[math-fun] half-life of Gordian's Knot puzzle
I spent a frustrating hour trying to solve the “Gordian’s Knot” puzzle, recently given to me by a friend. The principle of the puzzle is nice: six solid polyomino pieces, formed by making holes inside 1x5x7 rectangular slabs, arranged as pairs in three orthogonal planes and initially forming a very compact “nucleus”: http://www.amazon.com/Think-Fun-6820-ThinkFun-Gordians/dp/B000EGI4OO The goal is to completely remove one of the pieces. But it’s not a fun puzzle to solve because the pieces often jam and don’t slide very freely. It wasn’t too hard to write a short computer program that random-walks its way to the solution (at each step it picks at random one of the few legal moves). I’m sharing this with math-fun because it turns out to be a nice metaphor of radioactive decay. After a period of diffusive motion where all six pieces are “bound” together, an “alpha particle” is ejected, seemingly at a random moment. Unlike the Coulomb barrier that a real alpha particle has to tunnel through, the orange piece in this puzzle has to find its way through an entropic bottleneck. From the few decays I’ve observed up to now, I estimate the half-life to be several hundred moves. **************************************************************************************** Warning: exercise extreme caution when clicking the following link: https://www.dropbox.com/s/bxcc7h2am1e49ww/alphadecay.gif?dl=0 **************************************************************************************** -Veit
why the warning attached to the link? Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Fri, Aug 21, 2015 at 2:37 PM, Veit Elser <ve10@cornell.edu> wrote:
I spent a frustrating hour trying to solve the “Gordian’s Knot” puzzle, recently given to me by a friend. The principle of the puzzle is nice: six solid polyomino pieces, formed by making holes inside 1x5x7 rectangular slabs, arranged as pairs in three orthogonal planes and initially forming a very compact “nucleus”:
http://www.amazon.com/Think-Fun-6820-ThinkFun-Gordians/dp/B000EGI4OO
The goal is to completely remove one of the pieces. But it’s not a fun puzzle to solve because the pieces often jam and don’t slide very freely.
It wasn’t too hard to write a short computer program that random-walks its way to the solution (at each step it picks at random one of the few legal moves). I’m sharing this with math-fun because it turns out to be a nice metaphor of radioactive decay. After a period of diffusive motion where all six pieces are “bound” together, an “alpha particle” is ejected, seemingly at a random moment. Unlike the Coulomb barrier that a real alpha particle has to tunnel through, the orange piece in this puzzle has to find its way through an entropic bottleneck. From the few decays I’ve observed up to now, I estimate the half-life to be several hundred moves.
**************************************************************************************** Warning: exercise extreme caution when clicking the following link:
https://www.dropbox.com/s/bxcc7h2am1e49ww/alphadecay.gif?dl=0
****************************************************************************************
-Veit
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Aug 21, 2015, at 2:56 PM, Neil Sloane <njasloane@gmail.com> wrote:
why the warning attached to the link? math-fun member rant:
Great gifs, but please don't use DropBox. Although the link says ".gif", I initially only get a ".jpeg" still image. I then have to turn on Javascript & go through a who sequence of things (including telling DropBox I don't want to join them & put their buggy & insecure code on my machine) in order to actually download the .gif image.
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
You just have to set dl=1: https://www.dropbox.com/s/bxcc7h2am1e49ww/alphadecay.gif?dl=1 Then it will download the gif. On Fri, Aug 21, 2015 at 12:35 PM, Veit Elser <ve10@cornell.edu> wrote:
On Aug 21, 2015, at 2:56 PM, Neil Sloane <njasloane@gmail.com> wrote:
why the warning attached to the link? math-fun member rant:
Great gifs, but please don't use DropBox. Although the link says ".gif", I initially only get a ".jpeg" still image.
I then have to turn on Javascript & go through a who sequence of things (including telling DropBox I don't want to join them & put their buggy & insecure code on my machine) in order to actually download the .gif image.
