From: Rozberk Omniist To: Ed Pegg ; Herald Subject: Fw: [eternity] Digest Number 10 Date: Monday, July 05, 1999 8:46 AM ----- Original Message ----- From: To: Sent: Saturday, July 03, 1999 4:03 AM Subject: [eternity] Digest Number 10 > > --------------------------- ONElist Sponsor ---------------------------- > > How has ONElist changed your life? > Share your story with us at http://www.onelist.com > > ------------------------------------------------------------------------ > > There are 25 messages in this issue. > > Topics in today's digest: > > 1. Eternity Screen Solver v1.2 > From: "Christophe Weibel" > 2. Re: Against The Grain > From: "Christophe Weibel" > 3. Question > From: "Ing. Marco Polazzo" > 4. Re: Eternity Screen Solver > From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) > 5. Re: So, who are you guys, anyway ? > From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) > 6. WHAT DOES IT MEAN AGAINST THE GRAIN ? > From: pwadsworth@softworks.co.uk > 7. Re: Against The Grain > From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) > 8. Re: WHAT DOES IT MEAN AGAINST THE GRAIN ? > From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) > 9. benchmark > From: axel@itb.biologie.hu-berlin.de > 10. Re: Eternity Screen Solver v1.2 > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > 11. Re: benchmark > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > 12. Re: Eternity Screen Solver v1.2 > From: "Ronald Stewart" > 13. Re: benchmark > From: Roel van der Goot > 14. Starting piece(s) > From: "Mark Pursey" > 15. Re: benchmark > From: "Mark Pursey" > 16. Re: Question > From: "Staffan och Lotta" > 17. R: [eternity] WHAT DOES IT MEAN AGAINST THE GRAIN ? > From: "Ing. Marco Polazzo" > 18. Re: Eternity Screen Solver v1.2 > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > 19. Re: Eternity Screen Solver > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > 20. Re: Eternity Screen Solver > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > 21. Re: So, who are you guys, anyway ? > From: James Kittock > 22. Meteor, Delta, Heart > From: "Ralph Jackson" > 23. Re: Eternity Screen Solver > From: "Thomas Voigt" > 24. Re: Count check > From: redbaron@cix.compulink.co.uk (Richard Marsden) > 25. Complexity > From: "Thomas Voigt" > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 1 > Date: Fri, 2 Jul 1999 13:32:38 +0200 > From: "Christophe Weibel" > Subject: Eternity Screen Solver v1.2 > > > Hello! > > I've got the impression that the screen solver isn't looking for > against-the-grain solutions. Is that right? > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 2 > Date: Fri, 2 Jul 1999 13:55:12 +0200 > From: "Christophe Weibel" > Subject: Re: Against The Grain > > > Hello! > > Mark Pursey wrote: > > > Has anyone asked CM about grain directly? maybe he never > > intended for people to get stuck on this issue... > > If I was him, no matter what I intended or not, I wouldn't tell. After all, he > has a million pounds to lose... > > > BTW: are the 4 grain states in any way related to the 4 > > colour theorem? > > No, it's a coincidence... If we take each region that is in one of the four > grain state, of course none of the adjacent region is in the same grain state > (otherwise they would both form a single region). But you could do the same > with any number of colors: If two adjacent regions have the same color, you > just decide it's the same region... > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 3 > Date: Fri, 2 Jul 1999 14:35:03 +0200 > From: "Ing. Marco Polazzo" > Subject: Question > > Sorry to bore you, but I'm a little bit ignorant. > WHAT DOES IT MEAN AGAINST THE GRAIN ? (What is a Grain?) > > If someone could explain me..... I thanks him very much. > Bye :) > Marco. > > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 4 > Date: Fri, 2 Jul 1999 05:44:40 -0700 (PDT) > From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) > Subject: Re: Eternity Screen Solver > > Bob Harris typed something like this in a previous message: > > > 154 by Eternity Screen Solver v1.0 at > > > http://lalsoft.hypermart.net/ScreenSolver.htm. > > > > I downloaded this, but it appears I also need a 'screen saver component'. > > So I donwloaded that, but it appears I also need Delphi. > > What is Delphi? Is it free? Do I need it? > > Am I right, or can I just download the screen saver without having to load a > > bunch of other dominoes. > > > I think all you need is Windows 95, 98, or NT 4.0. > > The URL given above is incorrect -- it