From: To: Subject: [eternity] Digest Number 18 Date: Friday, July 09, 1999 4:30 AM --------------------------- ONElist Sponsor ---------------------------- ONElist: your connection to people who share your interests. ------------------------------------------------------------------------ There are 16 messages in this issue. Topics in today's digest: 1. Re: Ecentricity & retrospect From: Morgan Gary 2. Against the grain model From: Eugene Gill 3. Postscript From: Morgan Gary 4. Re: Against the grain model From: Morgan Gary 5. Against the grain model From: pwadsworth@Softworks.co.uk 6. Data Structures for eternity From: Mogens Jerløv 7. Re: Against the grain model From: N B 8. Re: Against the grain model From: Morgan Gary 9. Re: Data Structures for eternity From: falk.werner@zurichre.com 10. Re: Data Structures for eternity From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) 11. grain model and data structures From: "Mark Pursey" 12. Re: grain model and data structures From: Jason.Mccallion@ft.com (Jason Mccallion) 13. FW: [eternity] Welcome to eternity@onelist.com From: "Matt Watson" 14. Re: Welcome to eternity@onelist.com From: Kevin Pretorius 15. Re: Opinion please From: Chuck Deerinck 16. How was it constructed? From: Dsaund2773@aol.com _______________________________________________________________________________ _______________________________________________________________________________ Message: 1 Date: Thu, 8 Jul 1999 11:43:00 +0100 From: Morgan Gary Subject: Re: Ecentricity & retrospect I refer also to the increasing amount of torture and frustration that I'm subjected to just thinking about a realistic method of solution. contemplating where on earth I'm going to come up with at least 70 distinct & compounded heuristics in order that a search engine has at least chance of traversing a non-negligable proportion of the search tree within my lifetime. (And I haven't even started coding the search engine yet!) Oh the simple joys of the lottery! where your only problem is choosing the configuration of numbers on 67 lottery tickets to use that would maximise your chances. Ignorance is bliss. ---------- From: Jason.Mccallion@ft.com To: Morgan Gary Subject: Re: [eternity] Ecentricity & retrospect Date: Thursday, July 8, 1999 11:13 Morgan Gary on 08/07/99 09:56:00 To: eternity@onelist.com cc: (bcc: Jason Mccallion/LONDON/FINANCIAL TIMES) Subject: [eternity] Ecentricity & retrospect But what fun is the lottery??? From: Morgan Gary I'm going to integrate the discipline of hunches for my winning algorithm. This should reduce the search tree by several factors, assuming my hunches behave like ORACLES. :-) Anyhow, I hypothesize that the longer time spent by us lot, looking for the solution to Eternity, the more inclined we would be to advise newbie Eternites to forget that Eternity ever existed and go out & buy 67 lottery tickets instead! The odds are in your favour. (I approximate 67 with the price of Meter + Delta + Heart + Eternity) Gary --------------------------- ONElist Sponsor ---------------------------- Why do WOMEN ASTRONAUTS have such BAD HAIRCUTS? What happens if you CLEAN your self-cleaning OVEN? The DR. has answers:Click ------------------------------------------------------------------------ **************************************************************************** ************ *Please visit the web site of the Financial Times at http://www.ft.com * * * *This E-Mail is intended for the use of the addressee only and may contain confidential* *information. If you are not the intended recipient, you are hereby notified that any * *use or dissemination of this communication is strictly prohibited. * *If you receive this transmission in error, please notify us immediately then * *delete this E-Mail. * * * *postmaster@ft.com * **************************************************************************** ************ _______________________________________________________________________________ _______________________________________________________________________________ Message: 2 Date: Thu, 8 Jul 1999 12:16:02 +0100 From: Eugene Gill Subject: Against the grain model Hi I've been wondering how people have been modelling this puzzle. This is how i'm doing it. not finished yet. I'm trying to build a model which takes on the issue of against the grain pieces. I've found that this significantly complicates the model. My model is also basically made out of the edges of a drafter. Specifically opposite and