Material added 12 Jan 2020

- Plastic Pentagon
- Let p=1.32472... be the root of x^3 - x - 1, the plastic constant. The points in the figure are pairs of triples (a,b,c) used in sign(k) sqrt(|k|) where k=a p^0 +b p^1 + c p^2. Numbers on the lines represent integer powers of square roots of the plastic constant. In 3D there is a 19 point powered clique set.
- Every positive integer is a sum of three palindromes
- Every positive integer is a sum of three palindromes, Javier Cilleruelo, Florian Luca, Lewis Baxter: arxiv.org/abs/1602.06208.
- Biggest Little Polyhedra
- Biggest Little Polyhedra. A talk I gave at the G4G conference based on the Demonstartion Biggest Little Polyhedron.
- Heptahedra
- The 34 canonical heptahedra.
- Almost Perfect Tan Solution
- This is a complete set of triangles with side 1 to 11, and the same triangles scaled up by sqrt(2). Just a small square hole remaining.
- Magic Areas
- Magic square with areas.
- Mondrian Square 26
- A size 26 square divided into rectangles of area 18 to 24, each used twice in different orientations. As a puzzle, do the same with the 10x10 square.
- 51 points in 51 lines of 4
- A 51 point/line 4-configuration. The equations of the points are the same as the equations of the lines.
- tiling a rectangle with the smallest number of squares
- Let f(m,n) be the minimal squares to tile a rectangle. Can an integer multiple be tiled with fewer squares? I give a few thousand possible examples.
- Heilbronn 13
- An improvement to a solution by Peter Karpov. My coordinates: {{0, 0.0992502414}, {0, 1}, {0.0879381177, 0}, {0.6551614146, 1}, {0.7485503739, 0}, {1, 0.4613325715}, {0.96481495015, 0.0876289126}, {0.0879381177, 0.6145067772}, {0.8969384849, 0.90254564724}, {0.3450133066, 0.90150725976}, {0.5001806186, 0.1492347859}, {0.7613458201, 0.4419966218}, {0.3284895496, 0.6333566986}}.
- 27 lines of 4
- 25 points in 27 lines of 4.
- New Yorker Error
- This ad by Architectural Digest in the January 6, 2020 New Yorker magazine has a huge error.
- Integer Partitions
- Connecting Distinct and Complete Integer Partitions by George Beck has some nice new relations.
- Square into 46 45°-60°-75° Triangles
- A square can be divided into 46 45°-60°-75° triangles.
- Mondrian Cubes
- There are 11 distinct cuboids of volume 25 to 36 that can fit into a 7^3 box. Turns out they all fit perfectly in a unique way.

There are 13 distinct cuboids of volume 12 to 24 that can fit into a 6^3 box. Leave out the 1X3x5 and they all fit perfectly in a unique way. - Contiguous Partridge Tiling
- George Sicherman: The monodom also has a contiguous partridge tiling (not reverse partridge)! These are hard to find.

Material added 2 Jan 2020

- Colonel's New Year Puzzle
- George Sicherman: You can download my 2020 New Year Puzzle. My best regards to you all, and wishes for a very happy new year! (George also has a new page on Pentomino Pair Oddities)
- Order-6 Configuration
- At 96_6 Configuration, a discovery of L. W. Berman.
- Angle Numbers
- Each number has that many angles.
- 12 Octagon Toroid
- It's possible to make a toroid with 12 octagons. By Ivan Neretin. Part of Minimal surfaces for planar octagons and nonagons.
- Error-correcting Codes
- I like the free book Error-Correction Coding and Decoding. Many of the SpringerOpen books are free.
- Canonical Tetragonal Antiwedge Hexahedron
- The weirdest of the seven hexahedra, the tetragonal antiwedge, is a self-dual polyhedron that has a volume of 3.141 in its canonical form.
- Four-Chromatic, No 4-cycles
- Part of 4-chromatic unit distance graph with no 4-cycles.
- Orchard Problem
- As a part of Cultivating New Solutions for the Orchard-Planting Problem, I found a new sporadic solution:
- Space-filling Polyhedra
- I'd love to see lots of polyhedra based on On Space Groups and Dirichlet-Voronoi Stereohedra.
- Fractal Cow-Nautilus
- One of the possibilities of the Narayana Cow Triangle Fractal.
- A4 Paper Dissection
- I found this dissection of an area 200 A4 rectangle into smaller A4 rectangles. Rectangle dissection into similar rectangles. Related is the Delian Brick. I also have this long list of A4 Dissections from Patrick Hamlyn.
- Ghee Beom Kim
- I really like the math art of Ghee Beom Kim.