should be > > http://lalsoft.hypermart.net/screensolver.htm > > No capital letters in the filename! > > You don't need the Delphi screen saver component -- it's just a "wrapper" > program that turns normal programs into screensavers. > > You will need some way to decompress *.zip files to get to the > screensaver, though. > > -- > Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ > -------------------------------------------------------------------------- - > "You may outrank me, but a bath will change that." > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 5 > Date: Fri, 2 Jul 1999 06:04:50 -0700 (PDT) > From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) > Subject: Re: So, who are you guys, anyway ? > > Mike Leigh typed something like this in a previous message: > > I would be very interested in your representation of the drafters > > > > More than one person has asked about this, so > I've put a descriptive text file (same one I sent Bob Harris, > with some examples) out at > > http://www.ugcs.caltech.edu/~whuang/gp/drafters/repres.txt > > Essentially, the grid is divided into basic parallelograms, and > a two-digit number is assigned to each parallelogram. > > Some examples of the data files I use can be found in > > http://www.ugcs.caltech.edu/~whuang/prog/drafters2/ > > They have the extension *.dft > > -- > Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ > -------------------------------------------------------------------------- - > "You may outrank me, but a bath will change that." > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 6 > Date: 2 Jul 1999 13:10:26 -0000 > From: pwadsworth@softworks.co.uk > Subject: WHAT DOES IT MEAN AGAINST THE GRAIN ? > > If you look at the Eternity Board, it is made up of triangles, which form a Grid Patten ( see WWW.MATHPUZZLE.COM/ETERGRID.GIF ). > > If you then mark up, each piece with a part of the grid, you will see that each one is made up of 6 triangles. > > When you follow the grain, the lines marked on the piece, will follow the lines of the grid on the board. > > When you go against the grain, you offset one or more of those lines on the grid. This can be seen when you place Piece 135 and 134 togeather and then try to fit the shape to the grid. One of the pieces will be offset, the other will be okay. > > > When a piece is place on the board, the edges of the piece follow the lines or part of > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 7 > Date: Fri, 2 Jul 1999 06:14:27 -0700 (PDT) > From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) > Subject: Re: Against The Grain > > Mark Pursey typed something like this in a previous message: > > If against the grain solutions are ok, then what about > > solutions that involve a 30 degree rotation of pieces? There > > may (unlikely i admit, the area wouldn't add up) be > > solutions which involve this kind of rotation. 6 N edges is > > only 1% shorter than 7 S edges, and there's bound to be > > people (who haven't marked grids on their pieces) attempting > > wierd placements like this. > > My guess is that this will probably fail -- it'll be hard to get the > area to work -- some edges will have to be longer while other > edges have to be shorter, and there's a good chance they won't > accept such a solution. > > Of course, if you create a very large almost-regular dodecagon that's > off by a rotation of 30 degrees, send the solution to me first. :-) > > > BTW: are the 4 grain states in any way related to the 4 > > colour theorem? > > Not at all. > > -- > Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ > -------------------------------------------------------------------------- - > "You may outrank me, but a bath will change that." > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 8 > Date: Fri, 2 Jul 1999 06:16:19 -0700 (PDT) > From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) > Subject: Re: WHAT DOES IT MEAN AGAINST THE GRAIN ? > > pwadsworth@softworks.co.uk typed something like this in a previous message: > > From: pwadsworth@softworks.co.uk > > If you look at the Eternity Board, it is made up of triangles, which form a Grid Patten ( see WWW.MATHPUZZLE.COM/ETERGRID.GIF ). > > > > If you then mark up, each piece with a part of the grid, you will see that each one is made up of 6 triangles. > > > > When you follow the grain, the lines marked on the piece, will follow the lines of the grid on the board. > > > > When you go against the grain, you offset one or more of those lines on the grid. This can be seen