[math-fun] Fwd: Sticky Towers of Hanoi
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From: Alex Fink <finka@math.berkeley.edu> Date: April 10, 2010 11:21:52 PM PDT To: rjn@mathstat.dal.ca Cc: Thane Plambeck <tplambeck@gmail.com> Subject: Re: [math-fun] Sticky Towers of Hanoi
I think I've managed to piece together what the game was. Thanks to Aaron Siegel for jogging my memory.
Sticky Towers of Hanoi is played with the disks of an n-disk ToH set (the pegs can be disregarded). In the initial position all of the disks are separate. In a general position there will be stacks of fused disks, with top radius and bottom radius differing. A move is to pick up a stack S and set it on another stack whose top radius exceeds the bottom radius of S; this causes the two disks that come in contact to fuse. Normal (or misere) play convention.
This reduces to a game on posets, interval orders to be precise.
I remember analysing the game with Conway through n=8. I doubt I could find the results (the papers could be in any state of disorganization in either of two cities) but it doesn't seem like a difficult programming task to replicate or surpass it.
best, Alex
On 9 April 2010 09:11, <rjn@mathstat.dal.ca> wrote:
Thane,
I remember Alex Fink did a lot of work with Conway on this problem.
Richard
I remember writing a program for it, similar to one that Erik Demaine (who was also there) wrote, but I don't remember the rules. Erik?
Sent from my iPad
On Apr 8, 2010, at 9:49 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Sticky Towers of Hanoi was apparently invented by John Conway, while attending a Combinatorial Theory Workshop held at "BIRS" (Berkeley?) in June 2005, and attended by (amongst others) Richard Guy and (Thane?) Plambeck [we know what you did last summer]. See https://www.birs.ca/workshops/2005/05w5048/report05w5048.pdf
Is anyone in a position to disclose to us the rules pertaining to this mysterious diversion?
Fred Lunnon
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-- Richard Nowakowski Dept. Mathematics & Statistics Dalhousie University, Halifax NS, B3H 3J5 Canada
Phone (902)-494-6635 FAX (902)-494-5130
-- Richard Nowakowski Dept. Mathematics & Statistics Dalhousie University, Halifax NS, B3H 3J5 Canada
Phone (902)-494-6635 FAX (902)-494-5130
On 4/11/10, Thane Plambeck <tplambeck@gmail.com> wrote:
From: Alex Fink <finka@math.berkeley.edu> Date: April 10, 2010 11:21:52 PM PDT To: rjn@mathstat.dal.ca Cc: Thane Plambeck <tplambeck@gmail.com> Subject: Re: [math-fun] Sticky Towers of Hanoi
I think I've managed to piece together what the game was. Thanks to Aaron Siegel for jogging my memory.
Sticky Towers of Hanoi is played with the disks of an n-disk ToH set (the pegs can be disregarded). In the initial position all of the disks are separate. In a general position there will be stacks of fused disks, with top radius and bottom radius differing. A move is to pick up a stack S and set it on another stack whose top radius exceeds the bottom radius of S; this causes the two disks that come in contact to fuse.
I've obviously missed something at this point --- Why couldn't I just play disc 1 onto 2, 2 onto 3, ..., n-1 onto n, solving the "puzzle" optimally in n-1 moves?
Normal (or misere) play convention.
Aha --- it must be a "game" for k players, perhaps k = 2 (for now ...)
This reduces to a game on posets, interval orders to be precise.
And presumably the idea is to leave your opponent into a position where he has no legal move (etc. for misere).
I remember analysing the game with Conway through n=8. I doubt I could find the results (the papers could be in any state of disorganization in either of two cities) but it doesn't seem like a difficult programming task to replicate or surpass it.
best, Alex
Thanks to everyone who contributed. Fred Lunnon
On 9 April 2010 09:11, <rjn@mathstat.dal.ca> wrote:
Thane,
I remember Alex Fink did a lot of work with Conway on this problem.
Richard
I remember writing a program for it, similar to one that Erik Demaine (who was also there) wrote, but I don't remember the rules. Erik?
On Apr 8, 2010, at 9:49 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Sticky Towers of Hanoi was apparently invented by John Conway, while attending a Combinatorial Theory Workshop held at "BIRS" (Berkeley?) in June 2005, and attended by (amongst others) Richard Guy and (Thane?) Plambeck [we know what you did last summer]. See https://www.birs.ca/workshops/2005/05w5048/report05w5048.pdf
Is anyone in a position to disclose to us the rules pertaining to this mysterious diversion?
Fred Lunnon -- Richard Nowakowski Dept. Mathematics & Statistics Dalhousie University, Halifax NS, B3H 3J5 Canada
Phone (902)-494-6635 FAX (902)-494-5130
I met Alex at the recent Gathering for Gardner; we had a long language-shmooze with Solomon Golomb and some Russian and Japanese folks. Maybe he'd like to be a math-funster. A sharp kid. On Sun, Apr 11, 2010 at 12:32 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
On 4/11/10, Thane Plambeck <tplambeck@gmail.com> wrote:
From: Alex Fink <finka@math.berkeley.edu> Date: April 10, 2010 11:21:52 PM PDT To: rjn@mathstat.dal.ca Cc: Thane Plambeck <tplambeck@gmail.com> Subject: Re: [math-fun] Sticky Towers of Hanoi
I think I've managed to piece together what the game was. Thanks to Aaron Siegel for jogging my memory.
Sticky Towers of Hanoi is played with the disks of an n-disk ToH set (the pegs can be disregarded). In the initial position all of the disks are separate. In a general position there will be stacks of fused disks, with top radius and bottom radius differing. A move is to pick up a stack S and set it on another stack whose top radius exceeds the bottom radius of S; this causes the two disks that come in contact to fuse.
I've obviously missed something at this point ---
Why couldn't I just play disc 1 onto 2, 2 onto 3, ..., n-1 onto n, solving the "puzzle" optimally in n-1 moves?
Normal (or misere) play convention.
Aha --- it must be a "game" for k players, perhaps k = 2 (for now ...)
This reduces to a game on posets, interval orders to be precise.
And presumably the idea is to leave your opponent into a position where he has no legal move (etc. for misere).
I remember analysing the game with Conway through n=8. I doubt I could find the results (the papers could be in any state of disorganization in either of two cities) but it doesn't seem like a difficult programming task to replicate or surpass it.
best, Alex
Thanks to everyone who contributed.
Fred Lunnon
On 9 April 2010 09:11, <rjn@mathstat.dal.ca> wrote:
Thane,
I remember Alex Fink did a lot of work with Conway on this problem.
Richard
I remember writing a program for it, similar to one that Erik
Demaine
(who was also there) wrote, but I don't remember the rules. Erik?
On Apr 8, 2010, at 9:49 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
Sticky Towers of Hanoi was apparently invented by John Conway, while attending a Combinatorial Theory Workshop held at "BIRS" (Berkeley?) in June 2005, and attended by (amongst others) Richard Guy and (Thane?) Plambeck [we know what you did last summer]. See https://www.birs.ca/workshops/2005/05w5048/report05w5048.pdf
Is anyone in a position to disclose to us the rules pertaining to this mysterious diversion?
Fred Lunnon -- Richard Nowakowski Dept. Mathematics & Statistics Dalhousie University, Halifax NS, B3H 3J5 Canada
Phone (902)-494-6635 FAX (902)-494-5130
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
Allan Wechsler -
Fred lunnon -
Thane Plambeck