Material added 1 Jan 2020

- I'm in Art of Computer Programming
- A snapshot from Art of Computer Programming, Volume 4. (Pegg). Here's Knuth's Christmas Lecture.
- Shattering the Plane
- I've found a lot of new simple substitution tilings. These are also available as demo, Substitution Tilings. And a long image list of tilings. Related are Power Clique polyhedra, Wheels of Powered Triangles, and Mersenne Twister and Friends.
- Sparse Rulers
- I solved the upper bound problem for Sparse Rulers. Soon to be a blog article and proof. I also have a few demos: Sparse Rulers and Wichmann-like Rulers. I wrote Excess01Ruler that can make a sparse ruler for any length. The key to solving the problem is what NJA Sloane called "Dark Satanic Mills on a Cloudy Day". Also, there is my new demo Wichmann Columns.
- Venn Illusion
- Akiyoshi Kitaoka and Ed Pegg Jr. Based on Venn-5.

The left black circle appears to be smaller than the right one, though they are the same size. Probably won't be an Illusion of the Year. - Unit Distance Graphs
- In Dec 2017 I posted Moser Spindles, Golomb Graphs and Root 33. Aubrey de Grey really liked it and had some ideas for improvements. He then managed to solve the Hadwiger–Nelson problem. The latest 5-color graph is down to 510 points.
- Tetrahedra and Other Polyhedra
- Solid and Dihedral Angles of a Tetrahedron, Canonical Polyhedra, Similarohedrons, and the Tetartoid. The last program was used to make skew dice.
- Mondrian Art Problem
- Mondrian Art Problem, I solved it with Blanche dissections. My solutions ended up on Numberphile. I found weird bounds in Mondrian Art Problem Upper Bound for defect. I also found Possible Counterexamples to the Minimal Squaring Conjecture. Ponting Square Packing.
- Sum of Three Cubes
- 569936821221962380720³ + (-569936821113563493509)³ + (-472715493453327032)³ = 3
- Crossing Numbers 10&11
- There are no Cubic Graphs on 26 Vertices with Crossing Number 10 or 11.
- Incredible Rep-Tile
- Dmitry Mekhontsev (IFSTile.com) found this order 8 3D rep-tile. He has a whole page of rep-8 tilings.
- Graceful Graphs
- The Shrikhande Graph is graceful. And so is the toroidial graph next to it. PUZZLE: Fill in the blank squares with 4 integer values from 2 to 21 so that the 22 queen move differences are the values 1 to 22. Hint to make this solvable by logic: Two of the other numbers are 17 and 21. I also made more sextic toroidal graphs.
- OEIS
- Neil Sloane article at Quanta. And entry A326499 is mine. Also A307450.
- Rolling Polyhedra Graphs
- I've figured out a lot of Rolling Polyhedra Graphs, including all of the deltahedra. I haven't figured out a good embedding for the dodecahedron. I also like various new mirrored polyhedron sculptures. (and more mirrors) I also found some weird-rolling tetrahedra.
- Cut the Knot
- Alexander Bogomolny has died. Working with the family, I've been updating Cut-the-Knot and keeping the site alive.
- Wang Loops
- I like this puzzle by Aaron Wang.
- New Coverings Found
- L's in Circles, Triangles in Circles, and Circles carrying Circles.
- Configurations
- I wondered if there was a configuration of barycentric points and lines where the points and lines were the same. I found a lot of 24_3 solutions and a 27_4 solution.
- Facebook Puzzle Fun
- From the Puzzle Fun page. Patrick Mark Hamlyn: The 196 one-sided heptominoes arranged into 28 congruent shapes of 7 pieces each, 3-colored.
- Difference Set
- The {0,3,4,9,11}_21 difference set in circles and lines. All points 0-20 are connected by a circle or line. Can anyone do the {0,1,3,8,12,18}_31 (0-30) difference set?
- Me
- I'm doing okay. Here's a picture of me in my office at my latest birthday. Most of my recent work has been at Wolfram Community, Wolfram Demonstrations, Facebook, or StackExchange. Looks like I'm 6 years behind. So much more material to post.
- And one of me at the Periodic Table Table
- Puzzlium
- Puzzlium has worked with a lot of people recently. One by me from their Puzzle Box series: Arrange the numbers 1 to 9 in the boxes below so that each line of three boxes sums to 14. Three numbers have already been placed.
- Highway Interchange
- I liked this Highway Interchange.
- Robert Abbott
- Robert Abbott has passed away, leaving behind some great games and mazes like Where Are the Cows? For Elwyn Berlekamp, I rather like the Triangle game.
- Black Holes
- Neutron Star Map. Center of the Galaxy. Black Hole Visualization.

