# Any books about puzzle theory?



## ahmedkl (Nov 11, 2010)

I wanted to know if there any books related to puzzle theory?I have found articles on the internet but i don't like to read them on pc


----------



## vcuber13 (Nov 11, 2010)

have you thought about printing?


----------



## cuBerBruce (Nov 11, 2010)

_Adventures in Group Theory_ by David Joyner. If you don't want to buy the book, this pdf has much of the same material.

Of course, check the Articles section of Jaap's Puzzle Page if you haven't already, and particularly the page on Group Theory for puzzles which also lists some books at the end.


----------



## VP7 (Nov 11, 2010)

David Singmaster Notes on Rubik's Magic Cube (Enslow 1980/81)

http://www.amazon.com/Notes-Rubiks-Magic-David-Singmaster/dp/0894900439


----------



## Whyusosrs? (Nov 12, 2010)

http://www.amazon.com/Rubiks-Cubic-Compendium-Recreations-Mathematics/dp/0198532024

http://www.amazon.com/Handbook-Cubik-Math-Alexander-Frey/dp/0718825551


----------



## 4. (Nov 22, 2010)

I know this exactly opposite of what the OP is asking for but can anyone link me to some free .pdf's about puzzle theory?


----------



## SmartyGirl (Dec 22, 2010)

Are you able to get articles like this on eReaders. That would probably be another cool use for ereaders. Or do they only accept books?


----------



## shelley (Dec 22, 2010)

http://sporadic.stanford.edu/bump/match/rubik.pdf
http://sporadic.stanford.edu/bump/match/newcube.pdf


----------



## Lucas Garron (Dec 22, 2010)

Bump.

(I know, I know, it's only been 20 minutes. But he's awesome.)


----------



## shelley (Dec 23, 2010)

Yep.


----------



## Christopher Mowla (Jun 25, 2013)

I am guessing that this is a new document
Doc Benton's Fantastic Guide to Group Theory, Rubik's Cube, Permutations, Symmetry, and All that Is!

It was written by Christopher P Benton, a P.H.D. of mathematics. He appears to be a decent instructor, so perhaps this PDF might be worth looking at.

I didn't read it myself (I only skimmed), but I thought that I should just mention it because it appears that he speaks in very simple language, and he uses plenty of images to accompany the text (both of which I try to do myself when I make documents. For example see my supercube centers and odd parity document...I recently updated it (most of the changes were to the end of the document) for those who already have seen it). In addition, he seems to have a sense of humor which is a plus.

However, I have to admit that by just skimming it, it appears that those more experienced in group theory of the Rubik's cube will not learn anything new from this, but it might be something interesting to see at least once because he does use a lot of visuals.


----------



## Christopher Mowla (Apr 2, 2014)

Is anyone aware of this publication on the theory of efficiency of human solving methods to solve the 3x3x3? It's useless in my opinion (even more useless than the nxnxn god's number big O notation formula), but maybe someone else might be interested to read it. I think they over complicated things just to publish a dissertation, but that's just my opinion.

Edit:
7.5 years after I made the post, I am now editing it because the old link is broken.


----------



## cuBerBruce (Apr 3, 2014)

cmowla said:


> Is anyone aware of this publication on the theory of efficiency of human solving methods to solve the 3x3x3? It's useless in my opinion (even more useless than the nxnxn god's number big O notation formula), but maybe someone else might be interested to read it. I think they overcomplicated things just to publish a dissertation, but that's just my opinion.



Thank you for pointing this out, cmowla. I've met the author of this paper, and his advisor was on the God's Number team. I've known he's been working on analyzing the efficiency of algorithm-based solution methods. I'll read it over before commenting on it more.


----------



## Christopher Mowla (Aug 17, 2014)

I found out today that there is an undergraduate elective course on permutation puzzles at a Canadian university for those who wish to minor in mathematics.

You can download the course text from this page. I have only glimpsed at it, but Jamie speaks in an easy-to-understand language and uses plenty of visuals. It's interesting to note that he calls each cube law a "Fundamental Theorem of Cubology" and that he seems to use his own notation for presenting some concrete concepts in abstract form. This clearly seems to be a different presentation of the material, and thus I believe it was certainly worthy to let you all know about it.

Jamie has also recently posted two YouTube videos on twisty puzzles. They are very well-made, despite that they present very elementary content. (Video 1)(Video 2) I'm looking forward to the rest of the series!


----------



## Christopher Mowla (Dec 10, 2014)

I accidentally stumbled upon this short paper by Googling "4x4x4 method analysis" and clicking the first search result. (It takes a while to load on my browser, and thus it might be the case for others.) It's by two students at a university in Sweden for a bachelor's of science joint research project in 2013.

