From: To: Subject: [eternity] Digest Number 19 Date: Friday, July 09, 1999 9:58 PM --------------------------- 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. FW: [eternity] How was it constructed? From: Morgan Gary 2. Against the grain From: pwadsworth@softworks.co.uk 3. Scanning the sheet. From: pwadsworth@softworks.co.uk 4. Number of Piece's From: pwadsworth@softworks.co.uk 5. Re: Scanning the sheet. From: "Brendan Owen" 6. Re: Scanning the sheet. From: Eugene Gill 7. Re: Scanning the sheet. From: "Phillips, Roger" 8. US Sales From: =?iso-8859-9?Q?"TANOL_T=DCRKO=D0LU"?= 9. Re: Against the grain (definition) From: "Mark Pursey" 10. Re: How was it constructed? From: "Mark Pursey" 11. Re: How was it constructed? From: path@multipro.com.au 12. Eternity: Ridiculous thread... From: Jason.Mccallion@ft.com (Jason Mccallion) 13. Re: Eternity: Ridiculous thread... From: Morgan Gary 14. Re: Eternity: Ridiculous thread... From: Jason.Mccallion@ft.com (Jason Mccallion) 15. Re: Eternity: Ridiculous thread... From: Eugene Gill 16. Re: Against the grain (definition) From: "Ronald Stewart" 17. Re: Eternity: Ridiculous thread... From: "Ronald Stewart" 18. Re: Eternity: Ridiculous thread... From: Jason.Mccallion@ft.com (Jason Mccallion) 19. Re: Against the grain (definition) From: Morgan Gary 20. Re: Against the grain (definition) From: Eugene Gill 21. Initial questionaire answers From: "Gordon Rattray" 22. Eternity pieces From: "Thomas Voigt" 23. Re: Scanning the sheet. From: Paul Why 24. RE: [eternity] Postscript From: "Brendan Owen" 25. RE: [eternity] Postscript From: "Brendan Owen" _______________________________________________________________________________ _______________________________________________________________________________ Message: 1 Date: Fri, 9 Jul 1999 12:09:00 +0100 From: Morgan Gary Subject: FW: [eternity] How was it constructed? I think that with a set of 1000 pieces, it would not be that difficult at all to fill the Eternity board. Even easier if you did not attempt to introduce pieces *against the grain*. Has anyone actually generated ~1000 pieces similar to CMs and tried to fill the board with those? Obviously attempting to solve it this way would not make life easier because you'd *have* to choose the correct 209 pieces out of the 1000 in order for your solution to be similar to CMs. ---------- From: DSaund2773@aol.com To: MorganGA@logica.com Subject: Re: [eternity] How was it constructed? Date: Friday, July 9, 1999 11:32 I think C.M.'s suggested method of making Eternity would be nearly as difficult as reassembling the puzzle. Although I would like to believe C.M. And even if he did assemble in that fashion, there might be a programming possibility from the approach I mentioned. Dick ---------- From: Morgan Gary To: Dsaund2773@aol.com Subject: RE: [eternity] How was it constructed? Date: Friday, July 9, 1999 11:22 In the "Details of TV interview about Eternity" link on the www.mathpuzzle.com/Eternity.html page, the following quote explains how CM constructed the puzzle. "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." I believe that this is a plausable method of constructiong the board and have no reason to doubt it. Gary ---------- From: Dsaund2773@aol.com To: eternity@onelist.com Subject: [eternity] How was it constructed? Date: Friday, July 9, 1999 11:11 From: Dsaund2773@aol.com 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 --------------------------- ONElist Sponsor ---------------------------- How has ONElist changed your life? Share your story with us at http://www.onelist.com ------------------------------------------------------------------------ _______________________________________________________________________________ _______________________________________________________________________________ Message: 2 Date: 9 Jul 1999 12:01:07 -0000 From: pwadsworth@softworks.co.uk Subject: Against the grain When I replied to Morgan Gray message about against the grain, I listed the wrong piece. I should have listed piece 123. ( though the same can be true of 34 ) If you look at piece 123, as per the sheet given from eternity, and then place the BOTTOM cornor of the drawing on the bottom left 30 deg corner of the sheet you send into claim the prize. You can see that it can be place, not only against the grain, but also outside of the 4 triangles Morgen was talking about. ( see Scanning sheet ) The same is true of 34, only this time flip the piece over and use the coner on the left of the drawing. Both end up against the grain in true fashion What does this all mean ?? Well if you take a 30 Deg triangle and mark the longest line as 1, the middle line as 2 and the shortest line as 3. you will see that there is no way ( within the puzzle ) that you can match the number of Line 1 with Line 2, and so there can be No Against the Grain. I think what we should do is call it 'Outside of the