when you place Piece 135 and 134 togeather and then try to fit the shape to the grid. One of the pieces will be offset, the other will be okay. > > > > The best way is probably to look at > > http://www.mathpuzzle.com/vichtd1.GIF > > You'll see that three pieces don't go with the triangular grid that the > rest of the pieces do. > > > > -- > Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ > -------------------------------------------------------------------------- - > "You may outrank me, but a bath will change that." > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 9 > Date: 2 Jul 1999 14:29:43 -0000 > From: axel@itb.biologie.hu-berlin.de > Subject: benchmark > > Hello everybody, > > obviously many of us have written programs for > solving the eternity puzzle. I thought it would be > nice to have a benchmark test to see how well our > program are doing. So I took a hexagon of size 5 > and cut it into 25 neat pieces. I uploaded a jpg > picture of the pieces (bench25.jpg) into the shared > file area. Obviously the time for solving it depends > on the order of the pieces, but on a 400Mhz machine > my fastest time is around 35 minutes. > How are you doing ? > > Axel > > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 10 > Date: Fri, 2 Jul 1999 17:00:12 +0100 > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > Subject: Re: Eternity Screen Solver v1.2 > > That's true, for many af the same good reasons I've read on this onelist > these last days, I decided not to take care of the "against the grid" > positions when I established the data structures of E.S.S. a month ago. > > I could be wrong but I was convinced (and stay) that the Eternity puzzle > bears at the very last as many fully grid synchronized solutions than > against the grid ones. > > Nevertheless, I agree that it is possible that E.M. found a way to > demonstrate (based on a special unknown parity argument, for example) that > the Eternity grid could only accept "against the grid" solutions. If he did > it, so we would also be able to do it... So, as long as a demonstartion of > this conjecture will not be established. I will consider not to spend CPU > time on these more complex against the grid placement possibilities. The > search tree is already huge enough for me ! :-) > > > Beside this, I wrote a new FAQ file for the E.S.S. you could be interested > in the opinions I expose into it. So I join it to this message. > > P.F. Culand > Swiss Knife Software. > > > -----Message d'origine----- > De : Christophe Weibel > À : eternity > Date : vendredi, 2. juillet 1999 14:14 > Objet : [eternity] Eternity Screen Solver v1.2 > > > >From: "Christophe Weibel" > > > > > >Hello! > > > >I've got the impression that the screen solver isn't looking for > >against-the-grain solutions. Is that right? > > > > > >--------------------------- 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! > > > >------------------------------------------------------------------------ > > > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 11 > Date: Fri, 2 Jul 1999 17:08:57 +0100 > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > Subject: Re: benchmark > > Hum... I'm not certain this would be a valued benchmark. > > You should consider that the startegy to search the solution of puzzles > broadly depend of the size of such puzzles. Some costly checks made on each > piece placement could be disadvantageous in small puzzles (because the > branches are short and the benefice to cut them very small compared to the > cost of the check) and could be decisive in huge puzzles like Eternity... > (Read my FAQ file joind to my answer to Christophe Weibel message). > > P.F. Culand > Swiss Knife Software. > -----Message d'origine----- > De : axel@itb.biologie.hu-berlin.de > À : eternity@onelist.com > Date : vendredi, 2. juillet 1999 15:29 > Objet : [eternity] benchmark > > > >From: axel@itb.biologie.hu-berlin.de > > > >Hello everybody, > > > >obviously many of us have written programs for > >solving the eternity puzzle. I thought it would be > >nice to have a benchmark test to see how well our > >program are doing. So I took a hexagon of size 5 > >and cut it into 25 neat pieces. I uploaded a jpg > >picture of the pieces (bench25.jpg) into the shared > >file area. Obviously the time for solving it depends > >on the order of the pieces, but on a 400Mhz machine > >my fastest time is around 35 minutes. > >How are you doing ? > > > > Axel > > > > > > > >--------------------------- ONElist Sponsor ---------------------------- > > > >Find people who care about what you care about. > >http://www.onelist.com > >At ONElist: your connection to community. > > > >------------------------------------------------------------------------ > > > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 12 > Date: Fri, 2 Jul 1999 16:30:51 +0100 > From: "Ronald Stewart" > Subject: Re: Eternity Screen Solver v1.2 > > In your ScreenSolver FAQ, you say that you check *each* unfilled cell to be sure that a piece would fit. > > I think this is very wasteful - surely it would be much more efficient to check only those cells affected by your new placement? For the greatest chance of solving the puzzle by this method, any time-saving devices are useful. > Since you fill from the bottom, surely only the unfilled cells in partly filled rows need to be checked?? > > Furthermore, using Monckton's starting position means that only 208 pieces must be placed... surely this eliminates a whole trunk of 'tree' to begin with. I admit that you limit the number of solutions available to search for, but at least you can be sure there is one solution in the area you are searching. My intuition is saying that any pieces which can be placed will greatly decrease the total searching time (although my apathy is saying that I cannot be bothered to work it out). To use your analogy, there is no reason the believe that Monckton's branch is any more or less fruitful than any other, but we can be sure there is at least one fruit on it. Perhaps you should reconsider? > > Just my humble suggestions, > > Ron Stewart > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 13 > Date: Fri, 2 Jul 1999 09:40:12 -0600 (MDT) > From: Roel van der Goot > Subject: Re: benchmark > > > On Fri, 2 Jul 1999, [iso-8859-1] Pierre-François Culand wrote: > > > Hum... I'm not certain this would be a valued benchmark. > > > > You should consider that the startegy to search the solution of puzzles > > broadly depend of the size of such puzzles. Some costly checks made on each > > piece placement could be disadvantageous in small puzzles (because the > > branches are short and the benefice to cut them very small compared to the > > cost of the check) and could be decisive in huge puzzles like Eternity... > > (Read my FAQ file joind to my answer to Christophe Weibel message). > > > > P.F. Culand > > Swiss Knife Software. > > Agreed, you could however choose a problem that is unsolvable. > Then every program has to search the entire search space, the > program that returns fastest is the best program. > > Roel van der Goot. > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 14 > Date: Sat, 3 Jul 1999 01:42:26 +1000 > From: "Mark Pursey" > Subject: Starting piece(s) > > Are there any pictures (or accurate descriptions) of > starting piece(s) for eternity? Personally i would prefer to > use this info if it's available... > > Also, is everybody using the same piece order, ie the order > of pieces as they appeared in Ed Pegg's transcription? Are > the pieces actually numbered in the eternity set? > > MArk > > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 15 > Date: Sat, 3 Jul 1999 02:02:07 +1000 > From: "Mark Pursey" > Subject: Re: benchmark > > I couldn't download the jpg for some reason (438K seems a > tad large for a jpeg image!) > > Using 25 e-pieces (indexed from Ed Pegg's trans): > 0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 15, 19, 24, 33, 34, 38, 46, > 49, 109, 116, 117, 125, 126, 156, 208 > > My program filled a hexagon in 26 sec, 73 sec and 22 sec (3 > different times represent random reshuffling of piece order) > > Next size up (36 piece)... still working on it... > > I gather there are people here doing WAY better than that... > > Mark > > > From: axel@itb.biologie.hu-berlin.de > > > > Hello everybody, > > > How are you doing ? > > > > Axel > > > > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 16 > Date: Fri, 2 Jul 1999 18:15:16 +0200 > From: "Staffan och Lotta" > Subject: Re: Question > > Hi Marco, > > take a look at > http://www.ugcs.caltech.edu/~whuang/gp/drafters/againstXtheXgrain.GIF > The picture sums it up I think. > > Regards, > Staffan R. > > -----Original Message----- > From: Ing. Marco Polazzo > To: eternity@onelist.com > Date: den 2 juli 1999 14:40 > Subject: [eternity] Question > > > >From: "Ing. Marco Polazzo" > > > >Sorry to bore you, but I'm a little bit ignorant. > >WHAT DOES IT MEAN AGAINST THE GRAIN ? (What is a Grain?) > > > >If someone could explain me..... I thanks him very much. > >Bye :) > >Marco. > > > > > > > >--------------------------- ONElist Sponsor ---------------------------- > > > >ONElist: where real people with real interests get connected. > >http://www.onelist.com > >Join a new list today! > > > >------------------------------------------------------------------------ > > > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 17 > Date: Fri, 2 Jul 1999 18:42:17 +0200 > From: "Ing. Marco Polazzo" > Subject: R: [eternity] WHAT DOES IT MEAN AGAINST THE GRAIN ? > > > VERY THANKS to pwadsworth@softworks.co.uk for the kind explaination!!! > Marco. > > -----Messaggio originale----- > Da: pwadsworth@softworks.co.uk [mailto:pwadsworth@softworks.co.uk] > Inviato: venerdì 2 luglio 1999 15.10 > A: eternity@onelist.com > Oggetto: [eternity] WHAT DOES IT MEAN AGAINST THE GRAIN ? > > From: pwadsworth@softworks.co.uk > > If you look at the Eternity Board, it is made up of triangles, which form a > Grid Patten ( see WWW.MATHPUZZLE.COM/ETERGRID.GIF ). > > If you then mark up, each piece with a part of the grid, you will see that > each one is made up of 6 triangles. > > When you follow the grain, the lines marked on the piece, will follow the > lines of the grid on the board. > > When you go against the grain, you offset one or more of those lines on the > grid. This can be seen when you place Piece 135 and 134 togeather and then > try to fit the shape to the grid. One of the pieces will be offset, the > other will be okay. > > > When a piece is place on the board, the edges of the piece follow the lines > or part of > > --------------------------- ONElist Sponsor ---------------------------- > > Campaign 2000 is here! > http://www.onelist.com > Discuss your thoughts; get informed at ONElist. See our homepage. > > ------------------------------------------------------------------------ > > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 18 > Date: Fri, 2 Jul 1999 21:24:07 +0200 > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > Subject: Re: Eternity Screen Solver v1.2 > > > -----Message d'origine----- > De : Ronald Stewart > À : eternity@onelist.com > Date : vendredi, 2. juillet 1999 17:32 > Objet : Re: [eternity] Eternity Screen Solver v1.2 > > > In your ScreenSolver FAQ, you say that you check *each* unfilled cell to be sure that a piece would fit. > > That's no exactly true. In fact only few (well choosen) cells are checked. (about 5 to 15 cells need to be checked at each piece placement in E.S.S) > > I think this is very wasteful - surely it would be much more efficient to check only those cells affected by your new placement? > > > Be careful, this is not enough. When you place a piece on the left side of the board, this placement could transform a "fillable" cell on the right side to an unfillable one. (If the piece you just placed was the unic possible piece to fill the cell on the right side for example). > > For the greatest chance of solving the puzzle by this method, any time-saving devices are useful. > > > This is not so simple. If you mean "time-saving" to be an optimisation to do the same job faster, you're right. But if this means to eliminate (or simplify) some costly checks that could cut branches you should compare the cost of the suppressed check to the benefice of the resulting cut. > > Some people I've talked with had problems to understand this. So consider the following example: > > Suppose we were able to write a very costly but powerful function to analyse the resulting situation after each piece placement. Suppose this function (let's call it "Kasparov" ;-) would be so efficient that it could recognize (and eliminate) each situation that would ineluctably lead to a dead-end position where no piece would fit... Suppose this function to be so costly that it would need 1 minute to analyse the position. > > A solver program using this Kasparov function would never need to backtrack and would successfully crack the Eternity puzzle after 209 * N minutes. Where N is the average number of possible piece placements on a choosen specific cell of the grid in a given situation. (For example the lower left free cell, onto fill the grid from the bottom to the top like does E.S.S.) > > I have observed with E.S.S. that N is about 100 at the beginning of the grid filling and decreases down to ~20 at the 160th piece placement. So we can imagine that "Kasparov" would solve the grid in about less than 209 * 50 minutes ~= 150 hours... This would be a very powerful program ! Isn't it ? > > But on the other hand it would appear