David Breyer Singmaster is a retired American mathematics professor at London South Bank University in the United Kingdom. He is most famous for being an early adopter and enthusiastic promoter of the Rubik's Cube. His Notes on Rubik's "Magic Cube" which he began compiling in 1979 provided the first mathematical introduction to the Cube as well as providing one of the first published solutions. The book contains the cube notation which has become standard. He also has a huge collection of mechanical puzzles, which he stated in 2003 contained "perhaps 3000 puzzles, of which about 400 are Rubik Cubes and variants".
Singmaster's association with Rubik's Cubes dates from August 1978, when he saw a Cube (at that time a rarity) at the International Congress of Mathematicians in Helsinki. Some other mathematicians at the conference, including John Conway and Roger Penrose, already had one. Singmaster acquired a Cube from Hungarian mathematician Tamás Varga, and was able to solve it by early September 1978, taking about two weeks to develop a general solution. He devised his notation for recording moves (now known as the Singmaster notation) in December 1978. In June 1979 he wrote the first (non-Hungarian) newspaper article about the Cube in The Observer newspaper. He became one of the most enthusiastic and prolific promoters of Rubik's Cube during the early 1980s, and for two years even ran his own puzzle company, David Singmaster Ltd, which stocked puzzles and books. Throughout this period he shared an office with Morwen Thistlethwaite another prominent Rubik's Cube theorist.
Notes on Rubik's "Magic Cube"
By February 1979 Singmaster had written in manuscript form the first version of his "Notes on the 'Magic Cube'". The booklet contained his mathematical analysis of Rubik's Cube using basic group theory. The first edition became available (by mail-order) in October 1979. The book was subsequently expanded as results of his correspondence with other "cubologists" came in. The 5th edition was published in August 1980 and was retitled as Notes on Rubik's "Magic Cube". Although self-published, it was one of the few resources available for cubers until mid-1981 when there was a sudden explosion in cubing books. Even then it was still considered by many "THE book" on the Rubik's cube, with "the history, anecdotes, the math theory, and a solution." The book pioneered the Layer by layer approach for solving the Cube, and his solution notably begins with a White Cross. In 1981, at the height of the Rubik's Cube craze, the book was formally published by Penguin Books (UK), with a US edition by Enslow Publishers. There were also Dutch and Spanish translations. He estimates that he sold around 50 to 60,000 copies of his book. 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.
The first edition (October 1979) contained 10 sections plus an addendum totalling around 30 pages. Section 4 contained the group theory and the reader was advised to "skim through it" on first reading. For those wishing to solve the Cube the most important parts were: section 3 which described the notation; section 6 which described some basic commutators demonstrating how algorithms can be constructed; and section 9 which outlined the Layer-by-layer approach and provided some improved processes. Editions two, three and four followed in quick succession (Oct 1979 to Jan 1980) and contained new material in three short addendums as information from his correspondents came in.
The most important update came in August 1980 with the fifth edition. This nearly doubled the size of the book with a lengthy Fifth Addendum. This contained many new anecdotes, processes, and other theoretical results including some details of the Thistlethwaite Algorithm. Important for cubers was a small catalogue of algorithms, many just for the upper layer including 2-cycles, 3-cycles, flips and twists. There was also a list of pretty patterns (including his "cube in a cube in a cube" pattern which he had discovered himself). For the first time there was a separate step-by-step solution guide in its own section.
Singmaster had initially solved the Cube using a Corners First method (using basic commutators and conjugates) but by 1979 he had developed a Layer by layer method. In the first edition of his Notes (October 1979) he provided an outline of the method, together with suggestions for various algorithms. His solution steps are:
- 1) Put all bottom edges correctly in place.
- 2) Put all bottom corners correctly in place.
- 3) Put middle slice edges correctly in place.
- 4) Flip top edges so all U faces are up.
- 5) Make top orientations correct. [i.e. making a single U move]
- 6) Put top edges correctly in place.
- 7) Put top corners in their right positions.
- 8) Twist top corners into their correct orientations.
For the step-by-step solution from the 5th edition see this David Singmaster's Solution as webified by Jeffrey W Baumann.
Singmaster is also famous for his Cubic Circular newsletter published 1981-5. In total five magazines were published, of which three were double issues. The newsletters, which he considered as further addenda to his Notes, are an unparalleled source of historical information about Rubik's Cube and other twisty puzzles during the 1980s Cube craze.
- Notes on Rubik's "Magic Cube", David Singmaster. 1981. Penguin Books ISBN 0-140-06149-5 / Enslow Publishers ISBN 0-89490-043-9
- Handbook of Cubik Math, David Singmaster and Alexander H. Frey. The Lutterworth Press, 1982. ISBN 0-7188-2555-1
- Rubik's Cubic Compendium, by Ernő Rubik and four others. Edited with an Introduction and Afterword by David Singmaster. Oxford University Press, 1987. ISBN 0-19-853202-4
- The Cube: The Ultimate Guide to the World's Bestselling Puzzle, Jerry Slocum, David Singmaster, Wei-Hwa Huang, Dieter Gebhardt, Geert Hellings, Ernő Rubik. Black Dog & Leventhal, 2009. ISBN 157912805X
- Cubic Circular magazine published 1981-5 by David Singmaster (available online at Jaap's Puzzle Page)
- Singmaster, D. "The Hungarian Magic Cube." Mathematical Intelligencer 2:1. (1979) p. 29-30
- Singmaster, D. "Six-sided magic." The Observer. (17 June 1979) p. 40.
- Singmaster, D. "The Magic Cube." Games & Puzzles 76. (Spring 1980). p. 4-6.
- Singmaster, D. "The educational value of the Hungarian Magic Cube. In: Proceedings of the Fourth International Congress on Mathematical Education: Berkeley, California, U.S.A., 10-16 August 1980. Published: Boston: Birkhäuser, (c. 1983).
- Singmaster, D. "The incredible cube." Games & Puzzles 81. (Summer 1981) p. 4, 5, 10.
- Singmaster, D. "Cube news again." Mathematical Intelligencer 3:3. (1981) p. 107-108.
- Singmaster, D. "Moral and mathematical lessons from a Rubik Cube". New Scientist. (23/30 Dec 1982) p. 786-791.