From cube-lovers-errors@mc.lcs.mit.edu Thu Sep 17 17:18:28 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id RAA12950; Thu, 17 Sep 1998 17:18:27 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 14 Sep 1998 14:14:22 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Re: Weak Local Maxima, 6f from Start In-Reply-To: <14Sep1998.111621.Hoey@AIC.NRL.Navy.Mil> To: Cube Lovers Message-Id: > It turns out that 6f is indeed the shortest. There are two such positions > unique to symmetry which are 6f from Start, the Pons and one other. The > other one is quite pretty: > > L2 R2 D2 U2 B' F (6f*) > I didn't notice it originally, but this position is in the slice subgroup, and is only one slice move from Pons. Half turns such as L2 can be written equally well as either LL or as L'L', so we can write (L2 R2) as (L'R)(L'R) and (D2 U2) as (D'U)(D'U). Thus, the weak local maximum 6f from Start can be written as five slices, one slice short of Pons. L'R L'R D'U D'U B'F All we would have to do to get the Pons would be to add one more B'F slice. ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Thu Sep 17 20:27:13 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id UAA14346; Thu, 17 Sep 1998 20:27:13 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Chris and Kori Pelley" To: "Cube Lovers" Subject: DOGIC solution Date: Mon, 14 Sep 1998 18:01:56 -0400 Message-Id: <000a01bde02b$49b5aae0$da460318@CC623255-A.srst1.fl.home.com> Using Noel Dillabough's PUZZLER program for MS Windows, I was able to verify the basic moves needed to solve the new DOGIC puzzle. SPOILER WARNING! If you wish to solve the puzzle yourself, read no further. What seems fairly obvious is that the DOGIC is essentially a superset of Impossi-Ball, which is basically the corners of MegaMinx. On DOGIC, however, these corners have been flattened and could more properly be called "centers." Using classic 3x3x3 techniques, you can position and orient these pieces using the following moves: Center 3-cycle: (R' U L U') (R U L' U') Center orientation (pair): (R' D R) (F D F') U' (F D' F') (R' D' R) U Note that these faces refer to the large pentagons and must be "translated" to fit the dodecahedral nature of DOGIC. R, U, and L form a horseshoe, and F intersects all three. The D face is not really D, in fact it touches the U face at one point. The remaining triangular pieces turn out to be fairly trivial, and any two can be swapped with the simple sequence: R u R' u' In this case, R is a large pentagon and u is any intersecting smaller pentagon. A general strategy would be to manually place the top "centers" followed by their adjacent centers (if you have solved ImpossiBall this should not be difficult). Then apply the first two moves above to complete the remaining centers. Finally, place all the smaller triangles with the third move. Despite having more permutations than most magic puzzles, DOGIC seems to be fairly easy to solve. Chris Pelley ck1@home.com http://www.chrisandkori.com From cube-lovers-errors@mc.lcs.mit.edu Fri Sep 18 14:29:06 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA20307; Fri, 18 Sep 1998 14:29:05 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Tue, 15 Sep 1998 12:21:58 -0400 (EDT) From: der Mouse Message-Id: <199809151621.MAA19286@Twig.Rodents.Montreal.QC.CA> To: cube-lovers@ai.mit.edu Subject: Two-face and three-face subgroups I've been playing with the two-face subgroup [%] of the 3-Cube and got to wondering - how much work has been done on the two-face and three-face subgroups? Certainly the two-face subgroup "feels" like a much smaller object than even the 2-Cube (though perhaps more tedious for human solution), perhaps about the size of the Pyraminx. [%] Okay, strictly speaking there are two different two-face subgroups, but one of them is not even the least bit interesting. And what about the three-face subgroups? Certainly the three- and four-face subgroups are smaller than the whole Cube group, though ISTR that the five-face (sub)group is actually the whole thing. But how much smaller, and how difficult of human solution? I'd expect one of the three-face groups (the one involving two opposite faces - call it the L-F-R one) to be more tedious but no more difficult than the two-face group, whereas the other one (involving one face from each pair of opposite faces - U-F-R, say) should have more interest. In particular, the two-face subgroup is smaller than the set of all position that leave unchanged the cubies that the two-face subgroup never touches. (To put it another way, I'm saying that the subgroup generated by {R,F} is smaller than the set of positions of the full group that leaves unmoved the 11 cubies that don't touch either of those two faces - 7 if you don't count face cubies.) I can see a factor of 128 smaller, since it's not possible to flip edge cubies in the two-face group, but I haven't thought about the corners, so it may be even smaller than that. What about the three-face subgroups? The L-F-R subgroup is also smaller, if for no other reason than an inability to flip edge cubies, like the two-face group. But is the U-F-R subgroup the same as the subset of the full group that leaves untouched the 7 (4 if you don't count face centers) cubies in the DBL corner? What about human solvability? I've taught myself to solve the two-face group, and with the tools I developed (largely powers, reorientations, and inverses of F' R' F R) I feel confident I can handle the L-F-R three-face group or even the L-F-R-B four-face group. Can anyone comment on how humanly difficult the U-F-R group, or for that matter the U-F-R-L four-face group, is? der Mouse mouse@rodents.montreal.qc.ca 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B From cube-lovers-errors@mc.lcs.mit.edu Tue Sep 22 16:10:10 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id QAA17882; Tue, 22 Sep 1998 16:10:10 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 18 Sep 1998 15:52:33 -0400 (EDT) From: Nicholas Bodley To: Hana Bizek Cc: cube-lovers@ai.mit.edu Subject: Re: Rubik's cube kingdom In-Reply-To: <35F350B1.626F@ameritech.net> Message-Id: My apologies for a delayed reply. Hana's essay was rather philosophical, and contained some uncommon points of view; it was appropriate, in my opinion. One aspect of the Cube (and related puzzles) that seemed to be ignored is the remarkable ingenuity of their internal mechanisms. I maintain that the mechanism of the original (i.e., 3^3) Rubik's Cube is one of the most ingenious ever invented. I recall being very fatigued, riding the West Side IRT subway in NYC about 2 AM, perhaps, and catching sight of someone manipulating what must have been one of the very first Cubes, probably from Hungary*. I was fairly sure I wasn't hallucinating, but was very troubled that what I'd seen simply appeared impossible. I've been a somewhat-casual student of mechanisms all my life. *This was probably several weeks, or more, before the Scientific American article, and the later explosion of its popularity. My regards to all, |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Tue Sep 22 18:09:16 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA18211; Tue, 22 Sep 1998 18:09:15 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 17 Sep 1998 00:03:47 -0400 (EDT) From: Jerry Bryan Subject: More on Calculating Weak Local Maxima To: Cube-Lovers Message-Id: In the process of adding the code to my God's Algorithm program to calculate weak local maxima in the face turn metric, I realized that the algorithm I posted previously to do so was incomplete in one subtle but very important respect. This message will provide the missing piece to the algorithm. I have posted much of this before, but my program is in general jumping ahead by more than one move at a time. For example, suppose we can store all the positions up to five moves from Start. Then, we can determine all the positions which are eight move s from Start by calculating all the products xy where x is a position of length five and y is a position of length three. Obviously, just because the length of x is five and the length of y is three does not mean that the length of xy is eight. In fact, the length of xy could be anywhere from two through eight. To determine the true length of xy, we compare xy to the stored positions of length two, three, four, and five. In addition, we compare xy to the calculated positions of length six and seven, which are calculated in the same manner as is xy. If xy fails to match all such shorter positions, then its length is indeed eight. Next we focus on the quarter turn metric. For some fixed q in Q, the set of twelve quarter turns, what is the length of xyq if the length of xy is eight with the length of x equal to five and the length of y equal to three? First of all, it must be either seven or nine. Second of all, the length of yq must be either two or four. If the length of yq is two, then we know that the length of xyq must be seven. But if the length of yq is four, then we are still not sure. The reason is that there might be some u not equal to x of length five and some v not equal to y of length three such that xy=uv, but where the length of vq is two. If so, then the length of xyq is the same as the length of uvq which is seven. The basic idea is that if z=xy where the length of x is five and the length of y is three, then there may be many, many x and y pairs of length five and three respectively whose product yields z. The length of zq is nine only if for every such y the length of yq is four. Even if all but one yq is of length four, it only takes one yq of length two to spoil the pudding, as it were. The mechanism which I have posted previously to capture this concept is the Ends-with function E(z). E(z) is defined to the be set of all moves with which a minimal maneuver for z can end. So in the case at hand, since the length of z is eight, the length of zq is nine only if E(z) does not contain q'. E(z) can be calculated in the case at hand as the union of E(y) taken over all the y values of length three which can be composed with an x of length five to create z. Therefore, to say that E(z) does not contain q' is the same thing as saying that none of the E(y) contain q'. So far, so good and there is nothing new here which I haven't posted before. But let's consider the exact same issue in the face turn metric. If the length of x is five and the length of y is three, then the length of xy can be in the range of two through eight as before. And as before, if we compare xy with all positions of length two through seven without finding a match, then the length of xy is indeed eight. But this time we need to consider xyf, where f is some fixed face turn in the set Q+H of twelve quarter turns and six half turns. What is the length of xyf? For starters, it is either seven or eight or nine. Also, the length of yf is two or three or four. If the length of yf is two, then the length of xyf is guaranteed to be seven. If the length of yf is three, then the length of xyf is guaranteed to be no more than eight. But the length nevertheless might be seven, because as in the quarter turn case, there may be some u of length five and some v of length three such that uv=xy, but such that the length of vf is only two. If so, the length of xyf is the same as the length of uvf which is guaranteed to be seven. The definition of Ends-with is the same in the face turn case as in the quarter turn case, namely E(z) is the set of all face turns with which a minimal maneuver for z can end. If z=xy then E(z) can be calculated as the union of E(y) over all the y value s of length three which can be combined with an x value of length five to form z. To say that the length of zf is at least eight is the same thing is saying that E(z) does not contain f' which is the same thing as saying that none of the E(y) contain f'. Next, let's suppose that indeed E(z) does not contain f'. We are still left with the issue of whether the length of z is eight or nine, having eliminated seven as a possibility. The test is still the length of all the yf, with a length of two having been eliminated as a possibility. If all of the yf are of length 4, then xyf is of length nine. But if even so many as one of the yf are of length three, then xyf is of length 8. The mechanism I have posted before to capture this concept is the Ends-with2 function. E2(z) is a little tricky to describe. Informally, we might say that E2(z) is the set of all f in Q+H with which z can end without changing it's length. It is probably better to say that E2(z) is the set of all f in Q+H such that the length of zf' is the same as the length of z. The technique which I have posted before (and which I must now correct) to calculate E2(z) is to form the union of E2(y) over all y values of length three which can be combined with an x value of length five to form z. If the length of zf is eight or nine, then this mechanism is fine. But if the length of zf turns out to be seven, there is a problem. That is, there may be one y where the length of yf is two and where E(y) contains f, and there may be another y where the length of yf is is three and where E2(y) contains f. In such a case, both E(z) and E2(z) would contain f. Hence, we must always calculate E(z) prior to calculating E2(z), and we must omit from E2(z) any f values which are already contained in E(z). With this correction, everything works. A local maximum is a position z for which |E(z)|+|E2(z)|=18, a strong local maximum is a local maximum z for which |E(z)|=18 and |E2(z)|=0, and a weak local maximum is a local maximum z for which |E(z)| < 18 and |E 2(z)| > 0. All my examples have been specific to y values of length 3 for clarity of exposition, but the calculation of E(z) and E2(z) is totally general, and is the union of E(y) and E2(y), respectively, over all y values which can be used to form a z of the form z=xy, and with any values which are in E(z) omitted from E2(z). Finally, my programs also calculate a Starts-with and a Starts-with2 function, which are defined analogously. The same correction must be made to the Starts-with2 function as was made for the Ends-with2 function. Equivalently, we can define S(z)=E'(z') and S2(z)=E2'(z'), where E' and E2' are the set of all inverses of the elements of E and E2, respectively. