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Atom Stability, Triangles, Retrograde, Posts, Pentagons, and Partridges.
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News, Search Engines, References, and Everything I Like.
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The Octiamond sets -- The first run has
sold out. I've started a second run. Comments I've gotten recently:
"I just received your "Border Patrol" octiamonds set.
I'm stunned at its beauty (and I own most of Kadon's gems). Can't
believe you have produced such a gorgeous set at such an affordable price!
I may order a couple more soon."
"Thanks for the octiamonds - the sets, as you said, are
very attractive."
"I received the octiamonds last Thursday, and the Chaos
Tiles on Friday. I've been carrying around the octiamonds with me
showing them off and trying to get enough time to sit down and work (play,
really) with them."
"I got them today, as you predicted: a lovely little package
of almost Japanese elegance. I've been peeling them as I read my mail;
excellent little pieces that just demand to be shoved together."
"The octiamonds arrived today. I've peeled the tape off
about half of them so far and they're going to look reeeeaaallly nice."
"Oh I wanted to let you know that I got the Chaos Tiles
on Monday. The quality is unbelievable. I had no idea that
one person could go off and have something of that quality made by himself.
If anyone is ever going to make all the fair dice, you are sure the guy
for the job."
Chris Lusby Taylor used Zillions to help him find new rolling die mazes. He made a very nice one, which is now at Robert Abbott's site. You can download see his Zillions program here. A separate version for Arrow Cube mazes is here. The following is a maze I built with the latter. You need to move the cube to the lower right square. The bottom of the cube points down. The space underneath points up. The cube is the same as the one in the arrow cube maze here.
Patrick Hamlyn has come up with an insanely difficult puzzle, which I might produce with some sort of prize. I have Patrick's solution for this puzzle locked in my desk. If I make cubic hexomino sets, they'll come in a cube with the pieces in three colors. A similar, simpler puzzle with fifteen pieces is the threecolor puzzle (also with assistance from Patrick Hamlyn). Rearrange the pieces of the image to form another rectangle with no two pieces of the same color touching each other. No-one has solve that one, so I offer a hint: the whole solution was constructed around X.
Has anyone explored the polyforms made with solidly connected coins? The following diagram shows one way that coins can be stacked. Imagine another layer with 3 coins on top. How many different ways can 4 coins be glued together with face to face contact. Can any interesting figures be made with complete or partial sets of tetracoins?
Erich Friedman's Math Magic asks about optimal packing of squares of two sizes. Already, several discoveries have been made, perhaps you can add to them. In his archives, you can see answers to past challenges.
A new site for puzzle boxes is up -- The Karakuri Creation Group. Outside of Japan, the best source for puzzle boxes is Cleverwood. Their links page is quite nice.
An Iamond solver applet has been written by Daniel Elphick. It solves both hexiamond and heptiamond problems. You can buy them from Kadon here.
Here's a New York Times article from 1991 -- an interview with Monty Hall about the Monty Hall problem.
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. [On Sunday, I mentioned something else, but that was in error].
Ali Muniz has started a page devoted to polyomino covering problems.
Non-mathematical but catchy is the Combo 5 animation, featuring the kitchen staff of Wong Way Chicken.
I came up with a new puzzle for my similar dissections page. See if you can dissect the following figure into 4 similar shapes. It was solved by Joseph DeVincentis, Michael Reid, Serhiy Grabarchuk and Carlos Penedo. Last week's puzzle was solved by Joseph DeVincentis and Stephan Kloder.
Ken Knowlton puts together pictures using dice, dominoes, seashells, and jigsaw puzzle pieces. Amazing work.
The World Puzzle Federation is looking to add more countries. If your country isn't listed at their website, please contact them.
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.
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