adjacent edges of the 30 degree corner. (I call the adjacent edge a "long edge"). The hypotenuese edge is modelled as comprising of two rotated and translated opposite edges. Using this model I can find the adjacency of two pieces by finding matches in the position of their exposed edges. I call the equilateral triangles either "Hills" and "Valleys". I call the division of the equilateral triangles "Vertical", "Climbing" and "Decending" according to the slope of the division. When I was looking at w"ith the grain" solutions, I divided the grid into rectangles made up of equilateral triangles with a drafter on each side. however I found this inappropriate for "against the grain" so now my cells are the equilateral tirangles together with the against the grain inversions. Thus my cell structure is defined by the position of the "long ege. It can be Vertical,(Hill and Valley the same), Hill/Climbing, Hill/Decending, Valley/Climbing or Valley/Decending. On each of these long edges there are 4 ways of positioning the drafters. So this leads to one of 20 combinations of shape which can occur in each of my cells. Maybe this is over-complicated? Eugene _______________________________________________________________________________ _______________________________________________________________________________ Message: 3 Date: Thu, 8 Jul 1999 13:28:00 +0100 From: Morgan Gary Subject: Postscript Has anyone created a postscript version of the board & pieces that they would like to share with us? The bitmap versions from www.mathpuzzle.com don't scale very well when printed. _______________________________________________________________________________ _______________________________________________________________________________ Message: 4 Date: Thu, 8 Jul 1999 13:41:00 +0100 From: Morgan Gary Subject: Re: Against the grain model You could redefine each piece using the following mapping Replace every triangle in the old piece set with 4 triangles in the new piece set i.e. (borrowing Roger Phillips ascii set) + / \ / \ +--+--+ becomes + / \ / \ +--+--+ / \ / \ / \ / \ +--+--+--+--+ etc. Then, you can proceed with an algorithm that does not take in to account pieces *against the grain*. Note that you'll then be working with a grid 4 times as dense than before. Does this add too many redundant configurations? ---------- From: Eugene Gill To: 'eternity@onelist.com' Subject: [eternity] Against the grain model Date: Thursday, July 8, 1999 12:16 From: Eugene Gill Hi I've been wondering how people have been modelling this puzzle. This is how i'm doing it. not finished yet. I'm trying to build a model which takes on the issue of against the grain pieces. I've found that this significantly complicates the model. My model is also basically made out of the edges of a drafter. Specifically opposite and adjacent edges of the 30 degree corner. (I call the adjacent edge a "long edge"). The hypotenuese edge is modelled as comprising of two rotated and translated opposite edges. Using this model I can find the adjacency of two pieces by finding matches in the position of their exposed edges. I call the equilateral triangles either "Hills" and "Valleys". I call the division of the equilateral triangles "Vertical", "Climbing" and "Decending" according to the slope of the division. When I was looking at w"ith the grain" solutions, I divided the grid into rectangles made up of equilateral triangles with a drafter on each side. however I found this inappropriate for "against the grain" so now my cells are the equilateral tirangles together with the against the grain inversions. Thus my cell structure is defined by the position of the "long ege. It can be Vertical,(Hill and Valley the same), Hill/Climbing, Hill/Decending, Valley/Climbing or Valley/Decending. On each of these long edges there are 4 ways of positioning the drafters. So this leads to one of 20 combinations of shape which can occur in each of my cells. Maybe this is over-complicated? Eugene --------------------------- ONElist Sponsor ---------------------------- ONElist: your connection to like-minds and kindred spirits. ------------------------------------------------------------------------ _______________________________________________________________________________ _______________________________________________________________________________ Message: 5 Date: 8 Jul 1999 13:23:15 -0000 From: pwadsworth@Softworks.co.uk Subject: Against the grain model Regarding MorganGA@logica.com note