Grid / Triangle' as you could split each triangle into a number of smaller ones, and still make it fit. _______________________________________________________________________________ _______________________________________________________________________________ Message: 3 Date: 9 Jul 1999 12:08:33 -0000 From: pwadsworth@softworks.co.uk Subject: Scanning the sheet. Does some one have the ablity to scan the Sheet with all the pieces of Eternity, as supplied with the game, and save it so every one can have a copy. We may need CM permission as he has copyrighted it, but as this will be in the scanned document we are still giving him credit. The information is available be post, so people do not need to buy the game anyway. It would help as in place of trying an ASCI drawing we can ref the sheet and just tell people what to do with the piece. PS. I see we are at 210 members, how about the sugestion of evry one having one piece and picking a spot on the board. I am going with piece 123 Placed in the bottom right corner, within the triangles. _______________________________________________________________________________ _______________________________________________________________________________ Message: 4 Date: 9 Jul 1999 12:15:59 -0000 From: pwadsworth@softworks.co.uk Subject: Number of Piece's I would like to know the number of physical piece's that can be made from 12-30deg triangles (i.e. you must be able to mold the piece, as 12-30deg triangles in a row can not be molded ) If the number of pieces with actual 30deg triangles and sharp points could be emliminated. Then it would give an indication of how many CM really started with, as he only says 'Around 1000' pieces. Remember this could be the first of Three Games, with the next having about 500 pieces, and the last having over 1000. _______________________________________________________________________________ _______________________________________________________________________________ Message: 5 Date: Fri, 9 Jul 1999 22:31:53 +1000 From: "Brendan Owen" Subject: Re: Scanning the sheet. > PS. I see we are at 210 members, how about the sugestion of evry > one having one piece and picking a spot on the board. I am going > with piece 123 Placed in the bottom right corner, within the triangles. I'm going with piece 34, but I'm not sure where I'll place it yet. :) _______________________________________________________________________________ _______________________________________________________________________________ Message: 6 Date: Fri, 9 Jul 1999 13:35:05 +0100 From: Eugene Gill Subject: Re: Scanning the sheet. I don't have the puzzle, I have Ed Pegg's rendering of the pieces - but they are not numbered. So for no good reason I'll have piece Number 28. From: pwadsworth@softworks.co.uk PS. I see we are at 210 members, how about the sugestion of evry one having one piece and picking a spot on the board. I am going with piece 123 Placed in the bottom right corner, within the triangles. _______________________________________________________________________________ _______________________________________________________________________________ Message: 7 Date: Fri, 9 Jul 1999 14:15:55 +0100 From: "Phillips, Roger" Subject: Re: Scanning the sheet. Eugene Gill contributed to the silliest thread I've seen in a while: > So for no good reason I'll have piece Number 28. Ok, I'll adopt piece 143. Who's keeping track? -- Roger Phillips roger@spss.com "*canephor* (architecture) a female (or male) sculptured figure carrying a basket on the head" -- Chambers Dictionary on CD-ROM (1994) _______________________________________________________________________________ _______________________________________________________________________________ Message: 8 Date: Fri, 9 Jul 1999 16:22:49 +0300 From: =?iso-8859-9?Q?"TANOL_T=DCRKO=D0LU"?= Subject: US Sales Has anyone know if the game can current be found in US market (NYC, Miami, etc) ? I am flying to the states tomorrow and like to buy one. Thnx. _______________________________________________________________________________ _______________________________________________________________________________ Message: 9 Date: Fri, 9 Jul 1999 23:48:00 +1000 From: "Mark Pursey" Subject: Re: Against the grain (definition) > From: pwadsworth@softworks.co.uk > ... > > Well if you take a 30 Deg triangle and mark the longest line as 1, > the middle line as 2 and the shortest line as 3. you will see that > there is no way ( within the puzzle ) that you can match the > number of Line 1 with Line 2, and so there can be No Against the > Grain. If you have been taking 'against the grain' to mean aligning middle piece edges with the gridlines, then no, the pieces cannot be placed that way. Against the grain is more commonly understood (here) to refer to *translation* of a 'with grain' piece by half a triangle edge in one of the 3 available grid directions. Below