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Math Games
Social Golfer Problem Wolfram Demonstrations Dodecahedral Tilings Power Sums Melbourne: City of Math Snakes on a Plane Prime-generating Polynomials The Fano Plane G4G7 Kobon Triangles Beautiful References Times Square Magic From Keyfobs to Ringtones Sudoku Variations Vector vs. Raster Tournament Dice Deadly Rooms of Death Fair Dice Chessboard Tasks A Zillion Connection Games Keen Approximations NUMB3RS TV show Cyclopedia of Puzzles Sliding-block Puzzles Rulers and Gracefulness Hoffman-Singleton Game Ten Trillion Zeta Zeros Evil Numbers Manifolds in Genesis 64K or Less - Demoscene Modern Burr Puzzles Egyptian Fractions Nob Yoshigahara 2D Turing Machines WireWorld Multiplication Crossword Rules The Quantian Distribution Integer Complexity Supermagnetic Polyhedra Gaussian Numbers Number Games Guilloché Patterns Prime Megagap Wolfram Functions Site Cubic Symmetric Graphs Superflu Modeling Domino Graphs Sequence Pictures Square Packing Multi-state Mazes Loculus of Archimedes Matrix Revolutions Möbius Function Paterson's Worms Revisited
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Material added on Martin Gardner's Centerary
My poem for the Wolfram Blog
For today’s magic show:
A century ago,
Martin Gardner was born in Oklahoma.
He philosophized for his diploma.
He wrote on Hex and Tic-Tac-Toe.
The Icosian game and polyomino.
Flexagons from paper trim,
Samuel Loyd, the game of Nim.
Digital roots and Soma stairs,
mazes, logic, magic squares.
Squaring squares, the golden Phi.
Solved the spider and the fly.
Packing circles (with corrections),
ellipses, pi, and conic sections.
Martin GardnerPenrose Tilings and Wieringa Roofs
Tiling with PentominosHamiltonian Tours on Polyhedra

Group theory braids and primal gaps,
Latin squares, the four-color maps.
Hypercubes and Turing machines,
curves of constant width, eight queens.
The Klein bottle when cut in halfs,
helices and Graceful Graphs.
The Arecibo message, divisibility tests.
The Ulam spiral, parity checks.
Bracing buildings that won’t tilt,
trisections, Mrs. Perkins’s Quilt.
Pascal’s triangle, ternary scoring,
bouncing balls for water pouring.
Constrained geometry construction,
e and patterns of induction.
The abacus and random walks,
cyclic numbers, sliding blocks.
Pythagorean theorem, gears,
art of M. C. Escher, spheres.
Dominoes and overhang jutting,
infinite series, fair cake cutting.
Aleph-Null and Aleph-One.
For Game of Life, a glider gun.
Paterson’s worms and knotted torus,
paper folding, Nine Men’s Morris.
A problem solved by Andrew Wiles.
Pigeonholes and Penrose tiles.
Peg solitaire, a loop of string,
folded dragon curves, I Ching.
Rep-tiles and Borromean rings.
The pentagons of Marjorie Rice,
shuffling, “The Kiss Precise,”
tetrahedra, cycloids, dice.
Diophantine analyses,
geometric fallacies.
Dice nontransitivity,
special relativity.
The list meanders on for days,
but that’s enough to give him praise.
The Circles of DescartesGolden Spiral
Mazes on Various Surfaces
Dandelin Spheres for an EllipseMondrian Four Coloring
Magic Squares and DesignsOverhanging Cards
Graceful GraphicsKnot Explorer
Bicycle Wheels Using Curves of Constant Width
Random Chord Paradox
Ammann ChairCurry Triangle ParadoxLooney Gears
Originally published at the Wolfram Blog.

More on Martin Gardner
From the New York Times, The Guardian, BBC News,,
Material added 7 October 2014
Vacation Over
Time to get back to this. Will try to have at least three items a day for awhile as I plow through the backlog.
OEIS turns 50
Neil Sloane's OEIS turns 50. turns 50, and Alex Bellos writes it up in the Guardian as Neil Sloane: the man who loved only integer sequences. But that's not true, Neil loves lots of things, like lattices and sphere packings.
George Sicherman: I have not found any 5x5 pentapent solutions, but we can use the 7 tetrapents to make two congruent 28-pents, providing that we use one of the tetrapents in both figures. This figure is unique, but the tiling on the left is not.
TheMetagrobologist Magazine
TheMetagrobologist Magazine is a very snazzy only magazine devoted to puzzles.
Covent Garden Floating Market
A very nice illusion of a floating building.
Covent Garden
The mate-in-n problem of infinite chess is decidable
The mate-in-n problem of infinite chess is decidable -- a new paper at
Pangrammic Top Ten
Eric Harshbarger notes that last weeks top ten movies made a pangram.
Martin Gardner Centennial
Martin Gardner's 100th birthday is a few weeks away. Scientific American starts off the celebration.
Material added 20 March 2014
Pentahex Holes
George Sicherman - This weekend Abaroth sent me the attached picture of the 22 pentahexes. It has 33 holes, and is symmetric too. According to Andrew Clarke's Poly Pages, the old record was 30 holes.
Pentahax Holes
Toshihiro Shirakawa Polyboxes
Toshihiro Shirakawa has found a number of new polyboxes.