and splitting each triangle into 4 triangles, does not help with sorting out the Against the Grain problem. If you take piece 34 , A /- ----- |\ /\ | \/ \ ------- | /\ /| |/ \/ | -------- B and then place it along the edge where you have complete triangles, and on the left you have 5,2,5,2,5,2 going up at 30 deg. --------------------------------------- B \/\ /\ /\ /\ /\ /\ /\ /\ /\ \ \/ \/ \/ \/ \/ \/ \/ \/ \ --A--------------------------------- You will see that even if you draw 4 triangles per triangle, you can still place the piece against the Grain. It may seem that doing the 4 triangles will help, but it will also increase the amount of data that has to be checked, and therefore take even longer to solve _______________________________________________________________________________ _______________________________________________________________________________ Message: 6 Date: Thu, 08 Jul 1999 16:19:32 +0200 From: Mogens Jerløv Subject: Data Structures for eternity A lot of people obviously has a program running for analyzing eternity. I am still trying to find a good efficient data structure for this problem. Is there anyone with ideas regarding this or good websites with sourcecode. Currently I am using 55 x 30 array and dividing each triangle into 6 subtriangles. Each triangle is coded with 0=not occupied, 1=occupied and 2=out of border. It works, but I have a feeling there must be better ways to do this. Mogens Jerlov _______________________________________________________________________________ _______________________________________________________________________________ Message: 7 Date: Thu, 08 Jul 1999 07:08:39 PDT From: N B Subject: Re: Against the grain model I think you can effectively not worry about against the grain by splitting each equliateral triangle in six and treat the grid as being made up of 7524 of these mini triangles (7524 = 209 pieces * six triangles * six mini triangles). My ascii art isn't very good but if you make the following cut, then rotate it by 120 degrees and 240 degrees and make the cut again you get six segments. /|\ / | \ / | \ / | \ / | \ / | \ /______|______\ Now each piece is made up of 36 equally sized segements. Unfortunately, this multiplies the number of orientations / possible positions to place each piece by several orders of magnitude. Nick >From: pwadsworth@Softworks.co.uk >Reply-To: eternity@onelist.com >To: eternity@onelist.com >Subject: [eternity] Against the grain model >Date: 8 Jul 1999 13:23:15 -0000 > >From: pwadsworth@Softworks.co.uk > >Regarding MorganGA@logica.com note and splitting each triangle into 4 >triangles, does not help with sorting out the Against the Grain problem. > >If you take piece 34 , > > > A > /- > ----- > |\ /\ > | \/ \ > ------- > | /\ /| > |/ \/ | > -------- > B > >and then place it along the edge where you have complete triangles, and on >the left you have 5,2,5,2,5,2 going up at 30 deg. > > --------------------------------------- > B \/\ /\ /\ /\ /\ /\ /\ /\ /\ > \ \/ \/ \/ \/ \/ \/ \/ \/ \ > --A--------------------------------- > >You will see that even if you draw 4 triangles per triangle, you can still >place the piece against the Grain. > >It may seem that doing the 4 triangles will help, but it will also increase >the amount of data that has to be checked, and therefore take even longer >to solve > > >--------------------------- ONElist Sponsor ---------------------------- > >Attention ONElist list owners. >http://www.onelist.com >We've just added a "NO ATTACHMENTS" option. See homepage for details. > >------------------------------------------------------------------------ _______________________________________________________________________________ _______________________________________________________________________________ Message: 8 Date: Thu, 8 Jul 1999 15:13:00 +0100 From: Morgan Gary Subject: Re: Against the grain model I admit that my solution may be flawed, but the piece in your counter example will never fit in that place anyway because (assuming each equilateral triangle has sides of length 2) The length of the base side of the dodecahedron is 14 (7 triangle side lengths) and you are covering it with 2 1/2 triangle sides of length sqrt(3) which leaves (14 - 2 * sqrt(3)) of the dodecahedrons side to fill. This cannot be filled with *any* of the remaining pieces since there does not exist any positive integers i, j such that (remaining side length) - (all possible side lengths constructable) = 0 (14 - 2 * sqrt(3)) - 