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990 From cube-lovers-errors@mc.lcs.mit.edu Tue Sep 22 19:05:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA18829; Tue, 22 Sep 1998 19:05:00 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sat, 19 Sep 1998 09:13:58 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Re: Two-face and three-face subgroups In-Reply-To: <199809151621.MAA19286@Twig.Rodents.Montreal.QC.CA> To: der Mouse Cc: Cube Lovers Message-Id: On Tue, 15 Sep 1998 12:21:58 -0400 (EDT) der Mouse wrote: > I've been playing with the two-face subgroup [%] of the 3-Cube and got > to wondering - how much work has been done on the two-face and > three-face subgroups? Certainly the two-face subgroup "feels" like a > much smaller object than even the 2-Cube (though perhaps more tedious > for human solution), perhaps about the size of the Pyraminx. > The subgroup has been explored fairly thoroughly. For example, look in the archives 8/31/1994 for a summary of the first complete God's Algorithm search of this particular subgroup. There are a number of articles in the archives thereafter. has been searched in both the quarter turn metric and the face turn metric, and local maxima have been investigated as a part of the search. has a very small branching factor and a corresponding large diameter of 25 in the quarter turn metric, at least I think it's a large diameter for such a small group. Until Mike Reid recently showed that the diameter of G in the quarter turn metric was at least 26, the diameter of was the largest known for the 3x3x3 cube or any of its subgroups. Frey and Singmaster's book discusses both two face and three face subgroups, among other things giving their sizes. To my knowledge, no God's Algorithm searches have been performed for the three face subgroups. We have ||=73483200, so is slightly smaller than the corners group at 88179840. The 2x2x2 is 24 times smaller than the corners group, at 3674160. However, I am of the school of thought that tends not to equate the size of the group (or search space, for problems that are not actually groups) with the difficulty of the problem. ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Tue Sep 22 19:50:07 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA19137; Tue, 22 Sep 1998 19:50:02 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 21 Sep 1998 16:34:29 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Local Maxima which Fix the Corners, 12q from Start To: Cube Lovers Message-Id: I am making a run to calculate God's Algorithm out to 12 moves from Start in the quarter turn metric. It has been running several weeks, and will probably run several more. I have made some changes to my program to make it easier to extract the positions for local maxima, and to checkpoint the local maxima data. As a part of the checkpointing, I can actually see the local maxima as they are generated without having to wait for the program to end. It is becoming apparent that there are a *lot* of local maxima 12q from Start. It is already known that there are only four (unique to symmetry) which are 10q from Start (the shortest ones in the quarter turn metric), and that there are none 11q from Start. So I am a little surprised that I am seeing so many. I have looked at quite a few of them, and most of them are not all that interesting. But the ones which fix the corners are all quite pretty. Because the positions are being produced in lexicographic order, and because I am sorting by corners first, edges second, the positions which fix the corners are the first ones to appear. There are eight of them as follows. 1. F2 L2 F2 B2 R2 B2 2. F B' U2 D2 F' B R2 L2 3. F B R2 F' B' U D L2 U' D' 4. D' F B' R F R' F' B U F' U' D 5. F B R2 L2 F B U2 D2 6. R L' F2 B2 R L' F2 B2 7. F2 B2 U2 D2 R2 L2 8. R L' U D' F B' R2 L2 U D' #1 is a 2-H pattern (only four edge cubies are moved). #2 is a 4-H. #3 moves four edge cubies, leaving eight of the nine facelets the same color on four faces, and a solid color on the other two faces. #4 moves three edge cubies, leaving eight of the nine facelets the same color on all six faces. #5 has 2 H's, 2 checkerboards, and 2 solid faces -- with the respective H's, checkerboards, and solid faces opposing each other. #6 has 4 H's and 2 checkerboards, with the 2 checkerboards opposing each other. #7 is the Pons Asinorum, and is included only for completeness because we already knew that the Pons was a local maximum of length 12q. #8 has all six faces being sort of a "three colored checkerboard". Some of these positions may have appeared on Cube-Lovers in some other context, but the only one I recognize for sure is the Pons. In some ways, #4 is the most interesting to me, because it a simple 3-cycle on the edges, and who would have thought that such a position would turn out to be a local maximum? #1 and #3 both consist of two 2-cycles on the edges, and are about as striking to me as is #4. ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Wed Sep 23 12:37:03 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id MAA22987; Wed, 23 Sep 1998 12:37:03 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19980922204717.20206.rocketmail@web1.rocketmail.com> Date: Tue, 22 Sep 1998 13:47:17 -0700 (PDT) From: "Jorge E. Jaramillo" Subject: Moves to this pattern To: Cube-Lovers@ai.mit.edu Hi I just joined the list! I was wondering if someone could help me with a pattern that has been bugging me for a while. I have been able to solve the cube to this pattern so i know it is a valid one. I used one of those on-line solvers entered the pattern and then reversed the sequence the solver gave me and it indeed gets the pattern i want but somehow it seemed too many moves for me for such a simple pattern. the pattern I am talking about is: the 4 cubelets that make the vertex formed by FDR are exchanged with the vertex from BDL Can any one give me the set of moves to get to this pattern from a solved cube? Does this pattern have a name? [Here is a] set of moves (they work but I am sure there is a shorter way): D2 F B- L2 F- B D- F B- L F- B D2 F B- L2 F- B D F B- L- F- B F B- L- F- B D2 F B- L- F- B D2 R- D- R D- R- D2 R D2 L- D- L B D- B- L- D L2 D L- D- F- D- F D B- D- B D R D R- D F- B D B- F R D- R- T B- T- B- D- B- This long set of moves reminds me of something else: There are many Rubik cube annimations that you move the faces with either the keypad or the mouse. Does anyone know of one that follows sets of orders you write? It would be neat to try this long patterns in one of those simulators. Thanks === Jorge E Jaramillo From cube-lovers-errors@mc.lcs.mit.edu Wed Sep 23 19:54:38 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA26229; Wed, 23 Sep 1998 19:54:38 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19980922213222.29513.rocketmail@web1.rocketmail.com> Date: Tue, 22 Sep 1998 14:32:21 -0700 (PDT) From: "Jorge E. Jaramillo" Subject: Is it only mine? To: cube In order to solve the cube faster I developed a method that would turn a lot the middle faces. I don't know how you call them in this list I am talking about the face between Top and Bottom, the face between Right and Left and even the face between Front and Back. Well after twisting it a few times my cube came undone, fell apart and I thought "Damn made in Taiwan cubes" (although the ones I can buy here do not say where are they made). I was going through my second cube in a short while (I just regained interest in the cube a short while ago after say 15 years) and it fell apart again. I took off the plastic color of the center cubelet that came apart and found a screw and a spring that keeps the screw tight. I re screwed it but did not have any glue at hand so I kept on playing without the color of the center cubelet I was doing one of these center face moves and saw how the screw was turning counterclockwise in other words the way that makes the cube fall apart. Needless to say I had to re design my method. This long story is to ask if all the cubes are built this way or only the ordinary ones I can buy here? Thanks. === Jorge E Jaramillo From cube-lovers-errors@mc.lcs.mit.edu Fri Sep 25 18:05:43 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA07121; Fri, 25 Sep 1998 18:05:42 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <360964EA.D07A79F8@t-online.de> Date: Wed, 23 Sep 1998 23:15:22 +0200 Reply-To: Rainer.adS.BERA_GmbH@t-online.de Organization: BERA Softwaretechnik GmbH To: "Jorge E. Jaramillo" Cc: Cube-Lovers@ai.mit.edu Subject: Re: Moves to this pattern References: <19980922204717.20206.rocketmail@web1.rocketmail.com> From: Rainer.adS.BERA_GmbH@t-online.de (Rainer aus dem Spring) Jorge E. Jaramillo wrote: > the pattern I am talking about is: the 4 cubelets > that make the vertex formed by FDR are exchanged with > the vertex from BDL. R2 U R2 U2 B2 D L2 U2 L2 B2 D' B2 U2 Rainer adS PS If you have a WINTEL system you should download Herbert Kociemba's cube program. [ Moderator's note: Jerry Bryan provides another 13f process, R2 U' B2 R2 U2 R2 U' B2 U2 R2 U' B2 U2, which hasn't been proven optimal. Steve LoBasso has a longer one. ] From cube-lovers-errors@mc.lcs.mit.edu Sat Sep 26 00:05:04 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id AAA07745; Sat, 26 Sep 1998 00:05:03 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 25 Sep 1998 08:36:22 -0400 (Eastern Daylight Time) From: Jerry Bryan Subject: Summary of Local Maxima, Face Turn Metric To: Cube Lovers Message-Id: I have posted maneuvers for a number of specific strong and weak local maximal positions (the strong local maxima at 9f and 10f, and the weak local maxima at 6f) , but I haven't really posted a summary of the numbers. Here are the numbers I have so far. In order to complete the table through 10f from Start for weak local maxima, I would have to repeat a rather long run. As might be expected, it appears that the number of weak local maxima will greatly exceed the number of strong local maxima. As is the usual case, patterns are M-conjugacy classes (symmetry classes), and represent the number of positions which are unique up to symmetry. Distance Strong Strong Weak Weak from Lclmax Lclmax Lclmax Lclmax Start Patterns Positions Patterns Positions 0f 0 0 0 0 1f 0 0 0 0 2f 0 0 0 0 3f 0 0 0 0 4f 0 0 0 0 5f 0 0 0 0 6f 0 0 2 7 7f 0 0 1 6 8f 0 0 37 739 9f 2 32 327 13014 10f 6 107 ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 6 15:05:42 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id PAA07299; Tue, 6 Oct 1998 15:05:41 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Sun, 27 Sep 1998 20:35:33 -0400 (EDT) From: Jerry Bryan Subject: Corners Only, Ignoring Twist To: Cube-Lovers Reply-To: Jerry Bryan Message-Id: I have been playing around with the idea of trying to calculate God's Algorithm all the way to the bitter end for the group which results from ignoring all twists of the corners and flips of the edges. It's a pretty big group. The order is |G|/(3^7)/(2^11), which is about 9.7*10^12, call it about 10^13 to make it a round number. (Another way to calculate it is 8!12!/2.) This is probably right at the bare edge, maybe even slightly past the bare edge, of the size of problem I can handle right now, which makes it a worthy endeavor. Also, it would provide a lower limit on the diameter of G (although the limit might not be any better than the ones we already have), which again makes it a worthy endeavor. Such a result might be suitable as the estimator function required by IDA* searches. The distance from Start in the no-twist, no-flip group would certainly be a lower bound for every position where twist and flip *are* considered. My only hesitation about suggesting this group as a suitable IDA* estimator function is that there are obvious pathological cases such as the superflip where this function would be a very poor estimator. In developing a no-twist, no-flip version of the program, I decided to try it out on the corners only case. Here are the results. Distance from Patterns Positions Start 0q 1 1 1q 1 12 2q 5 114 3q 24 876 4q 119 4931 5q 301 12972 6q 364 15066 7q 166 6300 8q 3 48 Distance from Patterns Positions Start 0f 1 1 1f 2 18 2f 9 243 3f 68 2646 4f 302 12516 5f 418 17624 6f 170 7080 7f 14 192 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990 From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 6 16:52:26 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id QAA08831; Tue, 6 Oct 1998 16:52:24 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Fri, 2 Oct 1998 23:18:37 +0200 (METDST) From: Martin Moller Pedersen Message-Id: <199810022118.XAA19053@stargazer.daimi.aau.dk> To: cube-lovers@ai.mit.edu Subject: cubes at spielmessen in Essen There will soon be a big gathering for games in Germany - Essen a so-called Spielmessen. I am attending this gathering for the first time in three years so I am looking for companies who will came to the spielmessen and who sells cubes. The places is big so it would be nice for me to have same names to look for. and hopefully I will have a real 4x4x4 and 5x5x5 cube to play with in a few weeks :-) /Martin From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 6 18:38:32 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA10776; Tue, 6 Oct 1998 18:38:31 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: Date: Sun, 4 Oct 1998 11:12:27 -0600 To: cube-lovers@ai.mit.edu From: Steve LoBasso Subject: Cube Solver for Macintosh I just wrote a Macintosh port to Dik T. Winter's cube solving code. I put it on my web page at the link below. I haven't had a chance to make an info page for it so the link below is just the application. It will run on both 68k and PPC Native. Be warned the 68k version runs fairly slow and the initialization phase takes quite a while. Cube Solver By