From: To: Subject: [eternity] Digest Number 7 Date: Thursday, July 01, 1999 4:33 AM --------------------------- ONElist Sponsor ---------------------------- Who is the most visited e-mail list community Web Service? http://www.onelist.com ONElist.com - where more than 20 million e-mails are exchanged each day! ------------------------------------------------------------------------ There are 25 messages in this issue. Topics in today's digest: 1. Hexagons 'n' things From: "Mark Pursey" 2. Re: So, who are you guys, anyway ? From: "Miguel A. Sanchez Granero" 3. Re: Getting Eternity in the States From: redbaron@cix.compulink.co.uk (Richard Marsden) 4. 201 pieces From: Andreas Gammel 5. Re: So, who are you guys, anyway ? From: Wanderlei Santos Filho 6. Modeling From: "Ing. Marco Polazzo" 7. Re: Getting Eternity in the States From: Don 8. So, who are you guys, anyway ? From: "Christophe Weibel" 9. Re: Opinion please From: Derrick Schneider 10. Re: So, who are you guys, anyway ? From: "Ronald Stewart" 11. Re: Opinion please From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) 12. Re: So, who are you guys, anyway ? From: Jeff Quinn 13. Against the grain From: clive5@dvorak.amd.com 14. Re: Against the grain From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) 15. Re: Against the grain From: clive5@dvorak.amd.com 16. Re: Against the grain From: James Kittock 17. Re: Against the grain From: "Brendan Owen" 18. Re: So, who are you guys, anyway ? From: Paul Why 19. Re: So, who are you guys, anyway ? From: "Dave Jones" 20. Re: So, who are you guys, anyway? From: "Ralph Jackson" 21. Re: Opinion please From: redbaron@cix.compulink.co.uk (Richard Marsden) 22. Re: Getting Eternity in the States From: redbaron@cix.compulink.co.uk (Richard Marsden) 23. Re: So, who are you guys, anyway ? From: Pete Darby 24. Re: Against the grain From: "Miroslav Vicher" 25. Sample Puzzle on website From: "Ronald Stewart" _______________________________________________________________________________ _______________________________________________________________________________ Message: 1 Date: Wed, 30 Jun 1999 22:47:11 +1000 From: "Mark Pursey" Subject: Hexagons 'n' things Hi all, To test my program, i have been creating various hexagons from eternity pieces (to use as smaller puzzles), and have found that all sizes up to 64 pce can be built. I haven't yet found an 81 piece hexagon, but then it may take my solver a while to do so. Has anyone else been doing this, and if so, how high does this number go, the maximum possible being 196? (currently i am only looking with the grain). Also, has anyone encountered a largish shape which can be solved in more than one way with the same subset of [eternity] pieces, ie how is the case for multiple solutions looking? How about a regular shape that requires against the grain placement? In the rules for eternity it mentions a 'start' piece which is marked on the grid... any info on that? Mark Pursey / 27 / student / Sydney, Australia / yes i want the money _______________________________________________________________________________ _______________________________________________________________________________ Message: 2 Date: Wed, 30 Jun 1999 14:44:49 +0200 From: "Miguel A. Sanchez Granero" Subject: Re: So, who are you guys, anyway ? What's your..... name : Miguel Angel age : 25 occupation : mathematician city : Almeria country : Spain email : misanche@ualm.es homepage : none yet ------- Are you an active problem-solver, or just here out of general interest ? ------- Active, but in other field. ------- Do you hope that by listening to this list, you'll get the vital hint that'll make you win the prize ? ------- Not sure. ------- Do you own an Eternity puzzle ? ------- No ------- What's your best attempt by hand ? ------- 4 or 5. ------- What's your best attempt by computer ? ------- 154 by Eternity Screen Solver v1.0 at http://lalsoft.hypermart.net/ScreenSolver.htm. ------- What language / system / pc are you using ? ------- Turbo Pascal 7.0/W95-Dos/P100 ------- What algorithms / heuristics do you use for Eternity (brute force, backtracking, genetic algothims, simulated annealing, SECRET) ? ------- I'm still developing my program. At the moment, computer aid to solve "by hand". ------- Did you type in all 209 pieces yourself ? ------- No, I took them from Vicher. ------- Did you try any simpler variations of Eternity ? ------- No. ------- Do you know some other interesting web-sites ? ------- interesting? ------- Other hobbies ? ------- Reading, movies, play games, etc. ------- Other physical puzzles ? ------- Classical ones ------- Other programming projects ? ------- Some ideas, but no time. ------- Are you willing to show the group your source code (after removing your secret functions) ? ------- Maybe, once I finish and check it. ------- Any other stuff you like to add ? ------- ------- Do you know any other interesting problems ? ------- Yes ------- How are going to spend your 1000.000 pounds ? ------- after or before tax? :-) I don't know, yet. ------- What's the meaning of life ? ------- To LIVE. _______________________________________________________________________________ _______________________________________________________________________________ Message: 3 Date: Wed, 30 Jun 99 14:13 BST From: redbaron@cix.compulink.co.uk (Richard Marsden) Subject: Re: Getting Eternity in the States