It is about comparing the efficiency of the 3x3x3 Reduction method (pure reduction) with a K4 variant via computer implementation testing of approximately 10,000 solves. (From what I gather, the only difference between the "Big Cube Solution" and K4 is that the first layer cross dedges are paired after all 6 centers are complete.)

The algorithm they implemented (which was not disclosed in the paper) for method step execution is far from optimal (see the results in the "Discussion" section on page 28 of the PDF/page 25 of the paper), although they do seem to be closer to the move count of actual human _speed_ solves.

For the "Big Cube Solution", they might have used my F3L algorithm set to solve two wings simultaneously in the E layer and my and/or Thom's last layer ELL algorithms, as they mention using a set of algorithms for each step. However, seeing their upperbound move count, I am also doubting that.

Regardless, it's interesting to see some analysis on 4x4x4 human solving methods, and therefore I thought I would share it.


----------



## Christopher Mowla (Jan 16, 2016)

People on reddit are excited about this paper published in 2012.

This is what the author claimed about his work (on reddit). (You can read more in the abstract.)


Xiphias said:


> Rubik's cube can be realized as a semi-direct product between its subgroup of orientation and its subgroup of permutations [...] It has been done before, but not using the functions for orientation that I introduced, and according to my mentor, was not done properly until now.



He apparently used this for his master's thesis.
Also, here are some other papers that I found in the past year (I've been curious to see what's out there in comparison to my paper/book) that I never got to posting here (which might be of interest for those who don't know about them already).

I'm not for or against any of these papers (I didn't read them. I just skimmed through them, to be honest). I just want to let some know what's out there.

Move-count means with cancellation and word selection problems in Rubik's cube solution approaches
by Joseph Miller for a Phd disseration in 2012.

Rubik’s Cube Extended: Derivation of Number of States for Cubes of Any Sizeand Values for up to Size 25x25x25
by Ken F. Fraser (Revised in 2014.)

An Evolutionary Approach for Solving theRubik’s Cube Incorporating Exact Methods
by Nail El-Sourani, Sascha Hauke, and Markus Borschbach (2010)
and their follow-up paper (also published in 2010)
Design and Comparison of two EvolutionaryApproaches for Solving the Rubik's Cube

Rubik's Solving Approach by Edge-Centric Matching In Artificial Intelligence
by Hareesh B. N, Sangappa Kuragod, Mahesh K. Kaluti (2015)

The Rubik'S Crypto-Cube: A Trans-Composite Cipher
by Daniel R. Van der Vieren (2010)

Rubik's for Cryptographers: In Paper form|In article form
by Christophe Petit and Jean-Jacques Quisquater (2011)

Search methods for general permutation problems (Bachelor's thesis)
by Arthur Toenz (2012)

Zero Knowledge with Rubik's Cubes and Non-Abelian Groups
by Emmanuel Volte, Jacques Patarin, and Valerie Nachef (2011 or later)

On Rubik's Cube
by Olof Bergvall, Elin Hynning, Mikael Hedberg, Joel Mickelin, and Patrick Masawe (2010)

Higher Mathematical Concepts Using the Rubik's Cube
by Pawel Nazarewicz (2002)

The following isn't a paper about the Rubik's cube, but by the author solving twisty puzzles, he got an idea on how to expand on an old number theory topic. (For more info, read this paper, and watch this video, describing the background of what got him started in writing the following paper which ultimately earned him a fields medal in 2014.)

Higher composition laws I: A new view on Gauss composition, and quadratic generalizations
by Manjul Bhargava (2001)
Here are some papers on commutator theory (but the Rubik's cube is not mentioned: these are just math papers on permutations)

On Commutators in Groups (This paper talks about the history of commutators as well.)
by Luise-Charlotte Kappe and Robert Fitzgerald Morse (2004 or later)

Odd permutations are nicer than even ones
By Robert Coria, Michel Marcusa, and Gilles Schaeﬀer (2014)

Even Permutations as Conjugates of Two Conjugate Cycles (This was the work cited in the "My Ultimate Commutator Challenge Thread")
By Edward Bertram (1969)

_I believe the following are derivative works of the above._

Permutations as product of conjugate infinite cycles
By Edward Bertram (1971)

All even permutations with large support are commutators of generating pairs
by David Zmiaikou (2014)

A Property of Alternating Groups
by Henry Cejtin and Igor Rivin (2014)

Lastly, here's a paper on discussing constructing computer-assisted proofs. I thought since the proof that God's number is 20 (htm) and 26 (qtm) were proved in this manner, this might be interesting to some.

Future Prospects for Computer-Assisted Mathematics
by David H. Bailey and Jonathan M. Borwein (2005)


----------