Steve LoBasso slobasso@dtint.com Written using algorithm code by Dik T. Winter based on algorithm described by Herbert Kociemba. http://members.tripod.com/~slobasso/downloads/Cube_Solver.hqx -- Steve LoBasso mailto:slobasso@dtint.com Digital Technology International or mailto:slobasso@hotmail.com 500 West 1200 South, Orem, UT, 84058 http://members.tripod.com/~slobasso (801)226-6142 ext.265 FAX (801)221-9254 From cube-lovers-errors@mc.lcs.mit.edu Tue Oct 6 20:00:34 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id UAA12380; Tue, 6 Oct 1998 20:00:34 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu From: "Chris and Kori Pelley" To: Subject: That's Incredible! Date: Sun, 4 Oct 1998 22:37:28 -0400 Message-Id: <002701bdf009$180cb5e0$da460318@CC623255-A.srst1.fl.home.com> I recently obtained (courtesy of Peter Beck) the Rubik's Cube-a-Thon video from the TV show "THAT'S INCREDIBLE" and digitized it in RealVideo format. The file is rather large (18.1 megabytes) but it's worth a download if you're into cubic nostalgia. Eleven and a half minutes long, it features Minh Thai, Jeff Varasano, Kris Wunderlich, and others that may be on this list. Here's the URL: http://www.chrisandkori.com/incredible.htm It requires the RealPlayer 5.0 or later to view it. Note that you must download the file, then view it. I do not have a streaming video server. If anyone would like to host the file on a streaming server, please contact me. Chris Pelley ck1@home.com From cube-lovers-errors@mc.lcs.mit.edu Thu Oct 8 19:04:05 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA24808; Thu, 8 Oct 1998 19:04:04 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 8 Oct 1998 15:11:54 +0100 From: David Singmaster To: cube-lovers@ai.mit.edu Message-Id: <009CD656.72A81016.35@ice.sbu.ac.uk> Subject: Davenport's pattern The pattern given by Jacob Davenport is what I called a cube in a cube in a cube. I discovered this in 1979 or 1980 and was very pleased with it. Indeed, I used the cube in a cube as the logo of the late and much lamented David Singmaster Ltd. in 1980-1982 (approx. dates since I'm not where my records are). The pattern is in my Notes. There are various ways to generate the pattern, but the one that I can remember uses what Roger Penrose called the Y-commutator, which has the form FR'F'R. The reason this is the Y-commutator is that it affect the three edges adjacent to a corner and the corner and its three adjacent corners. I.e. the affected pieces form a Y, while the pieces affected by the ordinary commutator FRF'R' form a Z. Combining three Y-commutators as follows: FR'F'R RU'R'U UF'U'F gives a process that twists the corner and the three adjacent edges as a unit and twists an adjacent corner the opposite direction. NOTE - I'm doing this from memory and I have a suspicion that the middle group may need to be inverted?? By moving the odd corner to the right place adjacent to the opposite corner and applying the inverse of the above, one gets the same sort of pattern at the opposite corner and the odd corner has been restored. Now one 3-cycles the centers, as is easily done by a commutator of slice moves, and one has the cube in a cube. Now one can twist the two opposite corners to get the cube in a cube in a cube, though I find this not as visually dramatic as the cube in a cube. Someone - Mike Reid ? - sent me a minimal method for one of these patterns, but it's not very memorable. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Thu Oct 8 19:47:11 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id TAA24896; Thu, 8 Oct 1998 19:47:10 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 8 Oct 1998 16:45:31 +0100 From: David Singmaster To: cube-lovers@ai.mit.edu Message-Id: <009CD663.86DEF2D6.16@ice.sbu.ac.uk> Subject: Nicholas Bodley's message of 22 Sep 1998. Nicholas Bodley's message reminds me of when I wrote about the Cube in 1978 or early 1979, I think in the Observer, which seems to have been the first article outside Hungary. I mentioned that the mechanical problem seemed even harder than the mathematical problem and this led to about six submissions of mechanisms from readers. All but one of these were clearly impossible, but the last was Rubik's mechanism with slight differences - e.g. he had the undersides of the centers rounded. The submitter of this was a UK patent agent with obvious mechanical aptitude. However, one of my students, who had bought a cube from me, told me that a friend rang her up and asked if she had seen the hoax article about a cube that moved in all directions. The friend had just proven that such an object was impossible. My student had to disabuse her. When the cubes first came out of Hungary, we didn't know what the mechanism was and they were too precious to fiddle with. Roger Penrose said he had one face center piece come undone and he carefully wrapped thread around the exposed part of the screw and worked the screw into place and pulled on the thread to screw the screw back into the central piece. Sometime in late 1978, a friend had trouble with his cube and took a screwdriver to it and discovered the cover plates and the screw heads inside! Enough for now. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Fri Oct 9 18:40:38 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA02313; Fri, 9 Oct 1998 18:40:37 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <361E8D3F.6597@ameritech.net> Date: Fri, 09 Oct 1998 17:25:03 -0500 From: Hana Bizek Reply-To: hbizek@ameritech.net To: cube-lovers@ai.mit.edu Subject: comments on "davenport's pattern" David Singmaster claims to have discovered this pattern in 1979 or 1980, so it should be credited to him. In my own book I present a number of patterns, but I would never dare to claim authorship to any of them. Singmaster's comments prompted me to look at my own books. In CUBE GAMES (Taylor and Rylands} this pattern appears on the top of page 37.I have a strong suspicion this pattern could be a combination of the two cyclicity-three patterns on page 36 therein. One may use this pattern as a corner in a 3-color design. Design-construction is a step beyond pattern-construction. My question has not yet been satisfactorily answered. Has anyone seen construction of 3-dimensional "sculpture-like" designs? People referred me to Davenport's creations, but my own designs are quite different. Hana From cube-lovers-errors@mc.lcs.mit.edu Fri Oct 30 13:56:08 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id NAA17979; Fri, 30 Oct 1998 13:56:07 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Thu Oct 15 11:02:13 1998 Message-Id: <19981015145704.8314.rocketmail@attach1.rocketmail.com> Date: Thu, 15 Oct 1998 07:57:04 -0700 (PDT) From: "Jorge E. Jaramillo" Subject: Moves to this other pattern To: cube Please if this is not one of the purposes of this list someone let me know I don't meant to be rude. Could someone please tell me the moves to get from a solved cube to the following pattern: The top and bottom faces keep their colors. The 4 columns in the middle of every side face stay with their color. The left column on the front face moves to the right and the right column moves to the left. The left column on the back face moves to the right and the right column moves to the left. Thanks === Jorge E Jaramillo [ Moderator's note: We have a lot of requests for processes for various and have got a lot of optimal processes. Maybe the hard part is figuring out how to look them up. This is one of the "4-" patterns, and probably appears among the quasi-continuous partial isoglyphs. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Fri Oct 30 14:17:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA18032; Fri, 30 Oct 1998 14:16:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 26 Oct 1998 23:58:27 -0400 (EDT) From: Jerry Bryan Subject: 12q From Start To: Cube-Lovers Message-Id: |x| Patterns Lcl Positions Lcl Branching Max Max Factor 0q 1 0 1 0 1q 1 0 12 0 12 2q 5 0 114 0 9.5 3q 25 0 1068 0 9.368 4q 219 0 10011 0 9.374 5q 1978 0 93840 0 9.374 6q 18395 0 878880 0 9.366 7q 171529 0 8221632 0 9.355 8q 1601725 0 76843595 0 9.347 9q 14956266 0 717789576 0 9.341 10q 139629194 4 6701836858 42 9.337 11q 1303138445 0 62549615248 0 9.333 12q 12157779067 103 583570100997 2913 9.330 The last time a new level was calculated for the quarter turn metric was 4 February 1995. The cumulative number of positions now identified is 653625391832, or about 6.5*10^11. This is well past the "geometric halfway point" of sqrt(|G|), which is about 6.5*10^9. However, it is known that the diameter of G is at least 26q, strongly indicating that there is a bit of a tail to the distribution of positions by length. Of the 103 local maxima of length 12q, 70 of them also have their inverse as local maxima. For the other 33, the inverse is not a local maximum. For one of them, the inverse has 11 moves which go closer to Start. For seven of them, the inverse has 10 moves which go closer to Start. For eleven of them, the inverse has 8 moves which go closer to Start. For six of them, the inverse has 6 moves which go closer to Start. For two of them, the inverse has 4 moves which go closer to Start. And for six of them, the inverse has only 2 moves which go closer to Start. = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 2 09:40:50 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id JAA29402; Mon, 2 Nov 1998 09:40:48 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <363B1799.3534@hrz1.hrz.tu-darmstadt.de> Date: Sat, 31 Oct 1998 14:58:49 +0100 From: Herbert Kociemba Reply-To: kociemba@hrz1.hrz.tu-darmstadt.de To: cube-lovers@ai.mit.edu Subject: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks? About 2 weeks ago I received the following message and it seems to me that it might be interesting for you too: > Subject: > Use of RUBIK'S mark > Date: > Sun, 18 Oct 1998 21:05:31 EDT > From: > CK4IPLAW@aol.com > To: > kociemba@hrz1.hrz.tu-darmstadt.de > > > CLEARY, KOMEN & LEWIS, LLP > 600 Pennsylvania, Avenue, S.E. > Suite 200 > Washington, D.C. 20003-4316 > Telephone: 202 675-4700 > Telecopier: 202 675-4716 > E-Mail: ck4iplaw@aol.com > > > October 18, 1998 > > Via Electronic Mail > > Herbert Kociemba > kociemba@hrz1.hrz.th-darmstadt.de > > Re: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks > > Dear Mr. Kociemba: > > This firm is intellectual property counsel to Seven Towns Limited ("Seven > Towns"), the manufacturer and worldwide distributor of the RUBIK'S CUBE three- > dimensional puzzle and provider of an electronic version of the puzzle via its > official web site, which is located at http://rubiks.com. > > The RUBIK'S CUBE mark is famous throughout the world. The distinctive > overall appearance of the RUBIK'S CUBE puzzle also is a famous trademark owned > by Seven Towns. These marks are registered or are the subject of pending > trademark applications in most of the major countries of the world. > > It has come to our attention that your web site features a program under the > name of Rubik's Cube Explorer. I must advise that your unauthorized use of > the RUBIK'S CUBE mark owned by Seven Towns constitutes trademark infringement. > Specifically, the use of this mark in designating the origin of your program > confuses the public into believing mistakenly that it derives from, is > associated with, or is endorsed or sponsored by the owner of this commercial > symbol (i.e., Seven Towns). Moreover, apart from causing consumer confusion, > your use of the well-known mark dilutes its distinctive value in violation of > the federal and state anti-dilution laws. > > Seven Towns appreciates your interest in the RUBIK'S CUBE puzzle, and it > certainly does not wish to inhibit legitimate discussion of the puzzle on the > Internet or in any other medium. However, it also must be vigilant in > maintaining the value and integrity of its intellectual property. It cannot > afford to lose control over its commercial reputation, or damage to its > substantial goodwill, by permitting another party to use its trademarks or > trade dress in a manner that causes source confusion or otherwise dilutes > their selling power. Thus, Seven Towns requests that you remove from your web > site the electronic version of the RUBIK'S CUBE manipulative puzzle, and that > you discontinue any further use of the term RUBIK'S CUBE or any similar > designation in the prominent, source-indicating manner of a trademark. > > I hope that you are understanding of our client's position, and I thank you > in advance on behalf of Seven Towns for your prompt attention to this matter. > > Sincerely yours, > > //sjm// > > Scott J. Major Indeed the headline of my homepage at http://home.t-online.de/home/kociemba/cube.htm was "Rubik's Cube Explorer 1.5". So I removed the word "Rubik's" and added some note at the bottom of the page (...blah blah is not derived from, is not associated with blah blah...). I definitely will not remove the program from my homepage. This seems ridiculous. I know, that other cube fans received similar mail because they have some similar statements on their homepages now. What do you think about that? Herbert Kociemba From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 2 14:41:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA00366; Mon, 2 Nov 1998 14:41:00 -0500 (EST) Precedence: bulk Date: Sat, 31 Oct 1998 23:06:34 -0400 (EDT) From: Jerry Bryan Subject: All the Local Maxima at 12q To: Cube-Lovers Message-Id: I had originally decided not to post all the 12q local maxima because there are so many and because not all of them look all that interesting. But I have been looking at them a bit more, and I think it's worth the effort. Some of them will be very familiar and some of them not. I would highlight the following ones. #9 is a partial isoglyph -- four short T's (or four short U's). #57 is the well-known four spot. #68 is one of the more striking of several pseudo two spots. #80 is worthy of some study. It's the only one where the maximality of the inverse is 11 -- almost but not quite a local maximum. #97 along with #98 and #99 are very striking pseudo six spots. #97 and #99 are almost the same pattern, and it took me a while to see how they differ. In the table below, the right most column gives the maximality of the inverse of the pattern, where the maximality is the number of moves which go closer to Start. The maximality of the inverse gives an indication of how close the inverse comes to being a local maximum, with 12 indicating a local maximum. (The maximality of the pattern itself is not given, since it is 12 by definition.) The table gives the 103 local maxima of length 12q which are unique up to symmetry. 