In-Reply-To: <3779A714.A66A4F85@ibm.net> Also, my copy arrived yesterday, from Hamleys ("biggest toyshop in the World"). They charge $89 to the US including delivery (3 business days, but it took longer for me - possibly because the apts office didn't tell me I had two parcels waiting for me) http://www.hamelys.com So, anyone beat a dozen pieces? :-) Richard _______________________________________________________________________________ _______________________________________________________________________________ Message: 4 Date: Wed, 30 Jun 1999 15:14:56 +0200 From: Andreas Gammel Subject: 201 pieces > 154 by Eternity Screen Solver v1.0 at > http://lalsoft.hypermart.net/ScreenSolver.htm. a collegue here at the office just installed the screen saver and got a '201' in only 10 minutes. De we have a new record ? Andreas _______________________________________________________________________________ _______________________________________________________________________________ Message: 5 Date: Wed, 30 Jun 1999 10:15:43 EST From: Wanderlei Santos Filho Subject: Re: So, who are you guys, anyway ? What's your..... name : Wanderlei Santos Filho age : 32 occupation : Oracle DBA city : Curitiba country : Brazil email : wsantosf@hotmail.com homepage : none yet ------- Are you an active problem-solver, or just here out of general interest ? ------- Getting active after 1.000.000 incentives. ------- Do you hope that by listening to this list, you'll get the vital hint that'll make you win the prize ? ------- Maybe get some bits and pieces to help with the programs. ------- Do you own an Eternity puzzle ? ------- Waiting for delivery. ------- What's your best attempt by hand ? ------- ------- What's your best attempt by computer ? ------- ------- What language / system / pc are you using ? ------- Didn't decide/W95/K62-350 32MB ------- What algorithms / heuristics do you use for Eternity (brute force, backtracking, genetic algothims, simulated annealing, SECRET) ? ------- Probably some implementation of a manual method ------- Did you type in all 209 pieces yourself ? ------- Not yet. ------- Did you try any simpler variations of Eternity ? ------- No. ------- Do you know some other interesting web-sites ? ------- ------- Other hobbies ? ------- Hanging around with the kids (got 4!), movies (yeah, I've seen Episode I, but I couldn't find Spock). ------- Other physical puzzles ? ------- All I can put my hands on. ------- Other programming projects ? ------- This is gonan be my graduation project. ------- Are you willing to show the group your source code (after removing your secret functions) ? ------- Sure, if it works and after confirming delivery. ------- Any other stuff you like to add ? ------- ------- Do you know any other interesting problems ? ------- ------- How are going to spend your 1000.000 pounds ? ------- The rest of the family is trying to decide. Hope there'll be some leftovers after Disney trips and Teletubbies. ------- What's the meaning of life ? ------- Get ready for the next one. _______________________________________________________________________________ _______________________________________________________________________________ Message: 6 Date: Wed, 30 Jun 1999 15:36:02 +0200 From: "Ing. Marco Polazzo" Subject: Modeling Did anyone found a good method to make a model of the pieces ? -- Servotecnica S.r.l. Technical Dept. Manager Ing. Marco Polazzo _______________________________________________________________________________ _______________________________________________________________________________ Message: 7 Date: Wed, 30 Jun 1999 10:38:22 -0400 From: Don Subject: Re: Getting Eternity in the States At 02:13 PM 6/30/99 BST, you wrote: >From: redbaron@cix.compulink.co.uk (Richard Marsden) > >In-Reply-To: <3779A714.A66A4F85@ibm.net> >Also, my copy arrived yesterday, from Hamleys ("biggest toyshop in the >World"). They charge $89 to the US including delivery (3 business days, >but it took longer for me - possibly because the apts office didn't tell >me I had two parcels waiting for me) > >http://www.hamelys.com > > Didn't work , try http://www.hamleys.com/ _______________________________________________________________________________ _______________________________________________________________________________ Message: 8 Date: Wed, 30 Jun 1999 18:28:19 +0200 From: "Christophe Weibel" Subject: So, who are you guys, anyway ? QUESTIONS -------------- What's your..... name : Christophe Weibel age : 21 occupation : student city : Lausanne country : Switzerland email : christophe.weibel@epfl.ch homepage : www.epfl.ch/dmawww/~weibel ------- Are you an active problem-solver, or just here out of general interest ? ------- Active. Well, not yet. Future active, I hope. ------- Do you hope that by listening to this list, you'll get the vital hint that'll make you win the prize ? ------- Yes. It can't hurt. ------- Do you own an Eternity puzzle ? ------- Not yet. I'm waiting for one. ------- What's your best attempt by hand ? ------- 0 :) ------- What's your best attempt by computer ? ------- 151 using ScreenSolver. I hope to make my own program. ------- What language / system / pc are you using ? ------- Probably C, Unix, Silicon graphic O2 (300 Mhz, I think) ------- What algorithms / heuristics do you use for Eternity (brute force, backtracking, genetic algothims, simulated annealing, SECRET) ? ------- brute