2 * i - sqrt(3) * j = 0 ---------- From: pwadsworth@Softworks.co.uk To: eternity@onelist.com Subject: [eternity] Against the grain model Date: Thursday, July 8, 1999 14:23 From: pwadsworth@Softworks.co.uk Regarding MorganGA@logica.com note and splitting each triangle into 4 triangles, does not help with sorting out the Against the Grain problem. If you take piece 34 , A /- ----- |\ /\ | \/ \ ------- | /\ /| |/ \/ | -------- B and then place it along the edge where you have complete triangles, and on the left you have 5,2,5,2,5,2 going up at 30 deg. --------------------------------------- B \/\ /\ /\ /\ /\ /\ /\ /\ /\ \ \/ \/ \/ \/ \/ \/ \/ \/ \ --A--------------------------------- You will see that even if you draw 4 triangles per triangle, you can still place the piece against the Grain. It may seem that doing the 4 triangles will help, but it will also increase the amount of data that has to be checked, and therefore take even longer to solve --------------------------- ONElist Sponsor ---------------------------- Attention ONElist list owners. http://www.onelist.com We've just added a "NO ATTACHMENTS" option. See homepage for details. ------------------------------------------------------------------------ _______________________________________________________________________________ _______________________________________________________________________________ Message: 9 Date: Thu, 8 Jul 1999 10:16:07 -0400 From: falk.werner@zurichre.com Subject: Re: Data Structures for eternity With respect to "Currently I am using 55 x 30 array ....", here is my recommendation: I would use 3-dimensional coordinates, with the reference point in the middle of the board. Then it is really easy to calculate the 3 triangles which are the neighbors by adding or substracting 1 to exactly one of the three dimensions. Obviously, this results in 6 possibilities, whereas you have only 3 neighbors on the board. But the logic to determine which of the 6 are the 3 neighbors is absolutely simple. You just need to check the total x+y+z of the 3 coordinates for the piece you are calculating the neighbors for even or odd. If you want to split every triangle on the board in smaller triangles, I guess a forth dimension would be helpful. Falk _______________________________________________________________________________ _______________________________________________________________________________ Message: 10 Date: Thu, 8 Jul 1999 07:28:31 -0700 (PDT) From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: Data Structures for eternity Mogens Jerløv typed something like this in a previous message: > From: Mogens Jerløv > A lot of people obviously has a program running for analyzing eternity. > I am still trying to find a good efficient data structure for this > problem. Is there anyone with ideas regarding this or good websites > with sourcecode. > > Currently I am using 55 x 30 array and dividing each triangle into 6 > subtriangles. Each triangle is coded with 0=not occupied, 1=occupied and > 2=out of border. It works, but I have a feeling there must be better > ways to do this. My representation method is at http://www.ugcs.caltech.edu/~whuang/gp/drafters/repres.txt Each equilateral triangle is divided into 6 subtriangles, each of which is encoded with a bit. There is no reason to have separate encodings for "out of border" and "occupied". My source code is available at http://www.ugcs.caltech.edu/~whuang/prog/drafters2/ -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- "You may outrank me, but a bath will change that." _______________________________________________________________________________ _______________________________________________________________________________ Message: 11 Date: Fri, 9 Jul 1999 00:52:46 +1000 From: "Mark Pursey" Subject: grain model and data structures My model for allowing against the grain uses this kind of subdivision (4-subtriangles), and works. If you try drawing a piece against the grain on the normal grid, then subdivide the triangles, you should see that the piece is now *with* the smaller grain. I think its safe to assume that placing against this mini grain is illegal. Since people are discussing data structures, i might just mention that i'm not using cells at all, but outlines stored as turn-steps (remember LOGO). This of course may be a really stupid way to do it, but i'm curious as to whether anyone else uses a similar method. To force pieces with grain all i have to do is make each