Material added 1 Jan 2019

- Print 3D Puzzles
- Some discussion of Oskar van Deventer and George Miller is in the article The Puzzle Masters.
- Ever See A Tree in a Movie?
- Trees for movies are being outsourced to SpeedTree now.
- Martin Gardner -- The Best Friend Mathematics Ever Had
- Colm Mulcahy wrote a blog article on Martin Gardner.
- Snake Polyominoes
- Shade 16 squares in a 5x10 rectangle so that the remaining square make an obvious path. The resulting snake polyomino is unique.
- New Morpion bound
- Morpion Solitaire 5D: a new upper bound of 121 on the maximum score.
- Ruben's Tube
- Sound, fire, and sine waves are shown in a Ruben's Tube (youtube).
- Loss of a Mail Service
- For fifteen years, I had a system for doing updates involving mail sorting and sending messages to tabs. Sometimes dozens of tabs as I boiled down an update. Unfortunately, Yahoo decided to kill the mail service I was used to, and it's taken me a long time to recover. Part of the process was keeping up with the mail, which I find harder to do in the "new and improved" systems. I'll agree that they look better.
- Party Like it's 19999999...
- 2 10^1059002 -1, or 19999999999999...9999, is prime. It's the first near-repdigit prime found with over a million digits. Found by Serge Batalov.
- Impossible Fractal Sphere
- I liked this impossible fractal sphere.
- Attacking a Triangle
- For an order 20 triangle, 9 vertices can be selected that attack all other vertices.
- All the colors
- At allRGB, interesting math produces 4096x4096 images where every pixel is a different color.
- Doyle Spiral
- The Doyle spiral circle packing is quite beautiful.
- Lines through the United States
- Connect two points of the same US state with a straight line. What's the most other states the line can pass through? Lines through States has the answer.
- Prisoners Dilemma
- Prisoners do better with Prisoner's Dilemma than normal students.
- New Puzzles
- The 2013 Nob Yoshigahara Puzzle Design Competition has the 2013 entries and winners.
- Seven Consecutive Consonants
- A "backlit LCD screen" has 7 consonants in a row. Find some other items with this property.

1. A well-known phrase.

2. A well-known movie.

3. A 2nd grade math topic.

4. A beverage.

5. A piano tune.

Material added 7-11

- Puzzle Solving Cockatoos
- Cockatoos are rather good at solving parrot-friendly puzzles.
- Number Maze
- joedev made a great series of number mazes.
- Advance in Elliptic Curve Theory
- There are advances on the Minimalist Conjecture.
- Ancient Greek Geometry Challenges
- These geometry challenges are quite well done, all with an HTML5 interface.
- ANAGRAMATRON
- Bruce Oberg pointed me to Anagramatron, which scrapes Twitter and looks for anagrams.

I should not be awake right now = I wonder who she is talking to.

"Holy crap I'm late" ~ "metaphorically"

Absolutely apathetic = Especially about that. - 2
^{1061}-1 Factored Last Year - The Cunningham Project factored 2
^{1061}-1 last year. - Crawling Metal Polyhedron
- I liked this slow-moving walking metal polyhedron.
- Ghost Diagrams
- At Ghost Diagrams, shapes with rules try to fit together.
- Paul Nylander's Math Artwork
- I'm not sure if I've linked to Paul Nylander's Math Artwork site, yet.
- Proofs with Problems
- I liked the wikipedia Proofs with Problems, and also the mathoverflow discussion.
- Covering the Alphabet
- Queen Alexandra of Yugoslavia and Herbert Norman Schwarzkopf, Jr. are two names in Wikipedia that cover the alphabet. Is there a shorter pair of names with the same property?

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 ed@mathpuzzle.com.
My mail address is Ed Pegg Jr, 1607 Park Haven, Champaign, IL 61820.

**You can join my moderated recreational mathematics email list at http://groups.yahoo.com/group/mathpuzzle/.**My facebook page is at Ed Pegg Jr.