force and backtracking, I think ------- Did you type in all 209 pieces yourself ? ------- That's a question I wanted to ask: Where can you get a list of the 209 pieces? ------- Did you try any simpler variations of Eternity ? ------- Not yet (waiting for them...) ------- Do you know some other interesting web-sites ? ------- nope. ------- Other hobbies ? ------- mathematics problems ------- Other physical puzzles ? ------- Rubik's cube ------- Other programming projects ? ------- nope ------- Are you willing to show the group your source code (after removing your secret functions) ? ------- well... probably (if I ever do anything that's worth the trouble) ------- Any other stuff you like to add ? ------- I have the feeling I'm incredibly stupid to try to solve eternity... ------- Do you know any other interesting problems ? ------- How do I convince this great girl of going out with me? ------- What's the meaning of life ? ------- Having the courage to stop trying to solve your problems... And to live with them! _______________________________________________________________________________ _______________________________________________________________________________ Message: 9 Date: Wed, 30 Jun 1999 09:27:03 -0700 From: Derrick Schneider Subject: Re: Opinion please > I think we don't know enough yet to tell you the best way. > Monckton designed it to be impossible to solve with a computer, but we > have some very smart, very creative programmers here. (And me.) Who can > resist a challenge like that? Well, now, that gets into the question of how the puzzle was "designed." My understanding is that it went something like this. Mr. Monckton was working with the "polydudes," and built a set of the "dodecadudes," those pieces made up of 12 30-60-90 triangles. He eliminated those with too thin portions, and long sharp points. He was left with roughly 400 pieces. Using this superset, he filled in the dodecagon we're all coming to know and love, and wrote down the solution with its 209 pieces. This became the Eternity puzzle. This says several things to me: a) There are almost certainly multiple solutions to this puzzle. Since the puzzle wasn't designed in any optimal way, and given the number of pieces, this I believe is inevitable. If it is a unique solution, this is purely by chance, and the odds are very definitely against it. b) It wasn't really designed to not be solvable by computer. It's simply that it's got so many pieces that computing time will be fairly extensive. I'm curious. Is anyone setting up an "Internet-based" solver, wherein people can let their computers work on the puzzle (collaboritively) over the Internet? This has had good results for SETI, as well as cracking various "uncrackable" encryption problems. > The longer you see this list going without someone solving it, the more > likely it is that it'll be solved by someone who's been playing with it by > hand 'til they can 'feel' it. That said, I'm holding out hopes for the manual solvers (since I'm one of them). Derrick _______________________________________________________________________________ _______________________________________________________________________________ Message: 10 Date: Wed, 30 Jun 1999 18:12:35 +0100 From: "Ronald Stewart" Subject: Re: So, who are you guys, anyway ? QUESTIONS -------------- What's your..... name : Ronald Stewart age : 16 occupation : student city : nr London country : Do you know where London is? email : ron@rontrekker.freeserve.co.uk homepage : http://www.rontrekker.freeserve.co.uk ------- Are you an active problem-solver, or just here out of general interest ? ------- Don't have Eternity yet. As soon as I have it. ------- Do you hope that by listening to this list, you'll get the vital hint that'll make you win the prize ? ------- Of course I *hope* so, but I doubt it. I'm just here to share ideas. ------- Do you own an Eternity puzzle ? ------- Nope, looking out for it though. If I have to wait much longer, I will mail order. ------- What's your best attempt by hand ? ------- 0 so far! ------- What's your best attempt by computer ? ------- I plan to start with a Depth First algorithm, I understand the Screensaver uses a similar method. ------- What language / system / pc are you using ? ------- Dunno yet! ------- What algorithms / heuristics do you use for Eternity (brute force, backtracking, genetic algothims, simulated annealing, SECRET) ? ------- Brute force and backtracking! ------- Did you type in all 209 pieces yourself ? ------- I will, but for now has anyone done this? I would like to make the pieces up as groups of equilateral triangles, but I haven't seen them yet! ------- Did you try any simpler variations of Eternity ? ------- Not the smaller Eternity puzzles, but I'm useless at the typical ones. ------- Do you know some other interesting web-sites ? ------- hmm... http://www.merlinmystery.com/ ------- Other hobbies ? ------- ------- Other physical puzzles ? ------- I'm into the Merlin Mystery at the moment... but that hasn't gone anywhere since release. I got quite far with the Rubik's cube on my own (whoopee!), there were just a few squares I couldn't figure. ------- Other programming projects ? ------- nope ------- Are you willing to show the group your source code (after removing your secret functions) ? ------- hehe... of course. If you think it would be worthwhile! ------- Any other stuff