is a pentadude (5 drafters) with and then against the grain... notice that if the grid is subdivided the second case will become 'with the grain'. The two other ways of it being against the grain are to slide it up to the left and up to the right. / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ -----------*************-----------X----------- \ * * **\ / \ / \ * * * * \ / \ / \ * * * * \with the grain / \ * * * * \ / \ / \ * * * * \ / \ / -----*******************-----X-----------X----- / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ -----------X-----*************-----X----------- \ / \ * * / \ ** / \ / \ / \ * * / \ * * / \ / \ / * * * * against! / \ / * \ / * * \ * / \ / \ / * \ / * * \*/ \ / -----X-----*******************-----------X----- / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ Hey, wouldn't it be nice if the onelist auto-signature pointed at a FAQ for this list! _______________________________________________________________________________ _______________________________________________________________________________ Message: 10 Date: Sat, 10 Jul 1999 00:10:45 +1000 From: "Mark Pursey" Subject: Re: How was it constructed? If you allow reuse of pieces, it is not too hard to fill the eternity shape. Miroslav Vicher has done this, there is a piccy on his site. I tried this also and did it in about 5 minutes. Of the 209 pieces my solver used 138 distinct ones. The *interesting* thing is, i tried iterating this procedure, with my new piece set (and still allowing reuse of pieces) and my solver wasn't very happy at all (i didn't run it for that long but it was making pretty terrible progress). To get an idea of how hard it is to build a shape from an excess of pieces, i have been building regular hexagons, dodecagons, triangles and a large variety of oblongs using the eternity pieces (not allowing piece reuse) and found it amazing how consistently shapes can be built. Virtually every shape (with a correct area) works! Unfortunately (as one would expect) as the number of pieces required approaches the number of pieces available, the time required grows longer. Still, i have not had any of the sizes fail... except for the 2 small hexagons with sides of 2 and 4 mid edges. The largest shape i have built so far is a hexagon with sides of 12 mid-edges, comprising 108 pieces. Of course once i have built these shapes, it is a much harder task to 're-solve' them using the same fixed set. I haven't even re-solved my 36 piece hexagon yet... Mark ----- Original Message ----- From: Morgan Gary To: Sent: Friday, 9 July 1999 21:09 Subject: [eternity] FW: [eternity] How was it constructed? > From: Morgan Gary > > I think that with a set of 1000 pieces, it would not be that difficult at > all to fill the Eternity board. Even easier if you did not attempt to > introduce pieces *against the grain*. > _______________________________________________________________________________ _______________________________________________________________________________ Message: 11 Date: Fri, 9 Jul 1999 19:26:50 +0800 From: path@multipro.com.au Subject: Re: How was it constructed? Patrick M Hamlyn@MULTIPROGRAMMING 07/09/99 07:26 PM >A number of people have proposed ideas on how Eternity was constructed. Among them CM himself, so there's no need for us to speculate. He used a computer to help generate the pieces, and chose from those a set of over a thousand. He then tiled the dodecagon manually, a tedious job for sure, but trivially easy compared to the job he left us to do. At every step he had near a thousand pieces to choose from, near the end we have very few, and very few just isn't enough unless you chose the earlier pieces *very* wisely. Due to the amazing 'E-property', once you get down to around 60 pieces to choose from, the going gets awfully tough, no matter what shape you have left to tile. BTW, I'm up to 201 pieces placed. I have reasonable hope of being able to extend this several pieces, too. Unfortunately to get the last piece in using my algorithm I will probably need to place the 208th piece anything from several thousand to several hundred thousand times, and right now I would be very lucky to place 205 pieces. The saga continues. _______________________________________________________________________________ _______________________________________________________________________________ Message: 12 Date: Fri, 9 Jul 1999 15:41:13 +0100 From: Jason.Mccallion@ft.com (Jason Mccallion) Subject: Eternity: Ridiculous thread... Heres the first four suggestions. Eugene Gill: 123 - Placed in the bottom right of the grid, aligned with the grid traingles. P Wadsworth: 28 Brendan Owen: 34 Roger Philips: 143 Anymore? Jase. "Roger Phillips" on 09/07/99 13:15:55 To: eternity@onelist.com cc: (bcc: Jason Mccallion/LONDON/FINANCIAL TIMES) Subject: Re: [eternity] Scanning the sheet. From: "Phillips, Roger" Eugene Gill