very slow to novice users: only one move / minute ~= 0.02 moves / sec. > > It is very slow but it is much more efficient than another stupid very fast "piece/mover" program (let's call it "Marc"(*)) that would place 1million pieces/sec but would only backtrack when it is stucked in a dead-end situation where no piece would fit. "Marc" would appear very efficient to novice users: > > - "Hey I've written a program that process 1'000'000 moves/sec !!! That's much better that your ridiculous "Kasparov" program that didn't find anything for 100 hours..." said "Marc"'s author (*) to the programmer of "Kasparov"... > > ...But 1000 times the age of the univers later it would probably continue to search for a solution. Backtracking and backtracking again. > > (*) Marc is a friend of me that is writing a very fast (but stupid) competitor to my E.S.S... He don't want to understand my explanations ! Bad chance for him, and for the users of his program... > > Since you fill from the bottom, surely only the unfilled cells in partly filled rows need to be checked?? > > > Where did you read my source code ??? ;-) > > Furthermore, using Monckton's starting position means that only 208 pieces must be placed... surely this eliminates a whole trunk of 'tree' to begin with. I admit that you limit the number of solutions available to search for, but at least you can be sure there is one solution in the area you are searching. My intuition is saying that any pieces which can be placed will greatly decrease the total searching time (although my apathy is saying that I cannot be bothered to work it out). To use your analogy, there is no reason the believe that Monckton's branch is any more or less fruitful than any other, but we can be sure there is at least one fruit on it. Perhaps you should reconsider? > > > > Sorry I can't agree: > > To choose the Monckton's first proposed piece(s) only because you know that this branch contains at least one solution somewhere into this huge branch (bearing ~10^260 / 209 leaves !) is not very attractive. (Nevertheless, this is not a worst choice than mine) > > This is like to decide to go fishing in the Atlantic ocean only because you got somewhere the info that there is at least one fish into the Atlantic ocean and you got no info concerning the Pacific... > > If one of the two oceans would contain only one or maybe two (or even thousand) fishes and no fishes were present into the second ocean, I'm pretty sure you will come back with an empty bag whatever the ocean where you decide to go fishing ! > > To have a chance to succeed to crack the Eternity puzzle with brute force, we absolutely need that the puzzle's search tree would bear many billions of billions of different solutions... (see my opinion about the solutions density in the E.S.S. FAQ file) > > A soon that I'll become convinced that is not reasonable to expect so much different solutions to the Eternity puzzle I will definitively abandon the brute force strategy. > > P.F. Culand > Swiss Knife Software > > > Just my humble suggestions, > > Ron Stewart > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 19 > Date: Fri, 2 Jul 1999 22:10:17 +0200 > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > Subject: Re: Eternity Screen Solver > > > -----Message d'origine----- > De : Andreas Gammel > À : eternity@onelist.com > Date : vendredi, 2. juillet 1999 08:56 > Objet : Re: [eternity] Eternity Screen Solver > > > >From: Andreas Gammel > > > >Thanks for the new version. > > > >I have a few suggestions for version 1.3: > >add options to > >- see the individual pieces actually apear on the screen (refresh less then > 5 > >seconds). This would really look nice and make > > a lot more people download it > > I limited the refresh rate to 5 second because the drawing threads that draw > the grid computed by the search thread are very CPU time consuming. And I > thought that most people would find nice to view the search position as > often as possible and would so greatly slow down the search speed. (Your > question makes me think I was right...) > > >- set the size of the board on the screen (too small now) > > A screen saver is designed onto save the screen isn't it ? ;-) > > >- various color schemes to color the pieces (looks much nicer) > > In french we say: "des goûts et des couleurs..." That means that every > people would prefer different colors than those you choose. So you probably > are right. Such configuration option would be appreciated. > > >- non-moving board > > non moving