you like to add ? ------- Good luck to everyone! ------- Do you know any other interesting problems ? ------- How to buy Eternity on no budget? ------- What's the meaning of life ? ------- Trying to find the meaning of life. _______________________________________________________________________________ _______________________________________________________________________________ Message: 11 Date: Wed, 30 Jun 1999 10:28:05 -0700 (PDT) From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Opinion please Derrick Schneider typed something like this in a previous message: > understanding is that it went something like this. Mr. Monckton was > working with > the "polydudes," and built a set of the "dodecadudes," those pieces made up of > 12 30-60-90 triangles. He eliminated those with too thin portions, and long > sharp points. He was left with roughly 400 pieces. Using this superset, he Actually, the pieces made up of "drafter triangles" (30-60-90 triangles) are called "polydrafters." "polydudes" are the polydrafters after those with sharp points, etc. have been removed. That's the terminology Ed Pegg Jr. uses. I prefer to add the term "grid-aligned" to qualify whether the drafter fits onto a triangular grid. There are 13 didrafters, but only 5 grid-aligned didrafters. It's possible to have non-grid-aligned polydudes, but I'm not sure what we should call them. The Eternity puzzle uses dodecadudes. _______________________________________________________________________________ _______________________________________________________________________________ Message: 12 Date: Wed, 30 Jun 1999 12:47:40 -0500 From: Jeff Quinn Subject: Re: So, who are you guys, anyway ? > QUESTIONS > -------------- > What's your..... > > name : Jeffrey Quinn > age : 19 > occupation : Student (Computer Engineering) > country : USA > Are you an active problem-solver, or just here out of general interest ? Active. > Do you hope that by listening to this list, you'll get the vital hint that'll > make you win the prize ? Or give it. :) Oftentimes, things that people say inspire me to try new things which can lead to success, though they may not be the things mentioned. > Do you own an Eternity puzzle ? Still waiting for them to show up in USA. > What language / system / pc are you using ? Assembly language of course! Optimizing compilers still can't hold a candle to the speed of my code. > What algorithms / heuristics do you use for Eternity (brute force, > backtracking, genetic algothims, simulated annealing, SECRET) ? I am using all sorts of mathematics (geometry, number theory, etc) and the properties of the puzzle and its pieces to reduce the problem into several smaller ones and attack them where necessary with brute force. The hope is identify any and all certainties no matter how seemingly irrelevant. Also, by having a great number of ways to invalidate piece placements, the puzzle can be managed many orders of magnitude faster. If I ever get to "last stretch" it will probably be solved by intelligently directed brute force. My current estimates for the "last stretch" is that it will be composed of about 80 to 120 pieces placed with certainty and about 4 to 12 months solid of my solver running to place the remaining ones. These are very loose estimates, though. > Did you type in all 209 pieces yourself ? Nope, I did check them all though. > Did you try any simpler variations of Eternity ? The sample 6 piece puzzle. (By hand/eyes) > Other hobbies/Other physical puzzles ? Many puzzles in the high end of the Rubik's polyhedra difficulty spectrum. Tetris like games, various other geometric/spatial puzzles (tangrams, that brick game, etc.) > Other programming projects ? An emulator for an extremely complex machine (5 CPUs and a host of peripherals) and an operating system. > Are you willing to show the group your source code (after removing your secret > functions) ? Only after I solve the puzzle--whether or not I win the money. > Any other stuff you like to add ? I am curious as to how many people think that the winner of the money (if there is one) will be someone from this mailing list. I also wonder--if one of you *did* solve the puzzle--if would you announce it or keep quiet until your name was published on one of the judging days. > Do you know any other interesting problems ? Write the proof of Fermat's last theorem in the style of "Dr. Seuss." :) > How are going to spend your 1000.000 pounds ? That would be a nice side effect of solving the puzzle but it isn't really my main motivation. Supposing I did, I would first convert it to US dollars. Presumably this would not adversely affect the currency exchange market. After paying the taxes due on the money, I would invest the rest of it and perhaps live off the return. > What's the meaning of life ? I am far too left-brained to care. _______________________________________________________________________________ _______________________________________________________________________________ Message: 13 Date: Wed, 30 Jun 1999 13:04:05 -0500 (CDT) From: clive5@dvorak.amd.com Subject: Against the grain Hi folks, I'd like to get a discussion going about whether or not it is a good idea to be looking for "against the grain" solutions. [For those new to the puzzle, it is possible to place two or more pieces in such a way that they don't line up with the triangular grid underneath. See Wei-Hwa's