## All 3x3x3 involutions solved

Submitted by Andrew Skalski on Tue, 05/28/2024 - 16:14.Here are the total and 48-way symmetry reduced counts by distance:

d Total Unique by symmetry -------------------------------------- 0 1 1 1 6 1 2 3 1 3 72 2 4 39 4 5 960 25 6 886 41 7 12708 292 8 19526 506

## Does the STOP-cube have a second type of solution?

Submitted by ortwin on Mon, 01/29/2024 - 02:52.And those are all legit questions of course.

My name is Ortwin, I am a long time member of the twisty puzzle forum. Currently I am looking for the answer to question regarding a specific sticker modification of a 3x3x3 cube, but there did not seem to be much interest over there in the question. Walter Randelshofer who is also a member of this forum recommended to post it into this community, and hereby I do.

To get an idea what that "STOP-cube" is, you might want to have a quick look at the links to the topics in the twistypuzzle forum:

## Diameter of the M24 Conway puzzle is 45

Submitted by Paul Timmons on Wed, 02/08/2023 - 11:21.This is a well know puzzle in which there are two moves, one which rotates the central "clock" by one position

clockwise or counter-clockwise.

The other switches or swaps each pair of numbers with matching colours.

I decided to plug these values into GAP to investigate God's number for the underlying group for this puzzle

as it still seemed be unknown or undocumented anywhere at least.

Feeding these numbers into GAP we get:

S := (1,24)(2,23)(3,4)(5,22)(6,11)(7,8)(9,10)(12,21)(13,14)(15,20)(16,17)(18,19);

## Streamlined version of the solutions posted here on 22 September 2021

Submitted by Peter Tchamitch on Thu, 11/11/2021 - 10:29.that all the proposed sequences and algorithms (in the presentation that was linked to in that post)

are designed to solve the WTX and SSX** starting from a situation where one of the 12 solutions of

the WT/SS portion of the cube is already in place and the remaining task is to move on from there

to the other solutions in order to find the unique solution of the 12 which also results in the

characteristic ”valleys” of the WTX/SSX being solved (there is of course a 1/12 chance that the

starting solution just happens to be the right one) ** Please note the link at the bottom of the page

## Proposed solutions to the Wolf Tooth Xtreme and Skewb Star Xtreme

Submitted by Peter Tchamitch on Wed, 09/22/2021 - 03:32.Just to quickly recap: the problem in question was to find the best way to solve the custom hybrid cubes, the Wolf Tooth Xtreme and the Skewb Star Xtreme, which together constituted the Special Prize of the Skewb Star Special Challenge/Competition posted here on 14 June 2019

The top four pages of the presentation here show the state of affairs at the time of the 13 August 2019 post, a state of affairs which was subsequently summarized in the first paragraph of the 26 September 2019 post; in the rest of that post I then outlined, without going into detail, a practical improvement to the previous ”standard method” and added at the end that ”it remains to be shown formally exactly why the improved system described above works”

## Deficiency minus one presentation for the Tits Group

Submitted by Paul Timmons on Sun, 05/02/2021 - 04:27.has a transitive permutation representation on 2304 points.

A general formula for the number of edges in a n-cube is n.2^(n-1) to

be found in this extract from "Beyond the Third Dimension" by Thomas Banchoff

https://www.math.brown.edu/tbanchof/Beyond3d/chapter4/section05.html

It is worth mentioning another source here for a general formula

for the number of pieces of different types on a d-dimensional Rubiks' cube

## A Generalization on the Shamir Method

Submitted by Jerry Bryan on Sat, 07/18/2020 - 12:14.I have not posted in a very long time, but I have continued to work on ideas for a better program to calculate God's Algorithm for the full cube. The time has long passed where a single desktop class machine could make further progress on the problem as a whole. The search space is just too large for that. Instead, I have been working on ideas for a program that could at least visit all the positions in a single coset no matter how far the positions in the coset are from Start.

I have such a program which works, but its performance is not acceptable. Therefore, I'm not going to report anything about it. Instead, I'm going to report on a plan for a new and similar program which I believe will have acceptable performance. I have developed most of the pieces that will be required for this new program, but it will take me a few months to put all the pieces together. The main idea in the new program is very old and is not original with me. The idea borrows heavily from a message to the original Cube-Lovers mailing list by Alan Bawden on 27 May 1987. Alan's message was based on a talk given by Adi Shamir.

## Megaminx "cube in a cube" solved in 42 moves

Submitted by cubex on Sun, 03/29/2020 - 14:06.The sequence of moves in SiGN notation is:

BR2 U2' BR2' R2 U' F2 U2' L2 U' BL2 U2 BL2' U' L2' U' F2' U' R2' BR2 U2 BR

BL2' L2' R2' U2 R2' U' F2' R2 F2 U' F2' U R2' F2 U R2 U' R2 L2 BL2 BR2

The vid

## Jakub Stepo´s solutions to the two Skewb Star Competition problems

Submitted by Peter Tchamitch on Thu, 01/02/2020 - 06:45.Question 1

========

Let’s say that the cube is solved and ﬁxed in position. We have to ﬁnd out which positions are permissible while having solved cube.

## The latest on the Bonus Problem posted on 13 August 2019

Submitted by Peter Tchamitch on Thu, 09/26/2019 - 14:12.finding the easiest or most convenient Skewb Star or Wolf Tooth solution, depending on how the

SSX or WTX respectively were scrambled, and then, unless the characteristic valleys between the

corners of the Skewb Xtreme just happen to be spontaneously solved, proceeding from there to the

other Skewb Star or Wolf Tooth solutions in an orderly manner until the valleys are observed to be

correct. No matter how orderly, this method still involves trial and error, and the Bonus Problem

was basically asking for a way to eliminate that somehow. The SSX and WTX have only one