contributed to the silliest thread I've seen in a while: > So for no good reason I'll have piece Number 28. Ok, I'll adopt piece 143. Who's keeping track? -- Roger Phillips roger@spss.com "*canephor* (architecture) a female (or male) sculptured figure carrying a basket on the head" -- Chambers Dictionary on CD-ROM (1994) --------------------------- ONElist Sponsor ---------------------------- ONElist: your connection to like-minds and kindred spirits. ------------------------------------------------------------------------ **************************************************************************************** *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: Fri, 9 Jul 1999 15:49:00 +0100 From: Morgan Gary Subject: Re: Eternity: Ridiculous thread... CLAIM YOUR PIECES WHILE THEY STILL LAST 28: P Wadsworth 34: Brendan Owen 69: Gary Morgan 123: Eugene Gill - Placed in the bottom right of the grid, aligned with the grid traingles. 143: Roger Philips _______________________________________________________________________________ _______________________________________________________________________________ Message: 14 Date: Fri, 9 Jul 1999 15:59:37 +0100 From: Jason.Mccallion@ft.com (Jason Mccallion) Subject: Re: Eternity: Ridiculous thread... Morgan Gary on 09/07/99 14:49:00 To: eternity@onelist.com cc: (bcc: Jason Mccallion/LONDON/FINANCIAL TIMES) Subject: Re: [eternity] Eternity: Ridiculous thread... From: Morgan Gary CLAIM YOUR PIECES WHILE THEY STILL LAST 28: P Wadsworth 34: Brendan Owen 69: Gary Morgan 123: Eugene Gill - Placed in the bottom right of the grid, aligned with the grid traingles. 143: Roger Philips --------------------------- ONElist Sponsor ---------------------------- How has ONElist changed your life? Share your story with us at http://www.onelist.com ------------------------------------------------------------------------ **************************************************************************************** *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: 15 Date: Fri, 9 Jul 1999 16:02:54 +0100 From: Eugene Gill Subject: Re: Eternity: Ridiculous thread... Wait this is wrong I picked 28 It's - 123: P Wadsworth - Placed in the bottom right of the grid, aligned with the grid traingles. 28: Eugene Gill 34: Brendan Owen 69: Gary Morgan 143: Roger Philips -----Original Message----- From: Morgan Gary [SMTP:MorganGA@logica.com] Sent: Friday, July 09, 1999 3:49 PM To: eternity@onelist.com Subject: Re: [eternity] Eternity: Ridiculous thread... From: Morgan Gary CLAIM YOUR PIECES WHILE THEY STILL LAST 28: P Wadsworth 34: Brendan Owen 69: Gary Morgan 123: Eugene Gill - Placed in the bottom right of the grid, aligned with the grid traingles. 143: Roger Philips --------------------------- ONElist Sponsor ---------------------------- How has ONElist changed your life? Share your story with us at http://www.onelist.com ------------------------------------------------------------------------ _______________________________________________________________________________ _______________________________________________________________________________ Message: 16 Date: Fri, 9 Jul 1999 15:10:59 +0100 From: "Ronald Stewart" Subject: Re: Against the grain (definition) OK, anyone up for making a glossary of terms (ok, so it *is* really an FAQ) - Ron _______________________________________________________________________________ _______________________________________________________________________________ Message: 17 Date: Fri, 9 Jul 1999 16:07:44 +0100 From: "Ronald Stewart" Subject: Re: Eternity: Ridiculous thread... oooooooh.... I'll have piece number 19. What does that look like? _______________________________________________________________________________ _______________________________________________________________________________ Message: 18 Date: Fri, 9 Jul 1999 16:26:06 +0100 From: Jason.Mccallion@ft.com (Jason Mccallion) Subject: Re: Eternity: Ridiculous thread... CLAIM YOUR PIECES WHILE THEY STILL LAST Sorry Eugene... 123: P Wadsworth - Placed in the bottom right of the grid, aligned with traingles. 28: Eugene Gill 34: Brendan Owen 143: Roger Philips 69: Gary Morgan 19: Ronald Stewart 1: Jason McCallion Only 203 to go! Jase. **************************************************************************************** *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: 19 Date: Fri, 9 Jul 1999 16:33:00 +0100 From: Morgan Gary Subject: Re: Against the grain (definition) Eternity Glossary of Terms (Please feel free to update, append, or criticise this attempt) triangle - a square with three sides 30-60-90 - a 1 - root 3 - 2 triangle drafter - parity - CM - against the grain - algorithm - sequence of instructions heuristic - Eternity - board game brute force - running, blindfolded, as fast as possible in a maze. backtracking - the ability to remove a piece from the board as part of your algorithm. genetic