page: http://www.ugcs.caltech.edu/~whuang/gp/drafters/againstXtheXgrain.GIF for an example.] Obviously, not searching for these solutions cuts down the size of the search space tremendously, simplifies the programming, uses less memory, etc. The question is, what's the tradeoff? If against-the-grain solutions are relatively rare, then this is a good strategy. If they are relatively more plentiful than with-the-grain solutions, then this is a bad strategy. Miroslav Vicher seems to believe these solutions "cause trouble". Perhaps he would care to give us more details about this. Also, I think this against-the-grain stuff isn't really related to the parity issues, but I'm not sure. Thoughts? Clive Dawson Austin, TX _______________________________________________________________________________ _______________________________________________________________________________ Message: 14 Date: Wed, 30 Jun 1999 11:39:11 -0700 (PDT) From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Against the grain clive5@dvorak.amd.com typed something like this in a previous message: > I'd like to get a discussion going about whether or not it is > a good idea to be looking for "against the grain" solutions. > [For those new to the puzzle, it is possible to place two or > more pieces in such a way that they don't line up with the triangular > grid underneath. See Wei-Hwa's page: > http://www.ugcs.caltech.edu/~whuang/gp/drafters/againstXtheXgrain.GIF > for an example.] Where credit is due -- the image is from Bob Harris. > Obviously, not searching for these solutions cuts down the size of the > search space tremendously, simplifies the programming, uses less memory, > etc. Bob theorizes that any solution that has "against the grain" components will have only 90-degree angles in those components. > The question is, what's the tradeoff? If against-the-grain solutions > are relatively rare, then this is a good strategy. If they are > relatively more plentiful than with-the-grain solutions, then this is > a bad strategy. Miroslav Vicher seems to believe these solutions > "cause trouble". Perhaps he would care to give us more details about > this. Well, consider the trapezoid solution to the (grid-aligned) tridrafters (found by Miroslav Vicher) at: http://www.mathpuzzle.com/vichtd1.GIF This solution has an "against-the-grain" component in it. As it turns out (I've verified this with my program) -- ALL solutions to this trapezoid have such a component. (There aren't many). Is Monckton's solution to Eternity all grid-aligned? I'm not sure anyone knows for sure, but my guess is "no." I think one could probably assume that a grid-aligned solution exists. However, there are probably many more solutions where parts are against the grain -- anyone who writes a computer program for Eternity should consider whether considering such solutions is worth the trade-off in computation time. I've independently discovered (I later learned that other people had too, such as Patrick Hamlyn) that if you consider each piece as four times as big as it actually is (expand it by a factor of 2 in both dimensions), then the "against-the-grain" problem disappears. That's why if you look at my source code you'll see a program that takes a drafter set and expands it by 2 in every direction. > Also, I think this against-the-grain stuff isn't really related to > the parity issues, but I'm not sure. Yes and no. It brings up more, complex, parity problems, as I discovered when playing with the didrafters. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- "You may outrank me, but a bath will change that." _______________________________________________________________________________ _______________________________________________________________________________ Message: 15 Date: Wed, 30 Jun 1999 15:49:46 -0500 (CDT) From: clive5@dvorak.amd.com Subject: Re: Against the grain >Bob [Harris] theorizes that any solution that has "against the grain" >components will have only 90-degree angles in those components. By "component" you mean a contiguous cluster of pieces positioned against the grain. Yes, I think this follows from the fact that each individual Eternity piece can always be aligned with the grain. For example, there are no instances of (in fixed-width font): _______ \ |\ \ | \ \ | \ \ | \ \ | \ \|_____\ or __________________ \ | ,-' \ | ,-' \ | ,-' \ |-' \ | \| within any of the pieces. Therefore, since the transition between against-the-grain and with-the grain cannot occur within a single piece, it must occur at a piece boundary. And the only boundaries which makes this possible are the perpendicular legs of the drafters. (Is this a sufficiently rigorous "proof" of Bob's theorizing?!) Note this leads to the trivial observation that since the corners of the puzzle form 150-degree angles (30+60+60), this means that an against-the-grain component cannot fully include a corner, although it can include the 90-degree portion (30+60) of a corner. (But this doesn't mean it can't include two edges. In theory, it could include up to 4 edges!) Another (possibly useless) observation: pieces 20 and 39 are the only ones which do not contain a convex 90-degree angle. >...