1. F F L L F F B B R R B B 12 2. F B' U U D D F' B R R L L 12 3. F B R R F' B' U D L L U' D' 12 4. U' R' L B L B' R L' D L' U D' 12 5. F B R R L L F B U U D D 12 6. R L' F F B B R L' F F B B 12 7. F F B B U U D D R R L L 12 8. R L' U' D F' B R R L L U' D 12 9. F B U U D D F' B R R L L 12 10. U B' D F D' B' D F' D' B B U' 12 11. L B B R D D R' L B B L L 12 12. U R' U L' U' R' U L U' R R U' 12 13. F F U' D R R U D D B B D' 12 14. F B D D F B' L L U U F F 12 15. U D' F U D R' L' U D F U D' 12 16. U U R L F' B' U D' R R L L 10 17. R R U D F' B U' D F B' U' D 8 18. U U D D F B' R R L L B B 12 19. R' L F' B U U F F B B U' D' 12 20. U D' F F U' D R L F B' U' D 12 21. F B R' L D D F B' R' L U' D 12 22. L L U D' B B R L U' D B B 12 23. F L L F' D D F B' L L B B 12 24. F' R R F' U U F' B L L B B 12 25. F B U U L L B B L L U U 8 26. U' D' R L' F F B B L L U' D 4 27. U D R L' F F B B L L U D' 4 28. F B' U U B B L L B B U U 12 29. F' B U D L L B B R R U D 12 30. F' B U D R R F F L L U D 12 31. F B' U U F F R R F F U U 12 32. F B' U U L L B B L L U U 12 33. F B' U U R R F F R R U U 12 34. L L U D L L F' B R L U U 10 35. F' R R F U U F B' R R B B 12 36. L L F' B D D R R F F B B 12 37. L L F' B D D F F B B L L 12 38. D D F' B U D' F F B B U D' 10 39. F F R' L F B' U' D F F L L 12 40. U R' L F U D' R' L F F B B 8 41. U D R L F B' U D' R' L F F 12 42. U D F F U' D R L F B' U' D 12 43. U D B B U' D R' L' F B' U' D 12 44. F F R L' F B' U D' F F L L 12 45. U D F' B R L U' D B B U' D 12 46. U D F' B R' L' U' D F F U' D 12 47. F B' D R' L' U U R L D B B 8 48. B' U' D R' L B' U' D R R L L 6 49. B' U D' R L' F U D' R R L L 6 50. U D F' B' U' D L L F B' U' D' 8 51. U' F' U' D F B' U' D R R L L 2 52. U' F F B R' L U' D F F B B 8 53. D R R L F' B U' D R R L L 2 54. R U' F' B R L' U D' F F U D' 2 55. L F F B R L' F B' R R L L 2 56. L F F B U D' R' L F F B B 8 57. F B' U U D D F B' R R L L 12 58. F B' R L' U' D F' B' R L' U' D' 12 59. F B R L U D' F B R' L' U D' 12 60. F B' U U D D F' B U U D D 12 61. R L' U' D F' B L L U' D F F 12 62. R L B B U D' R R F B U D' 12 63. F B' U D' R L' F F B B U D' 12 64. F B R R L L U D' R' L' U D' 12 65. F B' U D' R L' B B U D' L L 12 66. F F U' D R R U D F F U U 12 67. F L L B U U F' B L L F F 12 68. B R L F F R' L' B U U L L 12 69. U' F B' L' U D' R L' F F B B 2 70. F B R' L' U D' F' B' R' L' U' D' 12 71. F B R L U D' F B R' L' U' D' 12 72. U' R L' U' D F B' R R L L U' 12 73. F' B R' L U' D B R' L U' D D 12 74. U' R' L F B' U' D F B B U' D 6 75. U R' L F' B U D' B F F U D' 6 76. F B U D R' L F F R' L U' D 12 77. R' L' F' B R R L L U D B B 12 78. R L F B' R R L L U' D' F F 12 79. F F R R F' B' U' D' L L U D 8 80. U U R' L F' B' U' D R R L L 11 81. U U D R L' B U D' R R L L 6 82. U D F' B U' D F B' U' D R R 12 83. F B' U D R L' B B R L' U' D 12 84. U D' F F U D' R' L' F B' U' D 12 85. B R L' D' F B' U D' R R L L 2 86. F' R' L U' F B' R' L U D' B B 12 87. F' R' L U' F' B R' L U' D B B 12 88. R' L F B' U D R R L L D D 12 89. F B R L' F' B R L' U D' F F 12 90. U' D' R L' F F U D' R R L L 12 91. F F R' L F' B' U' D' L L B B 10 92. F U D B B U' D' F R L U D' 10 93. R L U D' F B' R' L' F B' U' D 8 94. F B' U' D L L F B' U' D' F F 10 95. F B' U U D D F B' R' L' U D' 10 96. R' L L F' B U R L' F F B B 6 97. F B' U' D R L F' B U U B B 12 98. F B U' D R' L F' B D D B B 12 99. F B' U' D R L F B' D D F F 12 100. U' D F B' U D' F F B B U D' 12 101. U R L' F' U D' R L' F F B B 8 102. U D' R L' F' B U D' F F B B 12 103. F' B' L L U' D F B U' D R R 8 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) jbryan@pstcc.cc.tn.us Pellissippi State (423) 539-7198 10915 Hardin Valley Road (423) 694-6435 (fax) P.O. Box 22990 Knoxville, TN 37933-0990 From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 2 18:00:09 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA01157; Mon, 2 Nov 1998 18:00:08 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19981102164235.0094e100@mail.spc.nl> Date: Mon, 02 Nov 1998 16:42:36 +0100 To: cube-lovers@ai.mit.edu From: Christ van Willegen Subject: Re: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks? At 14:58 31-10-1998 +0100, you wrote: >About 2 weeks ago I received the following message and it seems to me >that it might be interesting for you too: [Message deleted for brevity] > >Indeed the headline of my homepage at > >http://home.t-online.de/home/kociemba/cube.htm > >was "Rubik's Cube Explorer 1.5". So I removed the word "Rubik's" and >added some note at the bottom of the page (...blah blah is not derived >from, is not associated with blah blah...). > >I definitely will not remove the program from my homepage. This seems >ridiculous. I know, that other cube fans received similar mail because >they have some similar statements on their homepages now. > >What do you think about that? > I had the same 'problem' a couple of months ago. A handheld computer users group I was active in, once published a program that could be described as 'well, it looks a bit like Tetris ((R), if those lawyers are reading this, as well :-), but it's a long way off the mark'. The program was published in our magazine, and was also placed on a web-page. A couple of months ago, I received a letter from a Belgian lawyer firm, addressed to the user's group. This user's group, by the way, died about 5 years (!) ago. They told us to 'cease and decist' (a couple of things), including publishing this article on 'our web-page'. Well, since this was someone else's web- page, there was nothing we could do about it. We told them (in friendly terms) that the user's group no longer existed, that we were not affiliated to the user having the article on his web-page, and that we nover sold the program. We haven't heard from them (not even a letter stating that they received our reply!) since. It's kinda sad: The program was for an HP28S. I would have _loved_ to see those lawyers type the program in (a couple of kilobytes, via the keyboard!), only to find out that it was 'almost, but not quite, entirely unlike Tetris' (Douglas, if you're reading this, quotes are ok, no?). Just tell them you will take down the name, and they will probably be off your back. Christ van Willegen From cube-lovers-errors@mc.lcs.mit.edu Tue Nov 3 06:37:22 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id GAA02996; Tue, 3 Nov 1998 06:37:21 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 2 Nov 1998 15:32:29 -0500 From: michael reid Message-Id: <199811022032.PAA24281@euclid.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: Re: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks? Cc: kociemba@hrz1.hrz.tu-darmstadt.de > > Re: Unauthorized Use of RUBIK'S CUBE and CUBE Design Marks > > > > Dear Mr. Kociemba: [ ... ] > What do you think about that? i think it's not good business strategy to attack the people who are the biggest fans of their product! to claim ownership of "the distinctive overall appearance of the RUBIK'S CUBE puzzle" is ludicrous! the changes you've described to your web page seem quite reasonable and appropriate (given the circumstances), without compromising too much. i hope you have no further trouble with seven towns. but if you do, please let me know about it. to make this situation even more ridiculous, i just checked out their "official" website, which features a java cube (http://rubiks.com/VRCUBE.html). their applet is stolen from karl ho"rnell! (http://www.tdb.uu.se/~karl/java/rubik.html) mike From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 9 17:39:21 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id RAA01496; Mon, 9 Nov 1998 17:39:20 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981104032938.14284.rocketmail@send102.yahoomail.com> Date: Tue, 3 Nov 1998 19:29:38 -0800 (PST) From: Han Wen Subject: Query for Corners-First Method Rubik Solution To: cube-lovers@ai.mit.edu Hi, Does anyone know of any websites that describe the Corners-first method of the solving the rubik's cube? I know of many layer-first methods such as Jiri Fridrich's (for which I have spent many hours learning), but I really haven't seen a comprehensive explanation of the corners-first method. I'm really curious to understand how anyone can solve the cube under 30secs by solving the corners first. -Han- From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 9 18:35:15 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id SAA01664; Mon, 9 Nov 1998 18:35:13 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Wed, 04 Nov 1998 16:41:26 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Local Maxima Whose Inverses are not Local Maxima To: Cube Lovers Message-Id: On 30 June 1997 I reported that if you could find a local maximum whose inverse was not a local maximum, then you could also find a longer local maximum. For example, suppose x is a local maximum in the quarter turn metric and x' is not. Then, there exists q in Q such that |x'q| = |x'| + 1 = |x| + 1. But we know that q'x is a local maximum and we also know that |q'x| = |x| + 1 because |q'x| is the same as |x'q|. Because we now have at 12q a good number of local maxima whose inverses are not local maxima as specimens, I have begun to wonder if the same process might be able to be repeated several times to yield progressively longer local maxima. For example, if x is a local maximum and (q1)x is a local maximum, might also (q2)(q1)x be a local maximum and also (q3)(q2)(q1)x etc. It seems to me that good candidates to investigate in this regard might be those local maxima at 12q whose inverses have a very small maximality. For example, if x is a local maximum where the maximality of x' is 2 (and there are several such cases), then we know that there are 10 local maxima of the form qx. I am not sure if I have time to investigate this question further, but I certainly would love to hear from anyone who has the time and the computing resources to do so. ---------------------- Jerry Bryan jbryan@pstcc.cc.tn.us From cube-lovers-errors@mc.lcs.mit.edu Tue Nov 10 06:10:31 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id GAA04442; Tue, 10 Nov 1998 06:10:31 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Sender: bosch@sgi.com Message-Id: <36477CAE.446B@sgi.com> Date: Mon, 09 Nov 1998 15:37:18 -0800 From: Derek Bosch To: Han Wen Cc: cube-lovers@ai.mit.edu Subject: Re: Query for Corners-First Method Rubik Solution References: <19981104032938.14284.rocketmail@send102.yahoomail.com> Here's the method I use to solve Rubik's Cube in 30 seconds or less. My notation is as follows: F = turn front face clockwise 90 degrees. F' = turn front face counter-clockwise 90 degrees. F" = turn front face 180 degrees. U = turn top face clockwise 90 degrees. R = turn right face " " " L = turn left face " " " B = turn back face " " " D = turn bottom face " " " ^ = move middle slice 90 degrees up. v = move middle slice 90 degrees down. OK. Now the order I do things is corners, edges on two OPPOSITE sides (Right and Left), followed by the middle slice edges. (1) Corners: I solve my corners a bit wierdly, but I find it is really fast. I position any four corners of the same color on a side. I don't care what colors are on the adjoining faces right now, as I fix them later. (1a) Once I have the 4 corners of the same color, I turn the cube so that those colors are on the down face. Now there are a few combinations that can occur on the top face: All corners on top face same color: Goto (1b) Three corners need to rotate clockwise (position like below o=no rotate) (+ = needs clockwise rotation) (- = needs counter-clkwise rot.) + + Move: R'U"RUR'UR and goto (1b) + o Three corners need counter-clockwise rotate: - o Move: RU"R'U'RU'R' and goto (1b) - - One corner needs clockwise rotate, One needs counter-clockwise rotate: 3 cases: + - Move: RU"RU"RUR" and goto (1b) o o - + Move: RUR'U'F'U'F and goto (1b) o o o - Move: R'URUBU'B' and goto (1b) + o Two corners need clockwise rotate, Two need counter clockwise: 2 cases: + - Move R"U"RU"R" and goto (1b) - + - + Move RUR"F'R"UR' and goto (1b) - + (1b) Now, you should have two opposite sides, with the corners of those two sides the proper color. We have to correct the 4 remaining sides to get corners in the right place, before we can move onto edges. To do this, count the number of sides that have the upper pair of corners the same color. Also counter the number of sides that have the lower pair of corners the same color. All four sides (upper and lower) corner pairs match. Goto (2) No sides' corner pairs match. Do Move R"F"R". Goto (2) One Bottom corner pair matches. Move that corner pair to the Down-Left position. Move R"UR"U'R"UR"U'R. Goto (2) One Top corner pair matches. Turn Cube over, and do previous moves. One Top and one Bottom pair matches. Move both corner pairs to the front face. Move R"UR"U"F"UF". Goto (2) All Bottom pairs match. Move R"UR"U"F"UF"U"L"UL". Goto (2) All Top pairs match. Turn Cube over, and do previous move. All Bottom pairs match. One Top pair match. Move Top Pair to Left-Upper position. Move R"UR"U'R"F"U'F"UF". Goto(2) All Top pairs match. One Bottom pair match. Turn Cube over, and do prev. (2) Solving two Opposite Sides. Now, all the corners should be solved. You should move the center of each cube to its respective corners, to get an X on each side (at least on two opposite sides). From now on orient the cube so that the two opposite sides are right and left. (2a) Solve three edges on the left face with the following