algorithims - ? simulated annealing - make pieces move about a bit with lots of energy, then watch them cool down to form a solid Eternity solution. SECRET - my winning ideas. ---------- From: Ronald Stewart To: eternity@onelist.com Subject: Re: [eternity] Against the grain (definition) Date: Friday, July 9, 1999 15:10 From: "Ronald Stewart" OK, anyone up for making a glossary of terms (ok, so it *is* really an FAQ) - Ron --------------------------- ONElist Sponsor ---------------------------- Attention ONElist list owners. http://www.onelist.com We've just added a "NO ATTACHMENTS" option. See homepage for details. ------------------------------------------------------------------------ _______________________________________________________________________________ _______________________________________________________________________________ Message: 20 Date: Fri, 9 Jul 1999 17:03:03 +0100 From: Eugene Gill Subject: Re: Against the grain (definition) -----Original Message----- From: Morgan Gary [SMTP:MorganGA@logica.com] Sent: Friday, July 09, 1999 4:33 PM To: eternity@onelist.com Subject: Re: [eternity] Against the grain (definition) From: Morgan Gary Eternity Glossary of Terms (Please feel free to update, append, or criticise this attempt) triangle - a square with three sides ^^^^^^ Yeah right. _______________________________________________________________________________ _______________________________________________________________________________ Message: 21 Date: Fri, 9 Jul 1999 18:35:19 +0100 From: "Gordon Rattray" Subject: Initial questionaire answers QUESTIONS -------------- What's your..... name : Gordon Rattray age : 26 occupation : Software engineer city : Glasgow country : Scotland email : grattray@atl.co.uk homepage : Subject: Eternity pieces Hi, some people wrote that they picked up the pieces on the internet. I've got a list of pieces as GIF images, but is there anybody who actually entered the pieces and made them available ? I would be really glad if I didn't have to type them in myself :-) 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: 23 Date: Fri, 9 Jul 1999 18:01:24 +0100 From: Paul Why Subject: Re: Scanning the sheet. In article <931522113.21556@onelist.com>, pwadsworth@softworks.co.uk writes >From: pwadsworth@softworks.co.uk > >Does some one have the ablity to scan the Sheet with all the pieces of Eternity, >as supplied with the game, and save it so every one can have a copy. I sent for a copy, then scanned it myself to use as a reference, but I'd rather not make it publicly available, because: In article <7k77kt$s9o@dfw-ixnews12.ix.netcom.com>, Ed Pegg Jr. wrote: > Yes, the Ertl >company wrote me and asked that I not post all the pieces at my site just >yet. They are about to launch the puzzle in the United States. They felt >that the list of pieces might hurt sales. So I've taken it off, for now. I realise that it costs nothing to send for a copy, but copyright is copyright nevertheless. In any case, the pieces on Ed's page were almost in the correct order anyway; just move piece 67 to position 70 (shifting the intervening pieces down), then swap 72 with 73, and the numbering will match Monckton's. There's also the advantage that this set (which can probably still be found *somewhere* on the web) is marked with drafter subdivisions, whereas the 'official' ones aren't. -- Paul Why paul@clastech.demon.co.uk _______________________________________________________________________________ _______________________________________________________________________________ Message: 24 Date: Sat, 10 Jul 1999 13:07:45 +1000 From: "Brendan Owen" Subject: RE: [eternity] Postscript Hi All, > Has anyone created a postscript version of the board & pieces that they > would like to share with us? I don't have a postscript version yet but here is a list of edges. Note that most of the straight edges are made up of a number of smaller edges. This is due to the way I computed the edges from my shape representation, but I have not got the time to make that more efficient. The table has the form > The bitmap versions from www.mathpuzzle.com > don't scale very well when printed. This should scale very well. I'll make a postscript version and post that soon. Regards Brendan _______________________________________________________________________________ _______________________________________________________________________________ Message: 25 Date: Sat, 10 Jul 1999 13:58:11 +1000 From: "Brendan Owen" Subject: RE: [eternity] Postscript Hi All, Attached is an encapsulated postscript picture of the eternity shapes. They are not packed very well. If anyone knows how to pack them in a dodecagon send me a picture and I'll create a postcript of that. :) Regards Brendan _______________________________________________________________________________ _______________________________________________________________________________