Large Polybox
Hamiltonian Circuit for Rubik's cube
A Hamiltonian solution for Rubik's Cube is known.
Seven, Eight, and Nine Touching Cylinders
Peter V. Pikhitsa1 and Mansoo Choi have a new paper, Seven, eight, and nine mutually touching infinitely long straight round cylinders.
Mark J. P. Wolf (from my work-in-progress book, 101 Enigmatic Puzzles)
Within the new Short Form 1, there is a loophole; with just the right amount of income, you don’t owe any tax at all. Find the one income amount that will result in zero tax owed when the tax form below is filled out. (docx answer)
Tax Problem
Recent Anagrams
Arlo Guthrie's The City of New Orleans = Steel light train confers "How are you?".
I Have No Mouth And I Must Scream = A dour time to humans vs. machine.
Captain America: The Winter Soldier = WARipedia historical reenactment.
American Institute of Bisexuality = Caution: extreme unsatisfiability.
Christopher Nolan films esoteric ~ techno-thriller for space mission. 
Worst-Case Scenario Handbook = Coordinate Seahawks-Broncos.
Electrochemical fluorination = Lime in the coconut for all I care.
Blockbuster motion picture = Put trust in comic book rebel.
Money is the root of all evil = Some love the irony of it all.
Let's run it up the flagpole = Telling "put up for the sale."
Institutional researcher = "In the literature" narcosis.
"A Tribute to Heroes" = He's about to retire. 
Hi, G. Washington! = How's it hanging?
Crimea votes to ~ act more soviet.
Interest group = Peers tutoring.
Heesch-2 Polyomino
Glenn Rhoads found the minimal Heesch 2 polyomino in his 2003 thesis "Planar Tilings and the Search for an Aperiodic Prototile". I haven't seen it elsewhere, so here's a picture:
Heesch-2 polyomino
Minimal Superpermutations
123412314231243121342132413214321 has all permutations of "1234", and is minimal. The shortest string for "12345" is unknown. These are called minimal superpermutations, and much harder to find than DeBruijn sequences.
Oskar Interview
An interview with Oskar is up, you can also head to Oskar's website, or Oskar's youtube channel.
George Sicherman -- Here is a little puzzle that I call the Vixelstar. Just put the pieces on the left together to make the star-shaped figure on the right. You may flip pieces over. Also, these pages were all added recently to Polyform Curiosities: Zucca's Challenge Problem for Tetracubes, Pentacubes in a Box, Galvagni Figures & Reid Figures for Polycairos, Tetrahendec Oddities, Pento-Pento-Trominoes, Pento-Pento-Tetrominoes, Quadruple Pentominoes, and Printable Polycairo Grid.
Similar Pentomino Shapes
Livio Zucca: Odette De Meulemeester, George Sicherman and I are trying minimal solutions for each Pentomino, such as the type in the picture.
similar pentominoes
Paths Through a Square
Take 12 points around a square, with points in the corners and 4 points on each side. Join up the points with 6 lines, with no lines connecting points on the same side. The correct answer is 200 ways to do it. If mirror symmetries are removed, then there are 121 ways to do it.
Paths Through a Square
Top cited Math Papers
Here's a list of the top cited math papers of all time.
Attractive Attractors
I liked this gallery of chaotic attractors.
The Gentle Art of Filling Space
A new book about the tiling patterns of Robert Reid is available.
How to Tie a Tie
How to knot a tie -- 177,147 distinct tie knots.
Weird Paper Sculptures
By making a huge stack of accordion-joined paper and then chiseling a bust out of it, surprisingly flexible heads can be made.
Longest Entertainment Assemble?
Star Trek original cast -- 25 years.
Jack Benny and Eddie "Rochester" Anderson -- 28 years.
Cheech and Chong -- 33 years.
Carson and McMahon -- 34 years.
Tom Baker and Louise Jameson -- 36 years.
Burns and Allen -- 36 years.
Marx Brothers -- 54 years.
Eddy Christiani and Frans Poptie -- 64 years.
Modeling a Perfect Pool Break
Modeling a perfect break in the game of pool with Mathematica. 
Frank Longo Themeless Crossword
This crossword fill for Fireball by Frank Longa is quite amazing.
Golly on Android
The excellent cellular automata program Golly is now available as Golly on Android.
Wordplay Blog
The Wordplay Blog at the New York Times has many nice problems, such as the Princess problem.
Temari Spheres
A 92-Year-Old grandmother creates a spectacular collection of embroidered Temari Spheres.
New Folding Record
MIT's Infinite Corridor was used to make a new folding record, breaking Britney Gallivan's paper folding record. I got her mentioned in the Numb3rs episode Identity Crisis.
No Four in a Plane
There are 38 ways to pick 13 points from a 5x5x5 grid so that no four points are in a plane. There is a unique solution for 8 points from 3x3x3, and 232 solutions for 10 points from 4x4x4. What are solutions for 6x6x6 and up?
Payback Percentages
Payback percentages are the amount a slot machine must return, and they are defined by law. According to a site explaining how to win at slot machines, the state with the lowest minimum payback is Nevada with 75%, and the state with the highest is Maine with 89%. I never would have guessed that. Much of optimizing life as a gambler now involves researching the law. For example, for poker, the site covers New Jersey Law as it relates to poker.
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 My facebook page is at Ed Pegg Jr.