at all ? > > A screen saver is designed onto save the screen isn't it ? ;-) > > > > >and what would be really cool: > >- provide a choice of different algorithms > > Why not. But it's already a complex job to write one... > > > - backtracking with settable number of look-aheads > > Not realy applicable in E.S.S. > > > - use piece-segments that slide towards eachother > > ??? What do you mean ? > > >- provide an algorithm interpreter that allows a logical algorithm to be > typed > >in by the screensaver user (I have some ideas for this one, which I could > send > >you) > > My god ! I thought about this, but seems a little complex to implement... > > > > > >cheers > >Andreas > > > > > > Thank you in any way for your suggestions. > > P.F. Culand > Swiss Knife Software > > > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 20 > Date: Fri, 2 Jul 1999 22:14:15 +0200 > From: "=?iso-8859-1?Q?Pierre-Fran=E7ois_Culand?=" > Subject: Re: Eternity Screen Solver > > > -----Message d'origine----- > De : Brendan Owen > À : eternity@onelist.com > Date : vendredi, 2. juillet 1999 09:04 > Objet : Re: [eternity] Eternity Screen Solver > > > >From: "Brendan Owen" > > > >Hi All, > > > > I have another sudjestion display the full solution. :) > > > >Rgeards > >Brendan > > I'll send you the first full solution received from an E.S.S. user as soon > that I will have sent it to Ertl ! ;-) > > > P.F. Culand > Swiss Knife Software > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 21 > Date: Fri, 2 Jul 1999 13:48:17 -0700 > From: James Kittock > Subject: Re: So, who are you guys, anyway ? > > > From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) > > > > More than one person has asked about this, so > > I've put a descriptive text file (same one I sent Bob Harris, > > with some examples) out at > > > > http://www.ugcs.caltech.edu/~whuang/gp/drafters/repres.txt > > I came up with a similar encoding, with a slightly > different encoding of numbers. Two differences I see > offhand are that full triangles add up to 7, rather than > 9, in my encoding and my encoding has the parts retain > their numbers when flipped vertically. For example: > > +---+---+ > /|\ 6|1 / > / | \ | / > / 1|6 \|/ > +---+---+ > > In terms of storing the values in a data structure, > I experimented with both parallelogram and triangular > arrays, and in the end opted for a triangular array > because I found it easier to work with in my program > than the parallelograms. With the parallelograms, > I found that I spent a lot of code (and possibly a > lot of runtime, although I didn't measure this) breaking > the parallelograms apart and putting them back together. > With the triangles, I can just operate on the cells directly. > > The triangular encoding also maps nicely onto a > rectangular array--the only tricky thing is that > each cell is only adjacent to three of its > neighbors, depending on its orientation. For > example, if cell (5,5) represents an "up" triangle, > then it is adjacent to (4,5) , (6,5), and (5,4), > but not to (5,6). > > --james > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 22 > Date: Sat, 3 Jul 1999 00:34:48 +0100 > From: "Ralph Jackson" > Subject: Meteor, Delta, Heart > > From: Ralph Jackson < ralph@jacksquiggle.freeserve.co.uk > > > Is it worth doing the little ones? > > Pete Darby in his 'Re: [eternity] So, who are you guys', records > >>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 > > It took me almost 2 weeks on and off to resort to a computer solver to do > meteor. It quickly found 34 solutions. These didn't include the duplicates > due to the 180 degree symmetry of the puzzle. The strange thing was they > hadn't been disallowed by the program. After a bug fix it found the other > 2062 solutions, this time including the duplicates - therefore potentially > 1048 different solutions. I haven't checked them. It might still be bugged. > > If Pete's source is right it seems Delta has more solutions (I'm in the > process of writing the solver - different style to meteor's solver). My > feeling is that it makes sense for that to be the case. One of the things > that becomes quickly obvious when playing with meteor is the large size of > the pieces relative to the puzzle space. Many piece placements force other > placements simply because of the lack of room. With Delta the same is not > true, with more of the puzzle space being filled before the constraints of > previously placed pieces narrow the choices. > > I recall someone (sorry don't remember who) posting