moves. U'^U - moves the edge piece in the Front-Down position to the Up-Left position. UvU' - moves the edge piece in the Back-Down position to the Up-Left position. This is easier done with a cube in your hand, and try and see how this works. This will mess up the centers and edges in the middle slice, as well as the Up-Right edge. Don't worry about this. As long as you keep this orientation, and rotate the left face to get ready for a new edge to be moved you can solve three out of four of the edges on the left face. (2b) Solve four edges on the right face: First, rotate the left face, so that the unsolved edge is in the Up-Left position. Then, using the following moves, solve all four edges (similarly to step 2a). U^U' - moves the edge piece in the Front-Down position to the Up-Right position. U'vU - moves the edge piece in the Back-Down position to the Up-Right position. (2c) Solve remaining edge on left face: 2 cases (other than already solved): edge in place, needs to be flipped: Use U'vUvUvU' otherwise, move edge to Down-Front position, using v or ^. if the front color (of the DF edge) is the same as the left face color, Use U'vU"vU' else Use vU^U"^U (3) Solve middle slice edges. First use ^ or v to position middle slice centers in proper faces. (3a) Position edges: 3 cases (other than all in place): only three edges out of place: position cube such that DF needs to go to UB and UB needs to go to UF. Use ^U"vU". all four edges need to move: if UF needs to go to DB, Use ^F"B"vF"B". otherwise, position so that UF needs to go to UB, Use U'^^U'^^. (3b) Flip required edges: 3 cases (other than no flips needed). all four need flipping, use FR'F'^U^U^U^UFRF' two edges need flipping, both on same face. Turn cube so that these edges are the UF and UB edges. use ^U^U^U"vUvUvU" otherwise, turn cube so UB and DF need flipping, use F"^U^U^U"vUvUvU"F" That should do it. I apologize for the roughness of this solution. I think diagrams would help it a lot. If you have any criticism or ideas that could help this solution become more readable, let me know. Note, this solution is very close to Jeff Verasano (sp) and Minh Thai's methods... D -- Derek Bosch "A little nonsense now and then (650) 933-2115 is relished by the wisest men"... W.Wonka bosch@sgi.com From cube-lovers-errors@mc.lcs.mit.edu Tue Nov 10 07:33:39 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id HAA04496; Tue, 10 Nov 1998 07:33:37 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 9 Nov 1998 19:15:58 -0500 (EST) From: Alchemist Matt Reply-To: Alchemist Matt To: Han Wen Cc: cube-lovers@ai.mit.edu Subject: Re: Query for Corners-First Method Rubik Solution In-Reply-To: <19981104032938.14284.rocketmail@send102.yahoomail.com> Message-Id: My page at http://www.unc.edu/~monroem/rubik.html describes a method that is sort of "corners first". Although, in my first step I say to solve the first layer before going on, one could effectively simply place only the four corners in the top layer, then move on to the four corners in the bottom layer (specified in steps 2 and 3), then begin filling in the gaps on the top and bottom layers (steps 4 and 5), and lastly finish the middle layer. In fact, a chemistry professor at my current school, Holden Thorp, competed in one of the Rubik's cube playoff contests that was aired on the TV show That's Incredible. Someone posted the video of it about a month ago (and mentioned it in this discussion list), and he saw it here at my school after I downloaded it. He then looked at my page and mentioned that the winner of the contest actually used the solution shown on my page (probably modified slightly). I can only solve a well-scrambled cube in 2 to 3 minutes using the solution, but I'm sure someone quite adept, nimble, and fast could push it to under one minute. (Please note this isn't "my" solution; I simply learned it from a book many years ago. Further, I have never been in a cube solving competition). Matt ----------------------------------------------------------------------- Matthew Monroe Monroem@UNC.Edu Analytical Chemistry http://www.unc.edu/~monroem/ UNC - Chapel Hill, NC This tagline is umop apisdn From cube-lovers-errors@mc.lcs.mit.edu Thu Nov 12 14:18:47 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id OAA24676; Thu, 12 Nov 1998 14:18:45 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981111170341.14375.rocketmail@send105.yahoomail.com> Date: Wed, 11 Nov 1998 09:03:41 -0800 (PST) From: Han Wen Subject: RE: Query for Corners-First Method Rubik Solution To: Noel Dillabough Cc: cube-lovers@ai.mit.edu Hi, Thanks for the link to your Puzzler program. You're not going to believe this, but you can still purchase the Professor's Cube (5x5x5) and the Megaminx! Since it's difficult... no, impossible to find anyone that sell these puzzles, I think it's worth mentioning. You can get them from Meffert's site: http://ue.net/mefferts-puzzles/ Your Puzzler program is a tremendously useful tool to develop moves. I've got 11/12 sides of the Megaminx solved. But for the last side, I need to figure out corner/edge twisting/permuting moves. You're Puzzler program's great for that. I'm surprised how many of my Rubik's cube moves can be applied with minor modifications to the Megaminx. -Han- ---Noel Dillabough wrote: > I actually solve all the cubes this way (or at least centers -> > corners -> edges for larger cubes) I just find it more logical and > easier to memorize than other methods. > You can check out my solution at > http://www.mud.ca/puzzler/puzzler.html. Its in the puzzler help > file under "solving the cube". I will be adding other solutions > soon that are clearer, let me know if you would like them I could > mail them to you. > -Noel. From cube-lovers-errors@mc.lcs.mit.edu Thu Nov 12 15:00:46 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.8/mc) with SMTP id PAA26362; Thu, 12 Nov 1998 15:00:45 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 12 Nov 1998 15:01:40 +0000 From: David Singmaster To: cube-lovers@ai.mit.edu Message-Id: <009CF1D5.D1348312.50@ice.sbu.ac.uk> Subject: Use of the name Rubik's Cube The lawyers are being obsessively zealous as the name is certainly well on its way to becoming a common noun. It was included in the Oxford English Dictionary in the mid-1980s. Other examples are Kleenex and Aspirin, which were both originally tradenames and their owners fought to retain them but eventually lost. Xerox is fighting a rear-guard action on its name. If you don't want to get involved in legal hassle, I suggest that you use the name Magic Cube which was the original name and is such a common term that they can't claim it is a trademark. DAVID SINGMASTER, Professor of Mathematics and Metagrobologist School of Computing, Information Systems and Mathematics Southbank University, London, SE1 0AA, UK. Tel: 0171-815 7411; fax: 0171-815 7499; email: zingmast or David.Singmaster @sbu.ac.uk [ Moderator's note: I am still dropping messages that consist mainly of generic comments on intellectual property issues. There a great variety of individualistic and contentious debate on these topics that you may follow in dedicated fora such as the Usenet group misc.int-property. I am not yet persnickety enough to elide the third and fourth sentences from the above, but they are on the edge. I will also note that the term "Magic Cube" is also used to refer to a cubical array of natural numbers whose orthogonal and diagonal rows sum to the same number, as a generalization of "Magic Square", so it is advisable to include context such as "The geometrical puzzle originally known as the Hungarian Magic Cube." ] From cube-lovers-errors@mc.lcs.mit.edu Wed Nov 18 12:52:47 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id MAA28044 for ; Wed, 18 Nov 1998 12:52:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 12 Nov 1998 17:05:37 -0500 (EST) From: Nicholas Bodley To: Han Wen Cc: Noel Dillabough , cube-lovers@ai.mit.edu Subject: Solutions (Was: RE: Query for Corners-First Method Rubik Solution) In-Reply-To: <19981111170341.14375.rocketmail@send105.yahoomail.com> Message-Id: On Wed, 11 Nov 1998, Han Wen wrote: {snips} }mentioning. You can get them from Meffert's site: }http://ue.net/mefferts-puzzles/ It might be of interest to mention that Meffert has solutions to many puzzles at his Web site. The Contributors section gives generous credit to a number of experts; they wrote the solutions. Best, |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Wed Nov 18 13:27:34 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA28426 for ; Wed, 18 Nov 1998 13:27:29 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.32.19981113091853.00948790@mail.spc.nl> Date: Fri, 13 Nov 1998 09:18:55 +0100 To: cube-lovers@ai.mit.edu From: Christ van Willegen Subject: MegaMinx/5^3 (Was: RE: Query for Corners-First Method Rubik Solution) At 09:03 11-11-1998 -0800, you wrote: >Hi, > >Thanks for the link to your Puzzler program. > >You're not going to believe this, but you can still purchase the >Professor's Cube (5x5x5) and the Megaminx! Since it's difficult... no, >impossible to find anyone that sell these puzzles, I think it's worth >mentioning. You can get them from Meffert's site: >http://ue.net/mefferts-puzzles/ Also, a store in The Netherlands sells these! Last time I was there (last saturday), they had; - a couple of 3^3's - a couple of 5^3's - skewb I can't recall if they had a Megaminx at that time. The store is based in Eindhoven. If anybody wants some, I can buy them and send them out. 5^3 costs F. 50 (about $25). 3^3 costs F. 10 (about $5). Before anybody gets this wrong: - I do not work for them, I'm a happy customer - I don't get paid to do this - I make no money out of this You can call them at: +31-40-2461376 Business hours are 0900 to 1800. The Netherlands is at CET (differs +6 hours with NY, +9 with CA) Christ van Willegen From cube-lovers-errors@mc.lcs.mit.edu Wed Nov 18 17:23:08 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA29198 for ; Wed, 18 Nov 1998 17:23:06 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981114070437.9789.rocketmail@attach1.rocketmail.com> Date: Fri, 13 Nov 1998 23:04:37 -0800 (PST) From: "Jorge E. Jaramillo" Subject: RE: Moves to this other pattern To: David Singmaster , Maybe (although I don't think so since some people already answered what I was asking) I made a mistake when describing the position I wanted to accomplish. What I wanted was: L B R L B R L B R F F F T T T F F F D D D L L L T T T R R R D D D B B B T T T B B B D D D L F R L F R L F R And until now the best solution is: F B L F2 T D- L2 B- T- D- F2 R- T- D L- R D === Jorge E Jaramillo From cube-lovers-errors@mc.lcs.mit.edu Wed Nov 18 18:05:42 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA29431 for ; Wed, 18 Nov 1998 18:05:41 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <365115AC.22369936@erco.com> Date: Tue, 17 Nov 1998 07:20:28 +0100 From: "michael ehrt" Reply-To: m.ehrt@erco.org To: Cube Lovers Mail Subject: Getting 2x2x2 cubes If anyone is interested in getting 2x2x2 cubes, during my holiday in the UK two weeks ago I found a shop in Sheffield which has them in stock. It's called "The Puzzle Shop" and in situated in Meadowhall shopping centre. The cubes are GBP 5 each, and they have a few other things like keyring 3x3x3s etc. Michael From cube-lovers-errors@mc.lcs.mit.edu Thu Nov 19 13:41:00 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA03513 for ; Thu, 19 Nov 1998 13:40:59 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981117105414.18936.rocketmail@attach1.rocketmail.com> Date: Tue, 17 Nov 1998 02:54:14 -0800 (PST) From: "Jorge E. Jaramillo" Subject: The Cylinder To: cube I was checking the Rubik official website and I was surprised not to find one product that I seem to find here (I live in Colombia South America) fairly easily. I am talking about the cylinder. When I first saw it I bought it and thought it was going to be some amazing and tricky to solve puzzle, it ended up being a 3x3 cube with the corners cut, so corner cubelets only have 2 colors and there are two types of borders, 8 borders with the usual two colors and 4 with only one. Does it mean that this cube was "invented" by some manufacturer other than Mr Rubik and that is not so common? === Jorge E Jaramillo [Moderator's note: I own such a puzzle, but I would call its shape an octagonal prism, rather than a cylinder. On mine, the solved position is not an octagonal prism because one beveled face is rotated 90 degrees, forming a decahedron whose faces are six rectangles and four irregular hexagons. I don't remember whether it was originally manufactured this way or whether I altered the color tabs. ] From cube-lovers-errors@mc.lcs.mit.edu Thu Nov 19 17:36:55 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA04360 for ; Thu, 19 Nov 1998 17:36:54 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Thu, 19 Nov 1998 15:00:06 -0500 (Eastern Standard Time) From: Jerry Bryan Subject: Re : The Cylinder In-Reply-To: <19981117105414.18936.rocketmail@attach1.rocketmail.com> To: "Jorge E. Jaramillo" Cc: cube Message-Id: Jorge E. Jaramillo's message of 17 Nov 1998 included: >[Moderator's note: I own such a puzzle, but I would call its shape > an octagonal prism, rather than a cylinder. On mine, the solved > position is not an octagonal prism because one beveled face is > rotated 90 degrees, forming a decahedron whose faces are six > rectangles and four irregular hexagons. I don't remember whether > it was originally manufactured this way or whether I altered the > color tabs. ] I also own such a puzzle, although I have never seen one in a store. I got mine at a garage sale for $0.25. I haven't played with it in a long time. But my best recollection is that it can be solved basically the same way as a 3x3x3 cube, except that *I think* (don't remember for sure) that the color scheme permits invisible swaps of identically colored pieces which can make the puzzle seem "impossible" to solve unless you realize that the identically colored pieces must be