From cube-lovers-errors@mc.lcs.mit.edu Tue May 12 15:55:03 1998 Return-Path: Received: from sun28.aic.nrl.navy.mil by mc.lcs.mit.edu (8.8.1/mc) with SMTP id PAA06770; Tue, 12 May 1998 15:55:02 -0400 (EDT) Precedence: bulk Errors-To: cube-lovers-errors@mc.lcs.mit.edu Mail-from: From cube-lovers-request@life.ai.mit.edu Tue May 12 14:24:43 1998 Message-Id: <35576405.5EC25A05@frontiernet.net> Date: Mon, 11 May 1998 16:48:05 -0400 From: John Bailey To: Cube-Lovers Subject: Solving a 4 Dimensional Rubik's type Cube Announcing a web page at http://www.frontiernet.net/~jmb184/solution.html which gives the explicit steps to solve a challenge configuration for a 2x2x2x2 (that's four dimensions) Rubik type cube. The challenge configuration is available at http://www.frontiernet.net/~jmb184/Nteract4.html. These pages do NOT require a Java enabled browser however, they do require Netscape 4.0 or Microsoft Explorer 4.0. This note is to solicit your judgments regarding the difficulty of the 4 Dimensional Rubik with no edge cubes (2x2x2x2.) I believe it is relatively easy, provided only that the simulation provides for the cyclic permutation move, (NE-->SW, SW-->NW, NW--->NE) Background: Posted on rec.puzzles dl April 21, 1998: A four dimensional articulated cube is on the web at http://www.frontiernet.net/~jmb184/4cube.html The result of marrying a Rubik's cube with a tesseract, this cube is 2x2x2x2. It has 16 corners and 24 faces. It does not have edge cubes and the corners have no orientation requirement. Only 4 colors are used. The solution space is thus roughly equivalent to that of a 3x3x3 Rubik if not smaller. It is rendered in Javascript and will run on Netscape 3.0 and 4.0 This posting caused about 25 hits to the page, but got no follow-up dialog on the rec.puzzles news dl. Note that in this first version, the corners are only identified by color, not by correct position. I wrote the page without having a clue as to how to solve it. In the process of just testing code I discovered that it is remarkably unchallenging, once you get a sense of which corners the various buttons rotate. (Flipping a glove from left-handed to right-handed can be done in 4-space, but is impossible in 3-space.) I may not be an unprejudiced solver, but I would rate the challenge only slightly harder than a 15 square slider puzzle. To increase the level of difficulty, a second version of the puzzle was developed. In this version, the solution requires that the corners are returned to their correct location. They still do not requires 4-space orientation. This version was announced in the following posting. Posted on the rec.puzzles dl May 2, 1998: A Four dimensional Rubik's Cube with solution. At http://www.frontiernet.net/~jmb184/Nteract4.html Re-designed to allow importing of 3D Rubik methods, this version uses (a slightly extended version of) standard Rubik cube naming of moves and positions, has a shortcut button for one of the common permutation moves and a scramble button to provide a challenge position. I rate the challenge as equivalent to solving two faces of a 3D Rubik cube. I am looking forward to your comments, opinions, and suggestions. I am especially interested in positions which cannot be solved or cannot be solved without extensive permutation moves other than the one included. This page has received about 50 hits. But again, there was no responding dialog on rec.puzzles news dl. The difficulty of the second version is higher, but I rated the challenge as equivalent to solving two layers of a 3x3x3 cube. The only obstacle, an ordinary solver might face, is finding the longish sequence required to permutate 3 of 4 corners. That's why I provided the shortcut button (which applies the actions: L'URU'R'LRUR'U' with one click.) Discussion: My concern is that people assume the puzzle is really hard and not worth the effort. It may be seen as somewhat like the sequences from one time pads which would be cryptographers who post and ask if anyone can decrypt them. To make it clear that a solution is not that difficult, I have now made a page which gives an explicit solution, with illustrations of each step and even some animation at http://www.frontiernet.net/~jmb184/solution.html There are obviously shorter sequences to obtain a solution, however this one has the value of providing clear checkpoints along the way, such that a solver can determine if they have missed a twist. I want and would welcome your judgment about how easy or hard the puzzle is. John Bailey jmb184@frontiernet.net http://www.frontiernet.net/~jmb184 May 11, 1998