## 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

## The Special Prize of the Skewb Star Special Challenge/Competition of 14 June has been won but the challenge is still open

Submitted by Peter Tchamitch on Thu, 08/29/2019 - 04:43.a member of the Cube Forum

The Special Prize has of course been sent to Mr. Stepo, but I would like to stress that the

challenge is still open and that everyone who sends in the correct answers by let´s say 31 December

2019 will have their names published here, as soon as the answers are received

After the tentative closing date of 31 December 2019, I was thinking of publishing here all the

actual worked solutions that may have been sent to me, and in this connection I can reveal ahead of time

that Jakub Stepo´s elegant and powerful solution will certainly be of great interest to Cube Forum

## 4x4 only two blocks from solved

Submitted by Rubikehv75 on Tue, 08/27/2019 - 12:24.White is solved

Red is solved

Yellow is solved

Green is solved except left highest row: yellow/blue orange block

Bleu is solved except right highest row: orange/green/yellow block

Yellow is solved except the above two blocks.

These two blocks should be switch but I have no idea how.

If I start again, the same problem will appear.

Any ideas?

## Bonus problem related to the Skewb Star Special Challenge/Competition, with Special Prize, of 14 June 2019

Submitted by Peter Tchamitch on Tue, 08/13/2019 - 02:28.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.

## New 5 spot pattern discovered for megaminx

Submitted by cubex on Wed, 06/19/2019 - 13:52.Thanks to Tom's web program at twizzle 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: megaminx patterns

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.

Mark

## An unsolved problem: how many solutions are there to the 8-Color Cube?

Submitted by Peter Tchamitch on Mon, 06/17/2019 - 15:27.The cube is very easy to make at home: numbered stickers are available everywhere and the whole

construction process takes only about 15 minutes.

As you can see, Walter Randelshofer and myself have managed to find a number of extra solutions

separate from the pre-existing design solution with its ”Superflip Centre” variant, however the real

problem remains: how many solutions are there, in theory, to the 8-Color Cube?--this is the tough