[Regarding tri-drafter trapezoid...] >This solution has an "against-the-grain" component in it. As it turns >out (I've verified this with my program) -- ALL solutions to this trapezoid >have such a component. (There aren't many). I hadn't noticed that! This certainly weighs heavily in favor of not eliminating against-the-grain solutions in the search. Clive Dawson Austin, TX _______________________________________________________________________________ _______________________________________________________________________________ Message: 16 Date: Wed, 30 Jun 1999 15:20:35 -0700 From: James Kittock Subject: Re: Against the grain My main thought on the issue is this: I believe it is about 90% likely that the puzzle was built by taking a triangular grid and chopping some of the triangles in half to make pieces that contain tridrafters. Therefore, I believe it makes the most sense to look for with-the-grain solutions first. --j > -----Original Message----- > From: clive5@dvorak.amd.com [mailto:clive5@dvorak.amd.com] > Sent: Wednesday, June 30, 1999 11:04 AM > To: eternity@onelist.com > Subject: [eternity] Against the grain > > > From: clive5@dvorak.amd.com > > Hi folks, > > I'd like to get a discussion going about whether or not it is > a good idea to be looking for "against the grain" solutions. > > [For those new to the puzzle, it is possible to place two or > more pieces in such a way that they don't line up with the triangular > grid underneath. See Wei-Hwa's page: > http://www.ugcs.caltech.edu/~whuang/gp/drafters/againstXtheXgrain.GIF for an example.] Obviously, not searching for these solutions cuts down the size of the search space tremendously, simplifies the programming, uses less memory, etc. The question is, what's the tradeoff? If against-the-grain solutions are relatively rare, then this is a good strategy. If they are relatively more plentiful than with-the-grain solutions, then this is a bad strategy. Miroslav Vicher seems to believe these solutions "cause trouble". Perhaps he would care to give us more details about this. Also, I think this against-the-grain stuff isn't really related to the parity issues, but I'm not sure. Thoughts? Clive Dawson Austin, TX --------------------------- ONElist Sponsor ---------------------------- ONElist: the best source for group communications. http://www.onelist.com Join a new list today! ------------------------------------------------------------------------ _______________________________________________________________________________ _______________________________________________________________________________ Message: 17 Date: Thu, 1 Jul 1999 08:51:19 +1000 From: "Brendan Owen" Subject: Re: Against the grain Hi All, > From: James Kittock > > My main thought on the issue is this: > > I believe it is about 90% likely that the puzzle > was built by taking a triangular grid and chopping > some of the triangles in half to make pieces that > contain tridrafters. > > Therefore, I believe it makes the most sense to > look for with-the-grain solutions first. > > --j Below is a quoat from a TV inteview with CM. Which out lines how he got to the puzzle pieces. "I asked Christopher how he had arrived at the pieces. He told me that he chose a lot of pieces on the basic framework, using a computer. He then eliminated those which had 30 degree angles (too sharp for a toy) and those which would be easy to break (so no pieces joined by narrow necks and no long thin projections). This left him with over 1000 pieces and an area to fill with them, which he did by hand, making sure he didn't repeat any piece. As he said, completing the puzzle is easy when you have a lot of pieces to chose from at the end, but it won't be so easy for anyone to repeat with the given set of pieces." Regards Brendan _______________________________________________________________________________ _______________________________________________________________________________ Message: 18 Date: Thu, 1 Jul 1999 00:33:35 +0100 From: Paul Why Subject: Re: So, who are you guys, anyway ? In message <37775D09.CC323D16@oce.nl>, Andreas Gammel writes: > name : Paul Why > age : 40 > occupation : Software Engineer > city : Stevenage > country : UK > email : paul@clastech.demon.co.uk > homepage : none >Are you an active problem-solver, or just here out of general interest? Active-ish, though I don't go looking for them. >Do you hope that by listening to this list, you'll get the vital hint >that'll make you win the prize ? No. If anyone devises a super-efficient solution strategy, they're hardly likely to tell the rest of us. At least, not until they've registered their own solution, by which time it'll be too late. >Do you own an Eternity puzzle ? No. I haven't even seen one. Soon after its release, I scoured the local toyshops, but only Toys R Us had heard of it, and the few copies they'd had were sold almost immediately. I cut a couple of shapes out of cardboard, just to help get the feel of it. >What's your best attempt by hand ? 2. >What's your best attempt by computer ? 