turn step odd or even and force them to stay that way. If i disable this rule, my solver automatically explores against the grain. these are my description of pieces 1-5 true 4 0 0 3 -3 3 1 0 4 0 0 0 0 0 true 4 0 0 3 -1 0 0 3 3 0 0 0 0 0 true 4 0 0 3 -1 0 1 3 2 0 0 0 0 0 true 4 0 0 3 -1 0 2 0 3 3 -2 0 0 0 true 4 0 1 3 -2 0 1 3 2 0 0 0 0 0 true means start along a 60 degree edge, each number represents a turn (0 = straight ahead 1 = 30 deg, 2 = 60 etc). The good thing about this format is that it is good for avoiding errors when typing it in... ie the number of steps is always even, and the steps must return to the same point. Note the extra zeros, one unit is half a triangle edge. (on 30 deg edges, 1 unit is standard height) One of the biggest problems with this format (apart from managing dynamic arrays) is what happens when the remaining outline gets pinched in the middle... it becomes a real pain! So if i dont chuck this whole (eternity) thing in, i'll probably be looking at a cell-based solver shortly. Mark ----- Original Message ----- From: To: Sent: Thursday, 8 July 1999 23:23 Subject: [eternity] Against the grain model > From: pwadsworth@Softworks.co.uk > > Regarding MorganGA@logica.com note and splitting each triangle into 4 triangles, does not help with sorting out the Against the Grain problem. > > If you take piece 34 , > > > A > /- > ----- > |\ /\ > | \/ \ > ------- > | /\ /| > |/ \/ | > -------- > B > > and then place it along the edge where you have complete triangles, and on the left you have 5,2,5,2,5,2 going up at 30 deg. > > --------------------------------------- > B \/\ /\ /\ /\ /\ /\ /\ /\ /\ > \ \/ \/ \/ \/ \/ \/ \/ \/ \ > --A--------------------------------- > > You will see that even if you draw 4 triangles per triangle, you can still place the piece against the Grain. > > It may seem that doing the 4 triangles will help, but it will also increase the amount of data that has to be checked, and therefore take even longer to solve > > > --------------------------- ONElist Sponsor ---------------------------- > > Attention ONElist list owners. > http://www.onelist.com > We've just added a "NO ATTACHMENTS" option. See homepage for details. > > ---------------------------------------------------------- -------------- > _______________________________________________________________________________ _______________________________________________________________________________ Message: 12 Date: Thu, 8 Jul 1999 17:25:40 +0100 From: Jason.Mccallion@ft.com (Jason Mccallion) Subject: Re: grain model and data structures Mark, I've used this sort of data strucutre in the solver for the smaller Heart puzzle. But then, the shapes of pieces in this are much harder to represent using a grid. Instead of using dynamic arrays, I've used a circular list. This is easy to traverse, and means I can ignore rotation, as I can just travel all the way around the piece, not caring where I start or finish. It also means flipping a piece is easy - just traverse the list in reverse. It does however produce some invalid piece positions, as there is no strict grid to put the pieces in, but these are identified easily enough. Jason. "Mark Pursey" on 08/07/99 23:52:46 To: eternity@onelist.com cc: (bcc: Jason Mccallion/LONDON/FINANCIAL TIMES) Subject: [eternity] grain model and data structures From: "Mark Pursey" My model for allowing against the grain uses this kind of subdivision (4-subtriangles), and works. If you try drawing a piece against the grain on the normal grid, then subdivide the triangles, you should see that the piece is now *with* the smaller grain. I think its safe to assume that placing against this mini grain is illegal. Since people are discussing data structures, i might just mention that i'm not using cells at all, but outlines stored as turn-steps (remember LOGO). This of course may be a really stupid way to do it, but i'm curious as to whether anyone else uses a similar method. To force pieces with grain all i have to do is make each turn step odd or even and force them to stay that way. If i disable this rule, my solver automatically explores against the grain. these are my description of pieces 1-5 true 4 0 0 3 -3 3 1 0 4 0 0 0 0 0 true 4 0 0 3 -1 0 0 3 3 0 0 0 0 0 true 4 0 0 3 -1 0 1 3 2 0 0 0 0 0 true 4 0 0 3 -1 0 2 0 3 3 -2 0 0 0 true 4 0 1 3 -2 0 1 3 2 0 0 0 0 0 true means start along a 60 degree edge, each number represents a turn (0 = straight ahead 1 = 30 deg, 2 = 60 etc). The good thing about this