Editing David Singmaster (section)

==Rubik's Cubes==
{{quote box
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| quote = The power of [[Conjugacy class|conjugation]] ... was the last point I understood; I remember lying awake thinking about it, seeing that I could move any four edges into the working locations and realising that this completed the general method for restoring the cube to its original state.
| source=&ndash;David Singmaster, ''[https://books.google.com/books?id=_n1vr0_RbXoC&pg=PA786 Moral and Mathematical Lessons from a Rubik Cube]'', [[New Scientist]], 1982
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Singmaster's association with [[Rubik's Cube]]s dates from August 1978, when he saw a Cube (at that time a rarity) at the [[International Congress of Mathematicians]] in [[Helsinki]].<ref name="twisty">{{Cite web|url=http://www.twistypuzzles.com/articles/spotlight-singmaster/|title=Interview with David Singmaster|publisher=Twisty Puzzles|access-date=4 January 2017}}</ref> Some other mathematicians at the conference, including [[John Horton Conway|John Conway]] and [[Roger Penrose]], already had one.<ref name="twisty"/>

Singmaster quickly acquired a Cube (in exchange for a copy of an [[M. C. Escher]] book) and was able to solve it by early September 1978.<ref name="twisty"/> He said that it took him "two weeks, on and off" to find a general solution for the Cube.<ref>{{Cite news|url=http://www.upi.com/Archives/1981/08/24/Now-meet-Rubiks-snake-Bigger-than-Rubiks-cube/9742367473600/|last=Jensen|first=Gregory|title=Now meet Rubik's snake – 'Bigger than Rubik's cube!'|date=24 August 1981|publisher=United Press International}}</ref> He devised his notation for recording moves (now known as the Singmaster notation) in December 1978.<ref name="morallessons">{{Cite news|last=Singmaster|first=David|title=Moral and Mathematical Lesson from a Rubik Cube|page=787|date=23 December 1982|newspaper=New Scientist|url=https://books.google.com/books?id=_n1vr0_RbXoC&pg=PA786}}</ref> In June 1979 he wrote one of the first articles about the Cube in ''[[The Observer]]'' newspaper.<ref>{{Cite news|author=David Singmaster|title=Six-sided magic|publisher=The Observer|date=17 June 1979}}</ref>

In October 1979, he self-published his ''Notes on the "Magic Cube"''.<ref name="publ">{{Cite web|url=http://anduin.eldar.org/~problemi/singmast/pubchron.html|title=Publications of David Singmaster|date=4 August 1996|publisher=anduin.eldar.org|archive-url=https://web.archive.org/web/20170116155532/http://anduin.eldar.org/~problemi/singmast/pubchron.html|archive-date=2017-01-16}}</ref> The booklet contained his mathematical analysis of Rubik's Cube, allowing a solution to be constructed using basic [[group theory]].<ref name="review">{{Cite news|author=<!--Staff writer(s); no by-line.-->|title=Review – Restore your cube|page=802|date=24 September 1981|newspaper=New Scientist|url=https://books.google.com/books?id=_0beD5LVNugC&pg=PA802|access-date=30 August 2017|archive-date=18 August 2020|archive-url=https://web.archive.org/web/20200818162232/https://books.google.com/books?id=_0beD5LVNugC&pg=PA802|url-status=dead}}</ref> In August 1980 he published an expanded 5th edition of the book retitled as ''Notes on Rubik's "Magic Cube"''.<ref name="publ"/> It included the results of his correspondence with other "cubologists", and included details on monotwists, U-flips, [[Cayley graph]]s, and [[wreath product]]s.<ref name="review"/> The book contained his own "step by step solution" for the Cube,<ref name="linkedresources" /> and it is accepted that he was a pioneer of the general [[Layer by Layer]] approach for solving the Cube.<ref name="ryanheise-beginner"/> The book also contained a catalogue of pretty patterns including his "cube in a cube in a cube" pattern which he had discovered himself "and was very pleased with".<ref>{{Cite web|url=http://www.cube20.org/cubelovers/CL26/015.txt|author=David Singmaster|date=8 October 1998|title=Davenport's pattern|publisher=cube20.org}}</ref> In 1981, at the height of the Rubik's Cube craze, the book was republished by [[Penguin Books]], with a US edition by [[Enslow Publishers]].<ref name="publ"/> There were also Dutch and Spanish translations.<ref name="publ"/> He estimated that he sold around 50 to 60&nbsp;000 copies of his book.<ref name="twisty"/> Much of the mathematical content of the book was later reworked by Alexander H. Frey in collaboration with Singmaster to create their ''Handbook of Cubik Math'' published in 1982.

Singmaster was described as "one of the most enthusiastic and prolific promoters of the Cube".<ref>{{Cite book|last=Lees-Maffei|first=Grace|title=Iconic Designs: 50 Stories about 50 Things|page=140|year=2015|publisher=Bloomsbury|isbn=978-0857853530}}</ref> In September 1981 he was said to be devoting "almost 100%" of his time to promoting, reporting, marketing and analysing the Cube.<ref name="herman">{{Cite news|url=https://books.google.com/books?id=jpr_dn_0IfEC&pg=PA678|last=Herman|first=Ros|title=Cubic mastery|date=10 September 1981|newspaper=New Scientist|access-date=4 January 2017|archive-date=19 August 2020|archive-url=https://web.archive.org/web/20200819133107/https://books.google.com/books?id=jpr_dn_0IfEC&pg=PA678|url-status=dead}}</ref> He soon began publishing a quarterly newsletter called the ''Cubic Circular'' which was published between 1981 and 1985.<ref name="twisty"/><ref name="herman"/>