]>
Domain of the Cube Forum - Cube lovers returns
http://forum.cubeman.org
To promote mathematical discussions about the Rubik's Cube and related puzzles.enThe Special Prize of the Skewb Star Special Challenge/Competition of 14 June has been won but the challenge is still open
http://forum.cubeman.org/?q=node/view/577
The winner of the Skewb Star competition posted here on 14 June is Jakub Stepo, who is<br />
a member of the Cube Forum<br />
<br />
The Special Prize has of course been sent to Mr. Stepo, but I would like to stress that the<br />
challenge is still open and that everyone who sends in the correct answers by let´s say 31 December<br />
2019 will have their names published here, as soon as the answers are received<br />
<br />
After the tentative closing date of 31 December 2019, I was thinking of publishing here all the<br />
actual worked solutions that may have been sent to me, and in this connection I can reveal ahead of time<br />
that Jakub Stepo´s elegant and powerful solution will certainly be of great interest to Cube ForumThu, 29 Aug 2019 05:43:13 -04004x4 only two blocks from solved
http://forum.cubeman.org/?q=node/view/576
Hello, I’m trying to solve the 4x4 for the first time but keep getiing the same mistake. <br />
White is solved <br />
Red is solved<br />
Yellow is solved<br />
Green is solved except left highest row: yellow/blue orange block<br />
Bleu is solved except right highest row: orange/green/yellow block<br />
Yellow is solved except the above two blocks.<br />
These two blocks should be switch but I have no idea how.<br />
If I start again, the same problem will appear.<br />
Any ideas?Tue, 27 Aug 2019 13:24:05 -0400Bonus problem related to the Skewb Star Special Challenge/Competition, with Special Prize, of 14 June 2019
http://forum.cubeman.org/?q=node/view/575
So far, no one has sent in the answers to the two questions posed in the Skewb Star Special Challenge/Competition which I posted here on 14 June 2019, so I thought that I would avail myself of this window of opportunity to add a further bonus problem.<br />
<br />
As I´m sure everyone immediately realized, the whole point of the Special Prize of the competition, the Skewb Star Xtreme, SSX, together with the Wolf Tooth Xtreme, WTX, is that solving these cubes is a practical application of knowing all of the solutions to the Skewb Star as well as how to alternate between them, in other words of having found a way to answer the two questions of the competition.Tue, 13 Aug 2019 03:28:46 -0400New 5 spot pattern discovered for megaminx
http://forum.cubeman.org/?q=node/view/574
<img src='http://www.maxhost.org/other/5-spot-pattern-megaminx' width=600>
<p>
Thanks to Tom's web program at <a href="https://twizzle.cubing.net" target="_blank">twizzle</a> I've discovered a new megaminx pattern. Quite a long time ago I realized that slice patterns could be adapted to the megaminx. The early results can be seen here: <a href="http://www.cubeman.org/mega2.html" target="_blank">megaminx patterns</a>
<p>
The notation to generate the 10 spot with Tom's program is (2L 3u')36. With more experimentation we should be able to find many more.
<p>
MarkWed, 19 Jun 2019 15:16:19 -0400An unsolved problem: how many solutions are there to the 8-Color Cube?
http://forum.cubeman.org/?q=node/view/573
The <a href="http://www.randelshofer.ch/rubik/virtual_cubes/rubik/eight-colored_faces/eightcolor_cube_1.html"target="_blank">8-Color Cube</a> is an extremely elegant problem, both in appearance and concept;<br />
<br />
The cube is very easy to make at home: numbered stickers are available everywhere and the whole<br />
construction process takes only about 15 minutes.<br />
<br />
As you can see, Walter Randelshofer and myself have managed to find a number of extra solutions<br />
separate from the pre-existing design solution with its ”Superflip Centre” variant, however the real<br />
problem remains: how many solutions are there, in theory, to the 8-Color Cube?--this is the toughMon, 17 Jun 2019 16:27:42 -0400Skewb Star Special Challenge/Competition, with Special Prize
http://forum.cubeman.org/?q=node/view/572
SKEWB STAR <br />
Special challenge/competition 24 October 2018<br />
by Peter Tchamitch<br />
www.petertchamitch.se<br />
<br />
Question 1:<br />
How many solutions are there to this puzzle?--in other words, in how many different ways<br />
is it possible to physically orientate a solved octahedron and a solved cube/skewb in relation<br />
to each other?<br />
<br />
Question 2:<br />
How many color-matchings (please see definition below) are there in total, in other words<br />
what is the sum of all the various color-matching values for all the various solutions?<br />
A “color-matching” is an instance of one of the sides of an octahedron-pyramid having theFri, 14 Jun 2019 04:04:04 -0400cubezzz.dyndns.org/drupal is once again active
http://forum.cubeman.org/?q=node/view/571
Hi folks,<br />
<br />
These old URLs should all work now:<br />
<br />
http://cubezzz.dyndns.org/drupal/?q=node/view/563#comment<br />
http://cubezzz.duckdns.org/drupal/?q=node/view/563#comment<br />
http://cubezzz.homelinux.org/drupal/?q=node/view/563#comment<br />
http://forum.cubeman.org/?q=node/view/563#comment<br />
<br />
MarkTue, 11 Jun 2019 00:00:55 -0400Optimal solutions to the Eliac puzzle
http://forum.cubeman.org/?q=node/view/570
The Eliac is a complex deep-cut 2-gen circle puzzle:<br />