format is that it is good for avoiding errors when typing it in... ie the number of steps is always even, and the steps must return to the same point. Note the extra zeros, one unit is half a triangle edge. (on 30 deg edges, 1 unit is standard height) One of the biggest problems with this format (apart from managing dynamic arrays) is what happens when the remaining outline gets pinched in the middle... it becomes a real pain! So if i dont chuck this whole (eternity) thing in, i'll probably be looking at a cell-based solver shortly. Mark ----- Original Message ----- From: To: Sent: Thursday, 8 July 1999 23:23 Subject: [eternity] Against the grain model > From: pwadsworth@Softworks.co.uk > > Regarding MorganGA@logica.com note and splitting each triangle into 4 triangles, does not help with sorting out the Against the Grain problem. > > If you take piece 34 , > > > A > /- > ----- > |\ /\ > | \/ \ > ------- > | /\ /| > |/ \/ | > -------- > B > > and then place it along the edge where you have complete triangles, and on the left you have 5,2,5,2,5,2 going up at 30 deg. > > --------------------------------------- > B \/\ /\ /\ /\ /\ /\ /\ /\ /\ > \ \/ \/ \/ \/ \/ \/ \/ \/ \ > --A--------------------------------- > > You will see that even if you draw 4 triangles per triangle, you can still place the piece against the Grain. > > It may seem that doing the 4 triangles will help, but it will also increase the amount of data that has to be checked, and therefore take even longer to solve > > > --------------------------- ONElist Sponsor ---------------------------- > > Attention ONElist list owners. > http://www.onelist.com > We've just added a "NO ATTACHMENTS" option. See homepage for details. > > ---------------------------------------------------------- -------------- > --------------------------- ONElist Sponsor ---------------------------- ONElist: your connection to people who share your interests. ------------------------------------------------------------------------ **************************************************************************************** *Please visit the web site of the Financial Times at http://www.ft.com * * * *This E-Mail is intended for the use of the addressee only and may contain confidential* *information. If you are not the intended recipient, you are hereby notified that any * *use or dissemination of this communication is strictly prohibited. * *If you receive this transmission in error, please notify us immediately then * *delete this E-Mail. * * * *postmaster@ft.com * **************************************************************************************** _______________________________________________________________________________ _______________________________________________________________________________ Message: 13 Date: Thu, 08 Jul 1999 13:57:44 -0700 From: "Matt Watson" Subject: FW: [eternity] Welcome to eternity@onelist.com ANSWERS -------------- What's your..... name : Matt Watson age : thirty-something occupation : Software Engineer/Scientist country : USA ------- How did you hear about this list (website / friends) ? ------- rec.puzzles, www.mathpuzzle.com ------- Are you an active problem-solver, or just here out of general interest ? ------- active problem-solver ------- Do you hope that by listening to this list, you'll get the vital hint that'll make you win the prize ? ------- sure, but I don't expect it ------- Do you own an Eternity puzzle ? ------- yes ------- What's your best attempt by hand ? ------- none yet ------- What's your best attempt by computer ? ------- none yet ------- What language / system / pc are you using ? ------- C & PowerPC assembly / Mac OS X / Power Macintosh G3 ------- What algorithms / heuristics do you use for Eternity (brute force, backtracking, genetic algothims, simulated annealing, SECRET) ? ------- A*, plus all the above ------- Did you type in all 209 pieces yourself ? ------- not yet ------- Did you try any simpler variations of Eternity ? ------- just the on-line version at hotbox ------- Do you know some other interesting web-sites ? ------- yes :-) ------- Other hobbies ? ------- baseball, softball, paddle-tennis, travelling, stand-up comedy ------- Other physical puzzles ? ------- those untangle-the-metal-pieces puzzles ------- Other programming projects ? ------- Operating System design/development ------- Are you willing to show the group your source code (after removing your secret functions) ? ------- sure ------- Any other stuff