swapped. It is also my best recollection that such a puzzle is mentioned briefly and is pictured in one of Douglas Hofstadters's cube articles in Scientific American back in the early 80's. So I don't think it is any kind of new invention. ---------------------------------------- Jerry Bryan jbryan@pstcc.cc.tn.us Pellissippi State Technical Community College From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 20 11:11:16 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id LAA07158 for ; Fri, 20 Nov 1998 11:11:15 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981117070139.11901.rocketmail@send103.yahoomail.com> Date: Mon, 16 Nov 1998 23:01:39 -0800 (PST) From: Han Wen Subject: Fwd: Re: HOW TO SOLVE THE PROBLEM OF THE PROFESSOR CUBE To: cube-lovers@ai.mit.edu I thought this would be of value to Rubik fans out there with Professor Cubes (5x5x5)... note: forwarded msgs attached. _________________________________________________________ ---Uwe Meffert wrote: [reprinted here with his permission] > Dear Mr. Wen > Thank you for your interest in my puzzles, I am sorry to hear that > you are having problems with the Prof. Cube. > You received one of the last ones from the last production batch and > the next production is not for another month. > What unfortunately happened is that when gluing the center small > caps excess glue fixed the screw to the plastic centre piece that it > should turn in. So when you turn these sections it will tighten / > loosen that one screw. > If you are skilful enough you can try and carefully remove the > centre label and then pry open and remove the centre cap of the blue > and orange side. Then try to remove the excess glue from around the > screw with a sharp object and try turning the screw with a > screwdriver firmly holding the plastic piece so you can break the > glue bond. Once the screw can freely turn inside the plastic part, > re-tighten it to the same tension as it was originally, so as to > allow smooth turning without any pieces falling out during play. > Then carefully using only very little glue fix the centre cap back > into place and re-attach the color label. > Good Luck and Happy Puzzeling. > Please let me know the outcome of this recommended procedure. > With warm regards > Uwe Meffert ________________________________________________________________ Date: Mon, 16 Nov 1998 22:57:20 -0800 (PST) From: Han Wen Subject: Re: HOW TO SOLVE THE PROBLEM OF THE PROFESSOR CUBE To: Uwe Meffert Cc: Jing Meffert Hi, My cube is all fixed. Thank you for your prompt reply. You were right, the glue used to fix the caps also fixed the spindle screw! Actually, your instructions gave me the perfect excuse to take your cube apart. I was dying to find out how the heck all these pieces are held together. Anyways, I popped of the caps carefully using a razor blade, scraped off all the excess glue, greased the screw head and before screwing it back together, I took all the pieces for one face out just to see and understand the engineering holding all the pieces together. Wow, what an amazing bit of engineering. It's like a cube spindle inside another cube spindle! Amazing. Actually, the center caps don't really need glue. They fit nice and snug, and it also leaves me the option to adjust the screw again in case it becomes loose. Now that I understand the mechanism, I've decided to only rotate faces clockwise to minimize the possibility that a counter-clockwise rotation will actually loosen one of the spindle screws. I still haven't messed the faces up though. I'm so close to finishing the Megaminx. I just have two edge pieces to swap on the last face! The other 11 sides were fairly straightforward to solve. I also got the corners of the last face fairly quickly by using Sune's move to twist corner pieces (a standard Rubik's cube move). However, getting those edge pieces was a different story. I had to develop quite a few moves to rotate and twist the edge pieces around. I'm close... so close..! :) I hope you keep inventing and making new puzzles. I eagerly click on your new releases on your web page quite regularly, hoping to find a worthy successor to the Megaminx or the Professor's Cube. Maybe a 7x7x7?!! Or a Buckyball? One can only imagine... -Han- From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 20 14:44:20 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA08578 for ; Fri, 20 Nov 1998 14:44:17 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3654ED01.E6D38EE8@hurstlinks.com> Date: Thu, 19 Nov 1998 23:16:01 -0500 From: "Guy N. Hurst" Organization: HurstLinks Sites On the Internet To: "Jorge E. Jaramillo" Cc: cube Subject: Re: The Cylinder References: <19981117105414.18936.rocketmail@attach1.rocketmail.com> I have seen one or both of these puzzles, and they were very different from each other. The cylinder, or prism, was actually the first cube I learned to solve, when my cousin from Luxembourg visited back in 1981. I have pleasant memories of it, because it was very well made and pleasing to view. It is harder to solve than the cube since the four of the edges are "cut", so it is impossible to match edges to centers - leaving the possibility of having to backtrack later and figure out which "corner" (and matching edge) is in the wrong place! But I had it down and could quickly readjust (usually had to swap corners diagonally in the top two layers if I found a single flipped edge left in the bottom layer when almost done solving it, if I remember). I liked it so much, I requested and obtained 4 more after my cousin returned to Europe! I would take them to school, one at a time, until (unfortunately) they all eventually disappeared. At least two were stolen out of my (locked) locker on different occasions. Someone else liked them, too. Anyway, I never found that puzzle in the US, and could only get it from my cousin in Europe. (Who I think may have gotten them from England). But the other puzzle, as described by the moderator, was available in the US back then, I think in the following year or so after my cousin visited, since one of my friends had one. But it wasn't as nice looking or well made. So I didn't care for it. It was more like the cube with its corners cut, forming rectangles and triangles in a spherical symmetry, as opposed to the prism from Europe which has four of its 3-piece-edges cut, forming only rectangles and having a cylindrical symmetry. Guy N. Hurst From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 20 15:16:19 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA08664 for ; Fri, 20 Nov 1998 15:16:18 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: Date: Fri, 20 Nov 1998 08:46:30 +0100 (CET) From: Bas de Bakker To: Cube-Lovers@ai.mit.edu In-Reply-To: (message from Jerry Bryan on Thu, 19 Nov 1998 15:00:06 -0500 (Eastern Standard Time)) Subject: Re: The Cylinder References: >>>>> "Jerry" == Jerry Bryan writes: [About the octagonal "cube"] Jerry> I haven't played with it in a long time. But my best Jerry> recollection is that it can be solved basically the same Jerry> way as a 3x3x3 cube, except that *I think* (don't remember Jerry> for sure) that the color scheme permits invisible swaps of Jerry> identically colored pieces which can make the puzzle seem Jerry> "impossible" to solve unless you realize that the Jerry> identically colored pieces must be swapped. Your recollection is not exact. There are no identically colored pieces to swap, but you can swap complete columns consisting of two "corners" (what would have been corners on the cube) and one "edge" without noticing. In fact, if you create an even permutation of those columns, there is no problem. But if you create an odd permutation, it will become impossible to solve the upper layer. Presuming you solve cubes in layers, the easiest way out is to not start at one of the octagonal layers (which seems the most natural way), but to start with a "side" layer. If you do it this way, it will always be possible to solve the last layer. I hope I'm making myself at least somewhat clear, Bas. From cube-lovers-errors@mc.lcs.mit.edu Fri Nov 20 17:41:06 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id RAA09316 for ; Fri, 20 Nov 1998 17:41:05 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <3.0.1.32.19981120105340.009ac040@icex5.cc.ic.ac.uk> Date: Fri, 20 Nov 1998 10:53:40 +0000 To: jbryan@pstcc.cc.tn.us From: "Andrew R. Southern" Subject: Space Shuttle. Cc: Cube-Lovers@ai.mit.edu, kingeorge@rocketmail.com I got a similar puzzle in the same way. Mine was called the "Space Shuttle". The lack of the name Rubik probably meant it wasn't from Rubiks. But since they only have a patent in Hungary, and everywhere else they are protected by copyrights on the name and the external appearence, this is probably legally legitimate. The colour scheme allowed the puzzle to be solved in more ways than the cube and so I reckon its easier. Each of the chamfered sides was coloured in a colour which did not relate to the rest of the puzzle, and so these were (within the boundaries of a 2-swap) possible to position ("correctly") in a few different positions. The mid-edges of the chamfered edges were rotationally symmetrical every 180 degreees and so, since they were all one colour, it was possible to have one (or three) of them rotated, and hence one of the other mid edges rotated and it would look majorly FUBAR'd. Once you'd realised what happened, the puzzle was easier than the cube though. -Andy Southern. From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 23 13:45:28 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id NAA18663 for ; Mon, 23 Nov 1998 13:45:28 -0500 (EST) Message-Id: <199811231845.NAA18663@mc.lcs.mit.edu> Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Fri Nov 20 22:15:27 1998 Date: Fri, 20 Nov 1998 22:13:38 -0500 (EST) From: Nicholas Bodley To: Jerry Bryan Cc: "Jorge E. Jaramillo" , cube Subject: Re: Re : The Cylinder In-Reply-To: Uwe Meffert had a printed color catalogue around 1985 that showed some very interesting moving-piece "group theory" puzzles (is that a proper term?). Although I have a copy safely stashed somewhere, I don't know where. I'm just about sure that one was a cylinder, possibly in three layers like layer cake; it also, iirc, had maybe three more "cutting planes" that were spherical sectors bounded by the cylinder. Rotating the pieces would exchange top and bottom. |* Nicholas Bodley *|* Electronic Technician {*} Autodidact & Polymath |* Waltham, Mass. *|* ----------------------------------------------- |* nbodley@tiac.net *|* The personal computer industry will have become |* Amateur musician *|* mature when crashes become unacceptable. -------------------------------------------------------------------------- From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 23 16:35:08 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA19314 for ; Mon, 23 Nov 1998 16:35:06 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <001e01be155b$9a456940$6bc4b0c2@home.icl.web> From: roger.broadie@iclweb.com (Roger Broadie) To: "cube" Cc: "Jorge E. Jaramillo" Subject: Re: The Cylinder Date: Sat, 21 Nov 1998 14:29:22 -0000 I was given a cylinder here in England in 1981. I no longer have the packaging, but I suspect it was Taiwanese, unless the Hungarians made this variant. It was my first cube puzzle, and its shape was so unappealing when disturbed that I put it on one side and got a genuine cube to learn on - well, almost genuine: it came from a street trader in Regent Street. The apparently impossible state is a monoflip of a top or bottom edge piece. There will be a matching flip of a middle-layer edge piece, but that will be invisible, since the piece has only one face. I wondered if it would be possible to get the puzzle into the solved shape and then restore the positions of the pieces without losing the shape, that is, only allowing turns from the group , where S and A are slice and anti-slice moves of the middle layers (I needed them). In fact it is not. There may always be a hidden flip in the middle layer and you can't correct that without moving the piece out of the middle layer, which needs a turn like F, and that destroys the shape. But if you cheat a little and make sure the flips are got right before the shape is finally restored, then it can be done. Andy Southern has already made the point about the flips. He also pointed out that the configuration is not unique because columns corresponding to the vertical edges on a normal cube can be swapped. As a rider to that point, the pretty pattern stripes on the normal cube is not distinguishable on the octagonal prism, because it's striped already. It should be possible to work out whether our moderator's puzzle came in the form he now has by counting stickers. The octagonal prism has 2 sets of 9 (the top and bottom) and 8 of 3 (the side columns). If I've grasped his configuration correctly, if it came in that form originally it should have 4 sets of 6 and 6 of 3. Roger Broadie [ Yes, my decahedron's stickers are incompatible with an octagonal prism solution. I just can't remember whether I replaced some of the stickers to make this new shape. --Dan ] From cube-lovers-errors@mc.lcs.mit.edu Mon Nov 23 18:13:16 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id SAA19716 for ; Mon, 23 Nov 1998 18:13:15 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981123071931.2655.rocketmail@send105.yahoomail.com> Date: Sun, 22 Nov 1998 23:19:31 -0800 (PST) From: Han Wen Subject: Method for Solving the Megaminx To: Cube-Lovers@ai.mit.edu Hi, Well, it took me a 2-3 days, but I finally solved the Megaminx. Whew. I know, big deal. It's been done.. many many times... over a decade ago. But, I thought some of the moves I found may of interest to some of the Megaminx aficionados out there. So, here it is, I apologize for its length: Solving the Megaminx faces 1-11 are fairly straightforward. Ironically, the larger number of faces makes it easier to solve than the Rubik's cube, because they provide a lot more "free lanes" to move