally described - the hexaflexagon (6 triangles per face) and tetraflexagon (4 or 6 squares per face) - plus the various flexagons made from other polygons (pentagons, hexagons, etc.). More recently, I’ve generalized this to point flexagons (point hinges instead of edges) and triangle flexagons made from any number of triangles per face (e.g. 5 isosceles triangles per face or 4, 6, 8, 10 or more right triangles per face). I’ve also created a number of puzzles on some of these triangle flexagons. My main page for these flexagons is http://loki3.com/flex/index.html. Enjoy!
2008 puzzles: Erich Friedman: Using each of the following collections of digits, along with the usual arithmetic signs ( + - x / ^ ), make a total of 2008. {1,3,8,8,8} {1,4,4,4,8} {2,3,8,8,8} {2,5,9,9,9} {2,7,8,8,8} {2,8,8,8,9} {3,4,8,8,8} {4,4,4,8,9} {4,5,8,8,8} {5,6,6,6,8}.
SSAN puzzle: Bernardo Recaman: I had great difficulty trying to remember my social security identity number, a long string of digits, until I realized that it is the largest number in which every block of two adjacent digits is a different prime or square number. What number is it?
The Complete Set of Oddities: Col. George Sicherman: Mike Reid and I have finally completed the catalogue of heptomino oddities. Every one of the 108 heptominoes has an oddity!

Demonstrations: Quite a few of the most recent Wolfram Demonstrations have been mine. I've been authorized to make an offer to the mathematical hobbyists and diagrammers out there. Mail me a proposal for something that hasn't been made as a mathematical demo, and include a short write up of your math hobbies. The best proposals will get a temporary Mathematica 6 license. As of today, over 2300 math demonstrations are online, and I'm hoping to break 3000 before the end of the year.

Math Factor: The latest Math Factor podcast is an interview with me. Through the miracle of post-editting, I sound amazingly good and smart. Search for Math Factor in iTunes to find it.
Nanomechatronics: Add a single letter to "nanomechatronics" and rearrange to get the full name and title of somebody currently in the news. ANSWER: nanomechatronics + J = Senator John McCain.
The Gewirtz and 77 Graphs: My contest from last month has been claimed by Jonathan Cross and Tony Forbes, who each used some ingenious methods to crack the 77 graph and the Gewirtz graph.
Approximation Puzzles: Erich Friedman: Using only + - x / ( ) and decimal points,
1) approximate pi to three significant figures with three 2's.
2) approximate e to four significant figures with four 7's.
3) approximate the euler gamma constant to four significant figures with four 8's.
45 Thousand Ballpoint Balls: Bathsheba Grossman: Hi, I thought you might like this (14 Meg): (main link, mirror 1). It's a lot of ball-point pen balls suspended between two glass plates, being vibrated by a small motor. It does these interesting things: crystal-like interface boundaries and fracture lines obviously, but also cellular automata-like features such as little triangular configurations that seem to propagate like Life gliders. This device belongs to Ward Fleming (pinscreens.net, he invented those pin screens that one makes faceprints on), and I couldn't help thinking it'd make a nice interactive installation somewhere.
The Hexacubes: Kadon Enterprises has put together a hexacube set for a collector.

The Griddle: David Millar has been managing to make a lot of puzzle updates at The Griddle. I like his series of Ghost/Vampire/Zombie mirror puzzles.

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