you like to add ? ------- not yet ------- Do you know any other interesting problems ? ------- yes :-) ------- What's the meaning of life ? ------- 42 -- no, blue! ------- How are you going to spend your 1000.000 ? ------- all in one place, if possible _______________________________________________________________________________ _______________________________________________________________________________ Message: 14 Date: Thu, 8 Jul 1999 22:27:56 +0100 From: Kevin Pretorius Subject: Re: Welcome to eternity@onelist.com ---------- From: eternity-owner@onelist.com[SMTP:eternity-owner@onelist.com] Reply To: eternity@onelist.com Sent: Wednesday, July 07, 1999 07:22 To: kevin.pretorius@btinternet.com Subject: [eternity] Welcome to eternity@onelist.com Hello, Welcome to the list. Please take a moment to review this message. There are lots of discussions going on, but none so far that provide any vital clues to solve the puzzle. It's mostly about the complexity, about representing the 209 pieces, the screen saver, the issue of parity, types of algorithms, smaller variations of trhe same puzzle, etc.. The best website for this puzzle is http://www.mathpuzzle.com/eternity.html. It contains links to all other vital Eternity links. We now (July 5, 99) have almost 180 members. And still going strong. To unsubscribe from this list, go to the ONElist web site, at www.onelist.com, and select the User Center link from the menu bar on the left. This menu will also let you change your subscription between digest and normal mode. I thought it would be a nice idea to get to know you a bit better. That's why I composed a little list of questions. I'd like you to fill it out, and send it to the list (eternity@onelist.com) just answer any question you feel like, but if you don't like it, then don't, its a free world... Andreas Gammel, List Owner QUESTIONS -------------- What's your..... name : Kevin Pretorius age : 43 occupation : Software Systems Project Manager city : Camberley, Surrey country : England email : Kevin.Pretorius@btinternet.com homepage : none ------- How did you hear about this list (website / friends) ? ------- >From the eternity web page http://www.mathpuzzle.com/eternity.html. ------- Are you an active problem-solver, or just here out of general interest ? ------- I will often use a computer to help solve mathematical type puzzles. ------- Do you hope that by listening to this list, you'll get the vital hint that'll make you win the prize ? ------- Only remotely. I don't actually believe that anyone will claim this price. ------- Do you own an Eternity puzzle ? ------- My brother does. ------- What's your best attempt by hand ? ------- haven't tried ------- What's your best attempt by computer ? ------- I'll let you know. I've only been coding since the weekend, but I have something basic up & running as of this evening. ------- What language / system / pc are you using ? ------- 'C' on my office Tecra laptop 233 MHz and home Gateway PC 90MHz (I really must update this soon) ------- What algorithms / heuristics do you use for Eternity (brute force, backtracking, genetic algothims, simulated annealing, SECRET) ? ------- I'm presently use a depth first, brute force search with one level lookahead ------- Did you type in all 209 pieces yourself ? ------- No. I started to, but then processed the pcs.txt list from http://alpha.ujep.cz/~vicher/puzzle/psc.htm the representation wasn't a good match to my own, but it was translatable. ------- Did you try any simpler variations of Eternity ? ------- Sure. I wasn't going to bother with Eternity at all, but then I was given the Delta puzzle as a gift. I quickly solved this using my PC and became hooked. ------- Do you know some other interesting web-sites ? ------- ------- Other hobbies ? ------- I'm interested in computer programming, maths, physics and home video ------- Other physical puzzles ? ------- ------- Other programming projects ? ------- Too many to mention. I Always have several on the go. ------- Are you willing to show the group your source code (after removing your secret functions) ? ------- Maybe. ------- Any other stuff you like to add ? ------- I'm new to these discussions, and I don't yet fully understand the definition of the 3 eternity parities, and going 'against the grain'. Any explanations welcomed. I note that the mathpuzzle site finds evidence for 'clustering' of pieces with like parity, but that's a long way from being useful in a solver. I'm guessing