pieces around. There's actually just one move you need to remember to solve these faces. It's the same move when solving the middle layer of the Rubik's cube, when you want to move edge pieces from the bottom layer to their respective position in the middle layer. Namely, D'R'DRF'RFR' Solving the last face, however, is another matter. The general strategy I followed is the same as some of the standard methods for solving the bottom layer of the Rubik's cube. Namely, I first solve the 5 corners, then I solve the 5 edge pieces. To solve the corners, I simply used Sune's move applied with slight modification to the Megaminx. For the remaining edge pieces, I had to develop moves that only moved the edge pieces around, while leaving the corners unchanged. Noel Dillabough's Puzzler program was an invaluable tool for helping me experiment with various edge moves. Anyways, the following are my notes describing some of the more useful moves I've found. I'm pretty sure they're not the most efficient method for solving the Megaminx, but they're the best I could come up with. ___________________________________________ Notation for Solving the Last Face corner pieces: F=Front Face, D=Lower Face, L=Left Face, R=Right Face The F and D faces are adjacent The last layer containing the corners you need to flip/permute should be positioned at the D-face ____________________________________________ Move for Solving the Last Face corner pieces: Name: Sune's Double-Swap Description: Sune's Rubik's Cube move applied to the Megaminx Number of pairs of corners swapped: 2 Number of corners twisted counterclockwise: 3 Move: R'D'RD'R'D'3R ____________________________________________ Strategy for Solving the Last Face corner pieces: - Position the corners - Twist the corners in place by applying Sune's Double-Swap move twice ============================================ Notation for Solving the Last Face edge pieces: F=Front Face, U=Upper Face, L=Left Face, R=Right Face The F and U faces are adjacent X= L'R U2 LR' F2 X'=L'R U'2 LR' F'2 X2= X X = (L'R U2 LR' F2) (L'R U2 LR' F2) Xa= L'R U2 LR' F'2 Y= LR' F2 L'R U2 The last layer containing the edges you need to flip/permute should be positioned as the F-face or the U-face depending on the move described below: _____________________________________________ Moves for Solving the Last Face edge pieces: Name: F Tricycle 1 Description: Permutes 3 adjacent edges clockwise on the lower left of the F-face No. Edges permuted: 3 No. Edges flipped: 2 Move: (Xa3 X'2)^2 Name: F Tricycle 2 Description: Permutes 3 adjacent edges clockwise on the upper half of the F-face No. Edges permuted: 3 No. Edges flipped: 2 Move: (Xa3 X2)^2 Name: U Tricycle 1 Description: Permutes 3 edges clockwise on the U-face No. Edges permuted: 3 No. Edges flipped: 2 Move: F' X2 Y'2 F Name: U Tricycle 2 Description: Permutes 3 edges counterclockwise on the U-face No. Edges permuted: 3 No. Edges flipped: 2 Move: F X'2 Y2 F' Name: Cross-country Tricycle Description: Permutes 3 edges across the U and F faces No. Edges permuted: 3 No. Edges flipped: 1 Move: (X2 X'2)^4 Name: U Bi-Flip 1 Description: Flips two opposite edges on the U-face No. Edges permuted: 0 No. Edges flipped: 2 Move: (Xa3 X'2)^3 Name: U Bi-Flip 2 Description: Flips two adjacent edges on the U-face No. Edges permuted: 0 No. Edges flipped: 2 Move: (X2 X2 X'2)^5 Name: Cross-country Bi-Flip Description: Flips two edges, one on the U-face, one on the F-face No. Edges permuted: 0 No. Edges flipped: 2 Move: (Xa3 X2)^3 Name: "W"-Cycle Description: Permutes all edges on the F-face in a "W" pattern No. Edges permuted: 5 No. Edges flipped: 2 Move: (X2 X2 X'2)^2 Name: "Figure 8"-Cycle Description: Permutes all edges on the F-face in a "Figure 8" pattern No. Edges permuted: 5 No. Edges flipped: 4 Move: (X2 X2 X'2)^4 ____________________________________________ Strategy for Solving the Last Face edge pieces: - You should only need to use F Tricycle and the Bi-Flip moves to completely solve the edges. The F Tricycle move usually needs to be applied twice. If anything is vague/unclear please feel free to request clarification. -Han Wen- From cube-lovers-errors@mc.lcs.mit.edu Tue Nov 24 16:09:26 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id QAA24075 for ; Tue, 24 Nov 1998 16:09:26 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: cube-lovers@ai.mit.edu From: whuang@ugcs.caltech.edu (Wei-Hwa Huang) Subject: Re: The Cylinder Date: 24 Nov 1998 18:53:56 GMT Organization: California Institute of Technology, Pasadena Message-Id: <73evc4$cq0@gap.cco.caltech.edu> References: roger.broadie@iclweb.com (Roger Broadie) writes: >I was given a cylinder here in England in 1981. I no longer have the >packaging, but I suspect it was Taiwanese, unless the Hungarians made >this variant. It was my first cube puzzle, and its shape was so >unappealing when disturbed that I put it on one side and got a genuine >cube to learn on - well, almost genuine: it came from a street trader >in Regent Street. There is a Taiwanese manufacture of the octagonal prism. I have part of one in my collection. (Got it when I was 10, and many cubies have disappeared since then.) I also have one of the "truncated cubes" mentioned earlier in this thread. I find the discussion on these two quite strange, since I always thought of these as cubes with weird cubies -- no more special than, say, that spherical "cube" they had a few years back. -- Wei-Hwa Huang, whuang@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- StethoPHONE, not stethoSCOPE. What do doctors SEE in those things anyway? From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 1 14:27:08 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA18757 for ; Tue, 1 Dec 1998 14:27:07 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu To: Cube-Lovers@ai.mit.edu From: "Andrew R. Southern" Subject: Uwe Meffert's Re-issueing of Prof. Cube Message-Id: Date: Mon, 30 Nov 1998 22:48:11 +0000 Dear Cube Lovers, I have written a website for Uwe Meffert (with input from both W. David Joyner and David Byrden) that can be found at: http://www.ue.net/mefferts-puzzles/ and was speaking with him earlier today. Uwe is going to make another batch of Professor Cubes (5x5x5) in the next week or so, and is taking orders through his site. This is a subject that is often raised on the newsgroup, and I hope people don't think of this as taking too much of a liberty. The website contains a credit card order page, information about the puzzles (including a solution to all of his popular puzzles) and multiple links to other pages. Whilst I am not involved with the day to day running of the website, if people would like their pages added to the links, please forward the URL to this address WITH A SHORT SUMMARY that will appear with the link. Puzzle available include some of the more recent ones (Orbix, Pyramorphix, Megaminx, Prof Cube). I am told that orders *may* still be on time for delivery before Chirstmas. I hope this has been of use to you guys, Andy Southern. a.southern@ic.ac.uk From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 1 15:45:22 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id PAA19069 for ; Tue, 1 Dec 1998 15:45:21 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Message-Id: <19981201060918.6975.rocketmail@send104.yahoomail.com> Date: Mon, 30 Nov 1998 22:09:18 -0800 (PST) From: Han Wen Subject: Method for Solving the Professor's Cube (5x5x5) To: Cube Lovers Cc: Charles Lin , Keith Miller Hi, Okay, another so what, big deal. I finally solved the Professor's Cube. For those who may not be familiar, the Professor's Cube is a 5x5x5 Rubik's cube. Whew that was hard. It took me a good 4 days to figure out all the moves. Gees, it made the Megaminx seem like child's play in comparison. Once again, Noel Dillabough's Puzzler program was an invaluable tool to visualize and experiment with various moves. Thanks Noel! For those brave souls who would like to conquer this beast, the following solution may provide some enlightenment. It's a layers solution, in contrast to the corners-first solution that I have seen posted on various web sites. Good luck to you. The Professor's Cube is a truly challenging puzzle. ______________________________________________________ Method for Solving the Professor's Cube (5x5x5) I will use Noel Dillabough's system for referring to various slices or layers, as described in his Puzzler's F1 help. ________________________________________ Notation: U - The upper slice u - One slice away from the upper slice e - The equator slice d - One slice away from the lower slice D - The lower slice L - The leftmost slice l - One slice away from the leftmost slice m - The middle slice r - One slice away from the rightmost slice R - The rightmost slice F - The facing slice f - Once slice away from the facing slice M - The facing middle slice b - One slice away from the back face B - The back slice I will use the words "slice" and "layer" synonymously. A "face" is one of the six outer slices; namely, U, D, L, R, F or B. Rotations of the middle slices e, m or M will be in the same direction as the U, R and F faces, respectively. Let y denote one of the slices. y - represents a clockwise 1/4 turn of the y-slice y' - represents a counterclockwise 1/4 turn of the y-slice y2 - represents a clockwise 1/2 turn of the y-slice (For example, Rrm represents clockwise 1/4 turns using the RIGHT-hand of the R, r and m slices. Ll represents clockwise 1/4 turns using the LEFT-hand of the L and l slices.) Finally, let's consider the pieces or cubelets on any given face. There are four types of cubelets: corners, edges, centrals and a center. For a given face, there are 4 corners, 12 edges, 8 centrals and 1 center. With these four types and the intersection of any two slices using Dillabough's notation, we can specify the location of any cubelet. For example, consider the F-face: LU-corner: the corner cubelet on the upper left-hand corner of the F-face re-central: the central cubelet adjacent and to the right of the center cubelet of the F-face _______________________________________ First Layer (U slice): Solving the first layer is fairly straightforward. Basically the same as solving the Rubik's cube. The central pieces are the only thing really different. _______________________________________ Second Layer (u slice): 1. First, solve for the mid-central pieces (F-face mu, B-face mu, L-face Mu, R-face Mu). Get one of the mid-central piece on the same color face, and then rotate it into position by using the "free lane" from the opposite face. For example, let's say we want have a mid-central piece at the re position of the F-face. Use the D-"free lane" of the B face to position the mid-central piece without affecting your newly completed U slice, by moving: B2 U2 F' U2 B2. 2. Now, solve for the left and right central pieces (F-face lu, ru, L-face bu, fu, etc). Here's where we'll use a genuinely new move. Position one of the left/right central pieces on the D-face so that it and the position you want to move the cubelet into lie in the save vertical slice. For example, let's say we want to move the left central cubelet into the F-face lu position. Position the left central cubelet at the D-face lb position and perform the following u-layer DF Swing move: >From the D-face lb position: l d' l' d' l d2 l' See how that works? The corresponding move at the D-face rb position is: >From the D-face rb position: r' d r d r' d2 r This same concept is used to move the left/right central pieces into position for both the Second (u-slice) and Fourth (d-slice) layers. "Hey, what if my left/right central piece is on the F face? How do I move the piece to the D face so that I can apply this move?" Good question. Position the piece on the F-face ld or rd position and apply the corresponding move described above. That should move the cubelet to the D face where you can then apply the move again to move it into the correct left/right central position. 