<br />
<img src='https://i.imgur.com/b5lE2kw.png' width=300><br />
<br />
The left circle rotates in increments of 90 degrees and the right circle rotates only by 180 degrees. There is a simulator of the puzzle <a href='https://www.stringham.me/eliac/'>here</a>.<br />
<br />
Using ksolve++ I made an optimal solver modified it slightly to turn it into a coset solver. The subgroup I used for the coset solver is the subgroup of positions where the 18 small triangles, 10 diamonds, and 2 squares are solved. There are 1600300800 arrangements of those 30 pieces and each coset has 3024000 solvable positions. Unfortunately since the puzzle is 2-gen, there isn't a good way to select a subgroup generated by a subset of the generators of the whole puzzle, which (as far as I can tell) is what is required in order to make the "pre-pass" trick work for sub-optimally solving cosets very quickly. So each coset needs to be solved optimally using a pure DFS, which takes quite a long time (about 1.5 hours on my laptop). Notice that the puzzle has a horizontal reflection symmetry so we only need to solve one coset in each symmetry class.Sat, 18 May 2019 17:13:03 -0400Remember to use http://forum.cubeman.org
http://forum.cubeman.org/?q=node/view/569
Hi folks,<br />
<br />
This is a notice that http://cubezzz.dyndns.org/drupal will probably stop working tomorrow. Please use http://forum.cubeman.org instead.<br />
<br />
The similar http://cubezzz.duckdns.org/drupal should also work.<br />
<br />
More news to come soon.Sun, 12 May 2019 20:58:33 -0400{4,3,3} 3 symmetry
http://forum.cubeman.org/?q=node/view/568
Hello, I am new to this forum and this is my first post. I know that maybe its content will seem trivial to some of you, but I am afraid that I am not so well versed in mathematics and programming, so I try to do at least something within my limited capabilities (I am 15.34 at the moment). <br><br />
<br />
Based on Dan Hoey’s calculations, I was able to calculate the number of essentially different positions up to symmetry of the four-dimensional analogue of the Rubik’s cube. However, it is quite probable that I have made some mistakes, as I have done it only by hand. Nevertheless, from the patterns observed I was able to make some interesting generalizations, presented later in this post.Sun, 24 Feb 2019 06:09:21 -0500The 2018 Computer Fewest Moves Challenge is Underway
http://forum.cubeman.org/?q=node/view/567
For the first time, the FMC will have solvers in the "NxNxN" category for up to 9x9x9 competing to solve 10 random scrambles in as few moves as possible. Also of note: There are now four solvers in the 5x5x5 section.<br />
<br />
For those who are interested, visit:<br />
<br />
http://cubesolvingprograms.freeforums.net/Thu, 18 Oct 2018 07:53:28 -0400Lower bound for the diameter of the 3-gen subgroup <U,F,R>
http://forum.cubeman.org/?q=node/view/566
What are the known bounds for the diameter of this subgroup? <a href='http://cubezzz.duckdns.org/drupal/?q=node/view/190'>This thread</a> gives a lower bound of 26 QTM but doesn't discuss HTM. I seem to recall a lower bound of 20 HTM from somewhere, but no upper bound. However, I recently found a position that requires 21 HTM:
<pre>U R F2 R U2 F2 U' F' R U F U R' F R2 U F R U2 R F'</pre>
Is this the first one known? Out of all 186624 positions with all pieces correctly permuted, this position and the inverse are the only ones requiring 21. Here's the full distribution:
<pre>
Depth PositionsSun, 02 Sep 2018 23:00:35 -0400Mad Octahedron
http://forum.cubeman.org/?q=node/view/565
<p align="justify">I have written a computer simulation of the octahedral twisty puzzle. It is available as freeware on the Apple App Store:</p>
<a href="https://itunes.apple.com/hr/app/mad-octahedron/id1400458838?mt=12" target="_parent">Mad Octahedron</a>Thu, 21 Jun 2018 10:47:47 -0400Future URL recommendation for the forum
http://forum.cubeman.org/?q=node/view/564
Hello everybody :)<br />
<br />
In the future I think it would be a good idea if we all used URLs of the form:<br><br />
http://forum.cubeman.org/?q=node/view/563#comment<br><br />
rather than<br><br />
http://cubezzz.dyndns.org/?q=node/view/563#comment<br><br />
dyndns.org has raised their prices every year and I'm considering <br />
dropping their service. Unfortunately if we do that a lot of old URLs will stop <br />
working, so I'm open to any clever ideas on what is the best way to deal with <br />
this problem. I'm committed to keeping the maxhost.org and <br />
cubeman.org domain names working for the long term, but<br />
I'm very unhappy with dyndns.Tue, 08 May 2018 17:47:42 -0400Three Million Positions in Four Metrics
http://forum.cubeman.org/?q=node/view/563
I optimally solved three million positions in four distinct metrics.<br />
These positions are distinct from the three million positions I ran<br />
some years back. Random numbers were generated with the Mersenne<br />
Twister algorithm. The four metrics I ran were quarter-turn metric,<br />
half-turn metric, slice-turn metric, and axial-turn metric (equivalent<br />
to the robot-turn or simultaneous-turn metric on the 3x3 cube).<br />
<br />
The generators for each metric are strict super- or sub-sets of the<br />
generators for the other metrics. The quarter-turn metric has 12<br />
generators, the half-turn metric has 18 generators, the slice-turnMon, 23 Apr 2018 11:52:52 -0400