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
I believe it is possible to use dropbox just to serve a file, no? You store the file in your dropbox Public folder and then Copy Public Link gives you a pointer directly to it--no extraneous software involved. --ms On 21-Aug-15 15:35, Veit Elser wrote:
On Aug 21, 2015, at 2:56 PM, Neil Sloane <njasloane@gmail.com> wrote:
why the warning attached to the link? math-fun member rant:
Great gifs, but please don't use DropBox. Although the link says ".gif", I initially only get a ".jpeg" still image.
I then have to turn on Javascript & go through a who sequence of things (including telling DropBox I don't want to join them & put their buggy & insecure code on my machine) in order to actually download the .gif image.
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Aug 21, 2015, at 11:37 AM, Veit Elser <ve10@cornell.edu> wrote:
I spent a frustrating hour trying to solve the “Gordian’s Knot” puzzle, recently given to me by a friend. The principle of the puzzle is nice: six solid polyomino pieces, formed by making holes inside 1x5x7 rectangular slabs, arranged as pairs in three orthogonal planes and initially forming a very compact “nucleus”:
http://www.amazon.com/Think-Fun-6820-ThinkFun-Gordians/dp/B000EGI4OO <http://www.amazon.com/Think-Fun-6820-ThinkFun-Gordians/dp/B000EGI4OO>
Interesting pricing by Amazon: One is $11.99, but two are $65.44. —Dan
The goal is to completely remove one of the pieces. But it’s not a fun puzzle to solve because the pieces often jam and don’t slide very freely.
It wasn’t too hard to write a short computer program that random-walks its way to the solution (at each step it picks at random one of the few legal moves). I’m sharing this with math-fun because it turns out to be a nice metaphor of radioactive decay. After a period of diffusive motion where all six pieces are “bound” together, an “alpha particle” is ejected, seemingly at a random moment. Unlike the Coulomb barrier that a real alpha particle has to tunnel through, the orange piece in this puzzle has to find its way through an entropic bottleneck. From the few decays I’ve observed up to now, I estimate the half-life to be several hundred moves.
**************************************************************************************** Warning: exercise extreme caution when clicking the following link:
https://www.dropbox.com/s/bxcc7h2am1e49ww/alphadecay.gif?dl=0 ****************************************************************************************
On 2015-08-21 12:04, Dan Asimov wrote:
On Aug 21, 2015, at 11:37 AM, Veit Elser <ve10@cornell.edu> wrote:
I spent a frustrating hour trying to solve the “Gordian’s Knot” puzzle, recently given to me by a friend. The principle of the puzzle is nice: six solid polyomino pieces, formed by making holes inside 1x5x7 rectangular slabs, arranged as pairs in three orthogonal planes and initially forming a very compact “nucleus”:
http://www.amazon.com/Think-Fun-6820-ThinkFun-Gordians/dp/B000EGI4OO <http://www.amazon.com/Think-Fun-6820-ThinkFun-Gordians/dp/B000EGI4OO>
Interesting pricing by Amazon: One is $11.99, but two are $65.44.
—Dan
They make it up in volume. --rwg
The goal is to completely remove one of the pieces. But it’s not a fun puzzle to solve because the pieces often jam and don’t slide very freely.
It wasn’t too hard to write a short computer program that random-walks its way to the solution (at each step it picks at random one of the few legal moves). I’m sharing this with math-fun because it turns out to be a nice metaphor of radioactive decay. After a period of diffusive motion where all six pieces are “bound” together, an “alpha particle” is ejected, seemingly at a random moment. Unlike the Coulomb barrier that a real alpha particle has to tunnel through, the orange piece in this puzzle has to find its way through an entropic bottleneck. From the few decays I’ve observed up to now, I estimate the half-life to be several hundred moves.
**************************************************************************************** Warning: exercise extreme caution when clicking the following link:
https://www.dropbox.com/s/bxcc7h2am1e49ww/alphadecay.gif?dl=0 ****************************************************************************************
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (6)
-
Dan Asimov -
Mike Speciner -
Mike Stay -
Neil Sloane -
rwg -
Veit Elser