3. Finally, solve for the left and right edges (F-face and B-face Lu, Ru). Use the classic Rubik's cube move to rotate an D-edge piece into one of the middle layer edge positions. Namely, if the cubelet is at the F-face rD or lD position and the destination position is F-face Ru or Lu then perform the following: F-Edge Swing Moves: Destination position F-face Ru: D' R' D R F' R F R' Destination position F-face Lu: D L D' L' F L' F' L _______________________________________ Third Layer (e slice): 1. Solve for the left/right central pieces (F-face le, re, L-face be, fe, etc). You'll notice that the DF Swing moves will not work here. Darn. Instead, we'll use the F-Edge Swing move adapted for the l and r slices. Position the cubelet at the F-face md position then perform the following: F-Central Swing Moves: Destination position F-face Re: d'r'dD rR f'F' r fF r'R' Destination position F-face Le: d l d'D' l'L' fF l' f'F' lL "Hey, what if my left/right central piece is on the D face? How do I move the piece to the F face so that I can apply this move?" Same problem. Position the cubelet at the D-face rM position then apply the Re F-Central Swing move. 2. Solve for the left and right edges (F-face and B-face Le, Re). Again, a slight variation of the F-Edge Swing move will do. Position the edge piece on the F-face mD position and perform the following: e-Layer F-edge Swing Moves: Destination position F-face Re: D' R' D rR F' R F r'R' Destination position F-face Le: D L D' L'l' F L' F' Ll ______________________________________ Fourth Layer (d slice): 1. First, solve for the mid-central pieces (F-face md, B-face md, L-face Md, R-face Md). This is one of the most difficult steps. The mid-central pieces will be on either the d-slice or on the D-face. To move them into there correct positions, you'll need to use a few modified Rubik's cube moves: Place the D-face as the U-face when applying these moves: The following sets of cubelets are affected by these moves: cL = (central L-face Lu, edge U-face LM and central U-face lM) cR = (central R-face Ru, edge U-face RM and central U-face rM) cF = (central F-face mu, edge U-face mF and central U-face mf) Mid-central Tricycle: move: T2(U) = F2 f2 Uu Ll r'R' F2 f2 L'l' rR Uu F2 f2 action: Permutes the three sets of cubelets (cL, cR, cF) clockwise: Mid-central Bi-Flip Tricycle: move: S2(B) = L'l' rR bB Ll r'R' U2u2 L'l' rR Bb Ll r'R' action: Permutes the three sets of cubelets (cL, cR, cF) clockwise and flips the cR and cF sets. Let's clarify "flipping". Let's say for the cR set you have the colors: blue, (blue, yellow), yellow corresponding to the three cubelets. After flipping the cR set you'll have the colors: yellow, (yellow, blue), blue. Use these two moves to position all the mid-central pieces for the Fourth Layer. Now, if you're lucky, and Murphy's Law says that you will be, you may end up in a configuration where you'll have three of the mid-central pieces positioned properly, but the fourth mid-central position will be on the D-face. Okay, now we're going to start having fun. Position the central cubelet at the D-face lM position (i.e. on the left-hand side). Place the D-face as the U-face and then apply the following sequence of moves: S2(B) T2(U') U2 T2(U) S2(B') U' S2(B') Yes, all that trouble just to move one mid-central cubelet from the U-face to the F-face. 2. Whew, congratulate yourself if you've made it this far. Now, solve for the left/right central cubelets, (F-face ld, rd, L-face bd, fd, etc). Position the left central cubelet at the D-face lf or rf position and perform the following d-layer DF Swing move: >From the D-face lf position: l d l' d l d2 l' >From the D-face rf position: r' d' r d' r' d2 r 3. Solve for the left and right edges (F-face and B-face Ld, Rd). Again, a slight variation of the F-Edge Swing move will do. Position the edge piece on the F-face lD or rD position and perform the following: d-Layer F-edge Swing Moves: Destination position F-face Rd: D' R' D mrR F' R F m'r'R' Destination position F-face Ld: D L D' L'l'm F L' F' Llm' ______________________________________ Fifth Layer (D slice): 1. Solve for the corner cubelets using standard Rubik's cube moves. First, position the corners in their correct locations using the usual corner swappers: Adjacent corners swap: R' D' R F D F' R' D R D2 Diagonal corners swap: R' D' R F D2 F' R' D R D And then rotate or twist the corners in position using Sune's move: Sune's 3-corner twister: : R' D' R D' R' D2 R D2 2. Solve for the mid-edges (mF, RM, mB, LM) using a slight modification to the Tricycle moves. Place the D-face as the U-face when applying these moves: Mid-edge Tricycle: move: F2 U Ll r'R' F2 L'l' rR U F2 action: Permutes the three edges (LM, RM, mF) clockwise: Mid-edge Bi-Flip Tricycle: move: L'l' rR B Ll r'R' U2 L'l' rR B Ll r'R' action: Permutes the three edges (LM, RM, mF) clockwise and flips the RM and mF. 3. Solve for the left/right edges (lF,rF, Rf, Rb, lB, rB, Lf, Lb). Now, we're going to have some serious fun. The hardest part of this step is not getting lost while performing the long sequence of moves. Also while spinning all these slices, another difficulty is preventing the cube from exploding and keeping the central pieces from twisting around. Again, place the D-face as the U-face with applying these collection of moves: LR-edge Tricycle: move: F2 U Lm'R' F2 L'mR U F2 action: Permutes the three pairs of edges ((Lf,Lb), (Rf,Rb), (lF,rF)) clockwise: LR-edge Bi-Flip Tricycle: move: L'mR B Lm'R' U2 L'mR B Lm'R' action: Permutes the three pairs of edges ((Lf,Lb), (Rf,Rb), (lF,rF)) clockwise and flips the Rf, Rb, lF and rF. To get those last remaining cubelets in place, a few more exotic moves are necessary: Definitions: T(x) = F2 U x F2 x' U F2 x1 = L r' R' x2 = L l R' x3 = L m' R' (T(x) is a generalized form of the Mid-edge Tricycle) X1 = T(x1) T(x1) T(x1) X2 = T(x2) T(x2) T(x2) X3 = T(x3) Name: Double pair F swap Description: Swap two pairs of edges: (lF - Lb) and (rF - Rb) Move: X2 X1 Name: Double pair F cross swap Description: Swap two pairs of edges: (lF -Lf ) and (rF -Rf ) Move: X1 X2 Name: Double pair R swap Description: Swap two pairs of edges: (Rb - Lf) and (Rf - lF) Move: X2 X1 X3 Name: Double pair R cross swap Decription: Swap two pairs of edges: (Rb - rF) and (Rf - Lb) Move: X1 X2 X3 Name: Double pair L swap Description: Swap two pairs of edges: (Lb - Rf) and (Lf - rF) Move: X3 X2 X1 Name: Double pair L cross swap Description: Swap two pairs of edges: (Lb - lF) and (Lf - Rb) Move: X3 X1 X2 Name: LRL-edge Bi-Flip Tricycle Description: Permutes (lF, Lf, Rf) edges clockwise and flip lF and Lf edges Move: X3 X1 Name: LLR-edge Bi-Flip Tricycle Description: Permutes (lF, Lb, Rb) edges clockwise and flip Lb and Rb edges Move: X1 X3 Name: RRL-edge Bi-Flip Tricycle Description: Permutes (rF, Lf, Rf) edges clockwise and flip Lf and Rf edges Move: X2 X3 Name: RLR-edge Bi-Flip Tricycle Description: Permutes (rF, Lb, Rb) edges clockwise and flip rF and Lb edges Move: X3 X2 With these collection of moves, you should be able to finish off the Professor's Cube! *Sigh* -Han- P.S. Thanks "Professor" Meffert. For those folks like myself who have wrestled and completed your 5x5x5 cube, we can only ask and plead, "What's Next?!!" :) From cube-lovers-errors@mc.lcs.mit.edu Tue Dec 1 19:18:47 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id TAA20686 for ; Tue, 1 Dec 1998 19:18:47 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 30 Nov 1998 23:13:51 -0500 From: michael reid Message-Id: <199812010413.XAA11878@euclid.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: new types of cyclic shifters a few months ago, i introduced the position superflip composed with four spot and showed that it had a new type of cyclic shifting property. i've now found some new ways to generalize cyclic shifting, and this in turn suggests some new positions to consider. first, some brief review. the position superflip is central, so it commutes with all turns. therefore, if x y produces superflip, so does y x . we can shift one turn at a time, removing the first turn of the sequence and shifting it to the end. in other words, if m produces superflip, then x m = m x for all turns x . clearly, any position m with the property that x m = m x for all turns x , is central, so the only such positions are superflip and start. i showed in an earlier message, that if x is any turn and m is superflip composed with four spot, then x m = m y , where y is x conjugated by the cube rotation C_U2 . more generally, we can ask for positions m such that for any turn x , there is another turn y satisfying x m = m y . for such a position, we can cyclically shift any maneuver, one turn at a time, by replacing the turn x^(-1) at the beginning with the corresponding y^(-1) at the end. some other positions with this property are: four spot, six spot, six spot composed with superflip. a new way to generalize this is to consider positions m such that for any turn x , we have x m = n x , where n is the same pattern as m , but perhaps in a different orientation. for such a position, we can cyclically shift any maneuver, by shifting the first turn to the end, and then conjugating by the appropriate cube symmetry. for example, consider the position in which the UFR corner is twisted clockwise, and the other seven corners are twisted counterclockwise. (i'll call this "1-7-twist" for now, but this pattern needs a better name.) this position is created by U F2 B' U B U D2 R2 U2 B U' D2 B U F2 B L2 B2 now, cyclically shift the U at the beginning to the end to get F2 B' U B U D2 R2 U2 B U' D2 B U F2 B L2 B2 U which produces a different orientation of the same position; this time, the ULF corner is twisted clockwise. now conjugate this maneuver by C_U to get R2 L' U L U D2 B2 U2 L U' D2 L U R2 L F2 L2 U which produces the original position, in its original orientation. actually, there are 3 cube symmetries by which one could conjugate, since the position has 3-fold symmetry. another position with this type of cyclic shifting property is 1-7-twist composed with superflip. we can combine both types of generalizations, and ask for positions m that have the property that for any turn x , we have x m = n y , where y is another turn, and n is the same pattern as m , but perhaps in a different orientation. for such positions, we can cyclically shift any maneuver by replacing x^(-1) at the beginning of the maneuver by the corresponding y^(-1) at the end, and then conjugating the whole maneuver by the appropriate cube symmetry. two such positions are: 1-7-twist composed with four spot, and 1-7-twist composed with four spot composed with superflip. here's all the examples of cyclic shifters that i know, along with minimal maneuvers: 1. central positions start (0q*, 0f*) superflip R' U2 B L' F U' B D F U D' L D2 F' R B' D F' U' B' U D' (24q*, 22f) F' B' D2 L' B2 L2 F2 U' D B' D2 R L D' F2 U' L2 D' F2 D' (20f*, 28q) 2. four spot F2 B2 U D' R2 L2 U D' (12q*, 8f*) six spot F B' U D' R L' F B' (8q*, 8f*) four spot composed with superflip U2 D2 L F2 U' D R2 B U' D' R L F2 R U D' R' L U F' B' (26q*, 21f) F U2 R L D F2 U R2 D F2 D F' B' U2 L F2 R2 B2 U' D (20f*, 28q) six spot composed with superflip R' U D R' U F' D R' B U' L' U' F' D F' B' D' R' F D F D' R2 (24q*, 23f) U2 F B' R F L2 F2 D B2 D2 R2 B' L2 F' D2 R2 D' B R B2 (20f*, 30q) 3. 1-7-twist F R' U' L' F' U' B' L' U' R2 F L' D' R' F' D' B' R' D' L2 (22q*, 20f) F R2 L' F L F B2 U2 F2 L F' B2 L F R2 L D2 L2 (18f*, 26q) 1-7-twist composed with superflip F R F' R U B L D B D' L' D L F B' R B D F R' (20q*, 20f) F R L' B L D F' L2 B D2 B' L' F2 B' D B U L B (19f*, 22q) 4. 1-7-twist composed with four spot F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' (22q*, 20f*) 1-7-twist composed with four spot composed with superflip F U' R' L F' U R L' U2 D' B R L F' R D' R' F2 L U' (22q*, 20f*) as usual, i give a maneuver which is minimal in both metrics whenever this is possible. i don't claim that i've found all positions in these categories, but these are all that i know. if you find any others, they'd be good candidates for positions far from start. mike From cube-lovers-errors@mc.lcs.mit.edu Wed Dec 2 14:51:54 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil (sun28.aic.nrl.navy.mil [132.250.84.38]) by mc.lcs.mit.edu (8.9.1a/8.9.1-mod) with SMTP id OAA24883 for ; Wed, 2 Dec 1998 14:51:53 -0500 (EST) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Date: Mon, 30 Nov 1998 23:39:25 -0500 From: michael reid Message-Id: <199812010439.XAA11918@euclid.math.brown.edu> To: cube-lovers@ai.mit.edu Subject: asymmetric local maxima based on the previous analysis, i can now give 2 asymmetric positions that are local maxima, namely 1-7-twist composed with four spot, and 1-7-twist composed with four spot composed with superflip. all previous examples of local maxima had some symmetry (although jerry bryan recently gave a bunch of new local maxima at distance 12q; perhaps these contain some other examples.) to show that a position is locally maximal, i must give a minimal maneuver that ends with each possible quarter turn. bear in mind that F2 = F F = F' F'. 1-7-twist composed with four spot: F L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' F2 (22q*) U' R' D L F' U' L' B U' B' U F2 U' D F R' U' F' L R2 (22q*) D' L B' D' L' F B2 D' F' U B R' D' B' L D' L' D R2 U (22q*) F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' (22q*) R' U L' F B D' F L' D B' L F' L' F D' B D' B L' U R' B (22q*) U' F L' U' B' L D R' U' R L2 F' U' L' F U' D F2 U B' (22q*) U' R' D L F' U' L' B U' B' U F2 U' D F R' U' F' R2 L (22q*) U' F' L U' L' U R2 U' D R B' U' R' F B2 U' F' D B L' (22q*) F' U' F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D (22q*) L B' D' L' F B2 D' F' U B R' D' B' L D' L' D R2 U D' (22q*) 1-7-twist composed with four spot composed with superflip: R' D' R B' R L F U2 D' R L' U B' R' L U' B U' R F2 (22q*) B U' R U' F B' R' U F' B U2 D' L F B R' B D' B' R2 (22q*) B D R B R L' U F' B' L' F L D' B2 U R' B L B D' U (22q*) F U' R' L F' U R L' U2 D' B R L F' R D' R' F2 L U' (22q*) U' D2 L F B R' F U' F' R2 B D' L D' F B' L' D F' B (22q*) U' F L' F B R U' D2 F B' D L' F' B D' L D' F R2 B' (22q*) U' F L2 B' D' B L' F B R U2 D' F' B U L' F B' U' L (22q*) B' D R L' U' D2 F R L B' R U' R' B2 L D' F D' R L' (22q*) R L' D F' R' L D' F D' R B2 L' U' L B' R L F U' D2 (22q*) these positions are also strong local maxima in the face turn metric. 1-7-twist composed with four spot: U D' B2 D F' D' F R' D' B' R U L' D' R2 L F' D' R' F (20f*) F L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' F2 (20f*) U' R' B D F' U' F B2 L' U' B' L U' D L2 U R' U' R F' (20f*) F' U' L' B U' B' U F2 U' D F R' U' F' R2 L U' L' D R (20f*) D R' D' R B' D' L' B U F' D' F B2 R' D' B' R U D' R2 (20f*) F B2 D' F' U B R' D' B' L D' L' D R2 U D' R F' D' R' (20f*) D' L B' D' L' F B2 D' F' U B R' D' B' L D' L' D R2 U (20f*) D' B D F2 B R2 B2 D F2 B' D B D' R2 U2 B2 U2 D2 F' U2 (20f*) F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D B' U' (20f*) L2 U R2 B D2 B L2 U' F' B2 D F D' R2 L2 D2 B2 L2 D' B (20f*) B L2 U F' L2 U' F' B U F D' L2 U F2 D F2 D' R2 U2 B2 (20f*) U' F L' U' B' L D R' U' R L2 F' U' L' F U' D F2 U B' (20f*) U' R' D L F' U' L' B U' B' U F2 U' D F R' U' F' R2 L (20f*) D2 F2 U' L2 U L2 D B2 U' L D R L' D' B2 L' D B2 R L2 (20f*) U' F' L U' L' U R2 U' D R B' U' R' F B2 U' F' D B L' (20f*) F' U' F B2 L' U' B' L U' D L2 U R' U' R F' U' L' F D (20f*) F2 B R2 D F' R2 D' F' B D F U' R2 D F2 U F2 U' L2 D2 (20f*) L B' D' L' F B2 D' F' U B R' D' B' L D' L' D R2 U D' (20f*) 1-7-twist composed with four spot composed with superflip: R L F' L U' L' F2 R D' B D' R' L B' D R L' U' D2 F (20f*) R' D' R B' R L F U2 D' R L' U B' R' L U' B U' R F2 (20f*) R L F U' D2 R' L D B' R L' D' B D' L F2 R' U' R F' (20f*) R F' L U' L' F2 R D' B D' R' L B' D R L' U' D2 F R (20f*) B U' R U' F B' R' U F' B U2 D' L F B R' B D' B' R2 (20f*) F' B D' L D' F R2 B' U' B R' F B L U' D2 F' B D R' (20f*) F D' B' R2 D' F R U B' L D2 B R2 U2 B2 U' R L2 B U (20f*) R2 U' F B2 R U R D' L' B2 D' R B U L' F D2 L B2 U2 (20f*) F U' R' L F' U R