that 'going against the grain' is about placing pieces such that their 30-60-90 triangles don't fit over the underlying equilateral grid. Why does anyone believe that this is a smart thing to do? ------- Do you know any other interesting problems ? ------- ------- What's the meaning of life ? ------- ------- How are you going to spend your 1000.000 ? ------- Quickly. _______________________________________________________________________________ _______________________________________________________________________________ Message: 15 Date: Thu, 8 Jul 1999 14:36:16 -0700 From: Chuck Deerinck Subject: Re: Opinion please The answer to multiple solutions is actually very simple. Take any two pieces that are adjacent in a solution, and if as a combination they are symmetrical, then you have at least two solutions. This works for any number of pieces, and the permutations of valid solutions goes up. This is only one class of permutations of a solution. The larger question of very different types of solutions, is much harder (i.e. I have no clue). > -----Original Message----- > From: Steve Nicholls [SMTP:Big.Steve@btinternet.com] > Sent: Thursday, July 08, 1999 12:11 AM > To: eternity@onelist.com > Subject: Re: [eternity] Opinion please > > From: "Steve Nicholls" > > Patrick, > > I have seen approach suggested elsewhere, though I am not convinced about > it's validity at this point. Given the way that Monckton reportedly > created > the puzzle it is highly unlikely he took this approach when originally > tiling eternity, therefore I believe it is highly unlikely that this > approach will result in Moncktons solution which is more likely to include > effectively "random" tiling patterns. > > Has anybody been able to prove at this point that there are multiple > solutions to eternity (excluding rotations/reflections)? If so, this > approach is definitely a sound one. I guess similar comments could (and > have been) applied to the screen saver that does not (intentionally) place > piece 34 at its published starting position. > > regards, Steve > > -----Original Message----- > From: path@multipro.com.au > To: eternity@onelist.com > Date: 06 July 1999 06:41 > Subject: Re: [eternity] Opinion please > > > >From: path@multipro.com.au > > > >Try fitting 'difficult' pieces together into 'easier' shapes. A difficult > >piece is basically one with more edges, eg #166 which has 12. If you make > >up 'combination pieces' with 'smoother' outlines, then you may be able to > >tile faster. You can make the combination pieces by manually fitting > >together groups of difficult and easy pieces until you get a 'nice' > shape, > >then cut out a piece of paper that shape, and write on it the numbers of > >the pieces that went to make it up (and their outlines, you don't want to > >have to solve another puzzle later). Repeat this a few hundred times > until > >you have a 'compound shape' for every difficult piece. If you can get > lots > >of difficult pieces into a shape, so much the better. Also, try to use > >*different* sets of pieces for each compound shape as far as possible. > You > >have to keep track of which pieces are used by each one when you use it, > so > >less pieces in common allows more options. Now you can tile using the > >pieces of paper (use Blue-tack/Prestick/whatever your local name is for > >that sticky stuff to hold the paper shapes in place). > > > > --------------------------- ONElist Sponsor ---------------------------- > > Having difficulty getting "in synch" with list members? > http://www.onelist.com > Try ONElist's Shared Calendar to organize events, meetings and more! > > ------------------------------------------------------------------------ _______________________________________________________________________________ _______________________________________________________________________________ Message: 16 Date: 9 Jul 1999 10:11:16 -0000 From: Dsaund2773@aol.com Subject: How was it constructed? A number of people have proposed ideas on how Eternity was constructed. Suppose C.M. found all the ways you can assemble six equilateral triangles. I count 10. He then assembles the puzzle. He then: Removes one drafter, adds one drafter. Or, " two " " two " " three " " three " " four " " four " We also know how many of each of the ten types there are. Dick Saunders _______________________________________________________________________________ _______________________________________________________________________________