0, so far. I've been struggling to think of an efficient way of representing the grid/pieces which would handle this wretched 'against the grain' problem. It effectively means that each piece can be placed with a resolution of half a unit in each direction. As yet, I'm not really satisfied with what I've come up with, and I don't like being beaten. It's far simpler to assume that there exists at least one solution in which the pieces all lie 'with the grain', and go ahead and implement a solver for that case. >What language / system / pc are you using ? C, Windoze 95, Pentium. >What algorithms / heuristics do you use for Eternity (brute force, >backtracking, genetic algothims, simulated annealing, SECRET) ? Brute force, with any short-cuts I can think of. Parity might become useful in the later stages, but getting to that happy position is the big problem. >Did you type in all 209 pieces yourself ? No; I got them from that nice Mr. Vicher. I hope he didn't make any typo's. :-) >Did you try any simpler variations of Eternity ? No; I've not been able to find any of those in the shops either. I wouldn't mind testing my program out on one or more of them (assuming the pieces are similar to the 'real' ones), but I've not found any web sites which would tell me what they look like. >Do you know some other interesting web-sites ? Not puzzle-related. >Other hobbies ? Badminton, quizzes, crosswords, thinking. >Other physical puzzles ? I have a small collection. I was a great fan of pentominoes in my youth, after reading about them in one of Martin Gardner's books. I later wrote an assembler program for my BBC Micro (for non-Brits: a 1MHz, 32k RAM, 6502 processor-based home computer, made by a company called Acorn in the early 80's - don't laugh). It took a couple of days using brute-force to find all 2339 solutions of the 10x6 rectangle, but at least the screen was memory- mapped, so it was interesting to watch. >Are you willing to show the group your source code (after removing your >secret functions) ? Unless it worked, they wouldn't want to see it. If it worked, I'm not sure I'd want to show them. >What's the meaning of life ? Ask John Horton Conway. -- Paul Why paul@clastech.demon.co.uk _______________________________________________________________________________ _______________________________________________________________________________ Message: 19 Date: Mon, 28 Jun 1999 21:56:58 +0100 From: "Dave Jones" Subject: Re: So, who are you guys, anyway ? QUESTIONS -------------- What's your..... name : Dave Jones age : 30 occupation : Aircraft fitter city : 10 mile from Chester country : UK email : delta45@lineone.net homepage : ------- Are you an active problem-solver, or just here out of general interest ? ------- I'm activly trying to solve eternity at moment ------- Do you hope that by listening to this list, you'll get the vital hint that'll make you win the prize ? ------- A problem shared is a problem halfed ------- Do you own an Eternity puzzle ? ------- yes ------- What's your best attempt by hand ? ------- 40 ------- What's your best attempt by computer ? ------- Non ------- What language / system / pc are you using ? ------- Home PC ------- What algorithms / heuristics do you use for Eternity (brute force, backtracking, genetic algothims, simulated annealing, SECRET) ? ------- Not deiced ------- Did you type in all 209 pieces yourself ? ------- Nearly ------- Did you try any simpler variations of Eternity ? ------- No ------- Do you know some other interesting web-sites ? ------- ------- Other hobbies ? ------- ------- Other physical puzzles ? ------- ------- Other programming projects ? ------- ------- Are you willing to show the group your source code (after removing your secret functions) ? ------- ------- Any other stuff you like to add ? ------- ------- Do you know any other interesting problems ? ------- ------- What's the meaning of life ? ------- 42 _______________________________________________________________________________ _______________________________________________________________________________ Message: 20 Date: Thu, 1 Jul 1999 01:12:10 +0100 From: "Ralph Jackson" Subject: Re: So, who are you guys, anyway? QUESTIONS -------------- What's your..... name : Ralph Jackson age : 32 occupation : Research Engineer city :Malvern country : UK email : ralph@jacksquiggle.freeserve.co.uk homepage : don't bother yet ------- Are you an active problem-solver, or just here out of general interest ? ------- Active. ------- Do you hope that by listening to this list, you'll get the vital hint that'll make you win the prize ? ------- Yes ------- Do you own an Eternity puzzle ? ------- Yes. I bumped into it in a shop on 31st May, thought it looked interesting and bought it. Sorry. ------- What's your best attempt by hand ? ------- Didn't bother counting ------- What's your best attempt by computer ? ------- Busy programming. ------- What language / system / pc are you using ? ------- C, AMD K6-2 400 (might borrow some spare Unix power at work) ------- What algorithms / heuristics do you use for Eternity (brute force, backtracking, genetic algothims, simulated annealing, SECRET) ? ------- Brute force but not ignorant. ------- Did you type in all 209 pieces yourself ? ------- No ------- Did you try any simpler variations of Eternity ? ------- All of them. This may be a mistake since I'm not concentrating on any one. ------- Do you know some other interesting web-sites ? ------- rec.puzzles got me to the best I've found so far. ------- Other hobbies ? ------- Kiting, hiking and trying to find time to spend with my daughter ------- Other physical puzzles ? ------- Generic tile/block puzzles. Another win-a-million tile puzzle called Diamond Dilemma from 9? years back. I missed the deadline and never finished it. ------- Other programming projects ? ------- Work stuff, Diamond Dilemma, Block/Tile puzzle designer. ------- Are you willing to show the group your