on the NG that Heart has > only one solution. I'm astonished. Having said that, the design of the > puzzle must reduce solutions: the grid is peculiar, being made from a > regular pattern of equilateral triangles and squares; the outline of the > puzzle space is irregular; and the pieces are formed from two equilateral > triangles and two (diagonally cut) half squares, which in the absence of > better knowledge and for no apparent reason a friend and I christened > 'bromptons'. There is no doubt that Heart is the most cunningly designed > puzzle of the 'short eternities' - maybe even more so than Eternity itself. > > Leaving Heart out of the equation, it seems to me that Eternity has fewer > constraints on individual, and small groups of, pieces. There are a number > of factors in this. The puzzle space is huge compared to the pieces; the > grid is regular and simple; the drafters cut a triangle in any of three > directions; and it has been shown that the grid need not be followed rigidly > by going against the grain. > > Where's all this going? The lack of constraints in Eternity suggest that > there are at least many thousands of solutions. The 'short eternities' offer > clues which while cutting the permutations down, may well limit you to one > possible solution. Is this a good idea? > > Comments? > > By the way, playing with Heart becomes much faster with a grid in the > background. I haven't marked the pieces but that probably helps too. > > Ralph. > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 23 > Date: Sat, 3 Jul 1999 01:29:34 +0100 > From: "Thomas Voigt" > Subject: Re: Eternity Screen Solver > > Hi, > > > >I have a few suggestions for version 1.3: > [...] > > >- set the size of the board on the screen (too small now) > > >- various color schemes to color the pieces (looks much nicer) > > > - use piece-segments that slide towards eachother > > oh my, are we talking about a fancy screensaver or about a program > designed to solve a complex problem ? :-) > > But seriously, are copies of the piece descriptions available ? > I could only find GIF images of the pieces ... > > tv > > -- > Thomas Voigt | spock@berlin.snafu.de, tvoigt@comitatus.de > ================================================================== > I have a message to deliver to the cute people of the world...if > you're cute, or maybe you're beautiful...there's MORE OF US UGLY > MOTHERF#^&^#$ OUT THERE THAN YOU ARE!! (Frank Zappa) > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 24 > Date: Sat, 3 Jul 99 05:53 BST > From: redbaron@cix.compulink.co.uk (Richard Marsden) > Subject: Re: Count check > > In-Reply-To: <000d01bec1dd$cc34d420$0400a8c0@its.unimelb.edu.au> > bdowen@ee.mu.oz.au (Brendan Owen) wrote: > > > Hi guys & gals! > > > > > > Can anyone verify the following sum of combination counts: > > > > > > Let Ni = Number of different ways piece i can be positioned within the > > > grid (assuming no other places are located). > > > > > > Sum(Ni) = 2715377 > > > > I get 1372296, but I don't place any against the grain. Also the > > number you > > have isn't divisiable by 12 which it should be unless you are fixing one > > shape in a particular direction. > > Thanks: > Finally got it working! Okay I've been doing other things, but had a > number of bugs - the most infuriating, were rounding errors in the > rotation code!!! > Anyway, got it to work with the first piece, and the rest then matched > perfectly! > > At an early stage, I performed the rotations by converting triangle > positions into centroid coordinates, then rotating these about an > arbitrary point, then converting back. > > Next job: Do something interesting with these combinations - I'm just > incrementing counters at the moment. > > > Richard > > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > > Message: 25 > Date: Sat, 3 Jul 1999 11:01:03 +0100 > From: "Thomas Voigt" > Subject: Complexity > > Howdy, > > everybody says that Eternity is NP-Complete. > Where can I find the proof ? (Or is it obvious ? :-) > > tv > > -- > Thomas Voigt | spock@berlin.snafu.de, tvoigt@comitatus.de > ================================================================== > I have a message to deliver to the cute people of the world...if > you're cute, or maybe you're beautiful...there's MORE OF US UGLY > MOTHERF#^&^#$ OUT THERE THAN YOU ARE!! (Frank Zappa) > > > ____________________________________________________________________________ ___ > ____________________________________________________________________________ ___ > >