Re: [math-fun] packing polyominoes?
I have a puzzle of 4 purple plastic pieces that sounds vaguely like what you're describing. They are arranged in a square, and each piece interlocks the next one around in a keyhole-shaped hole. (http://www.cs.brandeis.edu/~storer/JimPuzzles/SHAPE/JigSawFourPiece/JigSawFo...) That's not it, is it? It's available in pretty much all game stores. —Dan Mike Stay wrote: ----- My family recently gave me some packing puzzles for my birthday. One is a rectangle packing puzzle, where the rectangles' edges remain parallel to the sides of the tray; there are some pretty obvious algorithms for solving that one. The other is "Stewart's Coffin", which Martin Gardner pronounced "...the finest dissection puzzle of all time. It looks easy but is fiendishly difficult." It involves four laser-cut polyominoes and a tray that is just slightly too small in either direction for easy placement of the polynomials. Clearly the puzzle involves placing the pieces at an angle, but exactly which angle and how to arrange the pieces is the hard problem.
Are there algorithms for solving a puzzle like this other than brute force?
Here's a picture: https://pbs.twimg.com/media/C-jgT97VYAEvQG9.jpg
On Feb 27, 2018, at 1:10 PM, Dan Asimov <dasimov@earthlink.net> wrote:
That's not it, is it?
JB: "Now I'm wondering what the dimensions of the rectangle is, given say each square of a polyomino is 1 by 1." If you're having a tough time following along, I've created a picture of the rectangle, here: http://chesswanks.com/pot/area.png
I am getting (11x13)/gun(5). On Tue, Feb 27, 2018 at 2:36 PM, Hans Havermann <gladhobo@bell.net> wrote:
JB: "Now I'm wondering what the dimensions of the rectangle is, given say each square of a polyomino is 1 by 1."
If you're having a tough time following along, I've created a picture of the rectangle, here:
http://chesswanks.com/pot/area.png
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Thanks for link to pic, Hans. I get 143/5 for area. On Tue, Feb 27, 2018 at 1:36 PM, Hans Havermann <gladhobo@bell.net> wrote:
JB: "Now I'm wondering what the dimensions of the rectangle is, given say each square of a polyomino is 1 by 1."
If you're having a tough time following along, I've created a picture of the rectangle, here:
http://chesswanks.com/pot/area.png
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This is totally different from the Coffin's pentomino puzzle. What you describe is "4-Piece Jigsaw" (ThinkFun), originally designed by Keith Winegar (although a patent was improperly granted to someone else, later abandoned). It's four identical pieces that mutually interlock in a cycle, and is a great puzzle to figure out how to get it apart...and back together again! Nick On 2/27/2018 10:10 AM, Dan Asimov wrote:
I have a puzzle of 4 purple plastic pieces that sounds vaguely like what you're describing. They are arranged in a square, and each piece interlocks the next one around in a keyhole-shaped hole.
(http://www.cs.brandeis.edu/~storer/JimPuzzles/SHAPE/JigSawFourPiece/JigSawFo...)
That's not it, is it? It's available in pretty much all game stores.
—Dan
Mike Stay wrote: ----- My family recently gave me some packing puzzles for my birthday. One is a rectangle packing puzzle, where the rectangles' edges remain parallel to the sides of the tray; there are some pretty obvious algorithms for solving that one.
The other is "Stewart's Coffin", which Martin Gardner pronounced "...the finest dissection puzzle of all time. It looks easy but is fiendishly difficult." It involves four laser-cut polyominoes and a tray that is just slightly too small in either direction for easy placement of the polynomials. Clearly the puzzle involves placing the pieces at an angle, but exactly which angle and how to arrange the pieces is the hard problem.
Are there algorithms for solving a puzzle like this other than brute force?
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participants (5)
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Allan Wechsler -
Dan Asimov -
Hans Havermann -
James Buddenhagen -
Nick Baxter