source code (after removing your secret functions) ? ------- Once there's something worthwhile to show. ------- Any other stuff you like to add ? ------- I was going to use this to get a grip on C++ but you are all going too fast. I'll stick with C. ------- Do you know any other interesting problems ? ------- How to stay awake at work after programming eternity all night. ------- What's the meaning of life ? ------- I'm not going to get religious here. _______________________________________________________________________________ _______________________________________________________________________________ Message: 21 Date: Thu, 1 Jul 99 03:03 BST From: redbaron@cix.compulink.co.uk (Richard Marsden) Subject: Re: Opinion please In-Reply-To: <377A4557.B2E37124@ibm.net> > simply that > it's got so many pieces that computing time will be fairly extensive. > I'm > curious. Is anyone setting up an "Internet-based" solver, wherein > people can let > their computers work on the puzzle (collaboritively) over the Internet? > This has > had good results for SETI, as well as cracking various "uncrackable" > encryption > problems. I thought of this. The realistic number of team members doesn't dent the problem much, and lessens the prize. Ie. 1000 members cuts the prize to $1000/head, but only reduces the problem 3 orders of magnitude (out of >100 orders!!!) Richard _______________________________________________________________________________ _______________________________________________________________________________ Message: 22 Date: Thu, 1 Jul 99 03:03 BST From: redbaron@cix.compulink.co.uk (Richard Marsden) Subject: Re: Getting Eternity in the States In-Reply-To: <3.0.2.32.19990630103822.007d0be0@postoffice.worldnet.att.net> > >http://www.hamelys.com > > > > > Didn't work , try http://www.hamleys.com/ oops, typo! :-) Richard _______________________________________________________________________________ _______________________________________________________________________________ Message: 23 Date: Thu, 01 Jul 1999 09:28:34 BST From: Pete Darby Subject: Re: So, who are you guys, anyway ? > name : Pete Darby / Kelly Moorhouse > age : 27 / 24 > occupation : Helpdesk support / Nurse > city : CAnterbury > country : UK > email : pete_darby@bigfoot.com > homepage : none >Are you an active problem-solver, or just here out of general interest? Bit of both. >Do you hope that by listening to this list, you'll get the vital hint >that'll make you win the prize ? Hope, maybe. Expect, dear me no. >Do you own an Eternity puzzle ? Yes > >What's your best attempt by hand ? About 20-30 > >What's your best attempt by computer ? 0 >What language / system / pc are you using ? English & Gibberish languages, sheer luck & fumble system, pc is for OU coursework. & Civilization > >Did you type in all 209 pieces yourself ? No >Did you try any simpler variations of Eternity ? Kelly solved MEteor in 3 Hours, her mum solved Delta in one. Then again, I hear there are more solutions to Delta than meteor. Still working on Heart >Do you know some other interesting web-sites ? Not for Eternity >Other hobbies ? Games of all sorts (board, card, role playing, copmputer, etc.), Am Dram, hang on, is this a job application >Other physical puzzles ? Kelly is usually exceptionally good at them; hence the attempt to win us a mmillion. That, and if someone tells her it can't be done by hand... >Are you willing to show the group your source code (after removing your >secret functions) ? Since this would involve removing my girlfriends brain, I'll pass >What's the meaning of life ? To light a candle of meaning in the darkness of mere being. _______________ Pete Darby AKA Alex's Dad _______________________________________________________________________________ _______________________________________________________________________________ Message: 24 Date: Thu, 1 Jul 1999 11:35:08 +0200 From: "Miroslav Vicher" Subject: Re: Against the grain > > The question is, what's the tradeoff? If against-the-grain solutions > are relatively rare, then this is a good strategy. If they are > relatively more plentiful than with-the-grain solutions, then this is > a bad strategy. Miroslav Vicher seems to believe these solutions > "cause trouble". Perhaps he would care to give us more details about > this. > There are some rules for "against-the-grain" clusters. The boundary of cluster must be "perpendicular". From this follows that the cluster can touch the edge of puzzle only on one of four perpendicular sides. -> The cluster can't contain vertices of puzzle. In some situations it very difficult to continue with the solution - - if a cluster approachs any vertex - if two clusters are close to each other - if a cluster approachs the side he can't touch _______________________________________________________________________________ _______________________________________________________________________________ Message: 25 Date: Thu, 1 Jul 1999 11:30:55 +0100 From: "Ronald Stewart" Subject: Sample Puzzle on website So, how long did it take everyone to complete the sample 6-piece puzzle at http://www.eternity-puzzle.co.uk/ ? It "only" took me 13 minutes and 28 seconds. I told you I was good! Good luck to all in this quest! - Ron _______________________________________________________________________________ _______________________________________________________________________________