Layer By Layer
The first known publication of the Cross and Layer By Layer method appears in 1978 by Donald Taylor.
This information is from David Singmaster's Notes on Rubik's 'Magic Cube'.
The Group of a Coloured Cube (1978)
For verification, I contacted Georges Helm about the steps in The Group of a Coloured Cube. He kindly wrote out the steps. Helm's notation is K for edges, E for corners, P for permute, and O for Orient, and the numbers on the left indicate the layers. The picture above that he provided confirms Donald Taylor's steps.
About Donald Taylor.
David Singmaster published a Layer By Layer method in September 1979 in Notes on Rubik's 'Magic Cube'.
David Singmaster was initially using a Corners First method.
This is from page 16 and is dated 23 February 1979 on page 22.
There are two dates provided on page 22. The February date can be confirmed by reading his interview on TwistyPuzzles.com where he states "I then developed my solution method, looking for techniques that did not require major memorization. I produced a method using two basic processes: (F2R2)3 and the commutator [F,R], but it took some some fiddling. This appeared in the first version of my Notes in Feb 1979."
David Singmaster changed his method to a Layer By Layer method in September 1979.
This is dated 23 September 1979 on page 29.
This is confirmed in the TwistyPuzzles.com interview by the statement "The next major insight was the use of double level commutators. I recall Peter McMullen telling me about the Cambridge group using moves that only affected one or two U pieces. At first this seemed silly, but then commuting this with U gives easy useful processes. I realised that the square and the cube of the commutator [F,R] gave easy moves that affected just one corner in the L face and this allowed me to produce easy processes for moving and twisting corners. From this, I built up the method given in my Notes, initially in Oct 1979, then developed in detail and made into a separate handout in Aug 1980."
David Singmaster states that he was aware of Layer By Layer methods from others before he started using it.
This appears in the same section as the description of his Corners First method dated 23 February 1979, before he changed to a Layer By Layer method.
It seems that David Singmaster developed his Layer By Layer method based on the other Layer By Layer methods that he had seen others using. Looking at his statement, from before he published his own Layer By Layer method, that others had been using Layer By Layer methods.
Other Layer By Layer methods were published in 1979
Gaskin, John: Cubist Rescue Service -Emergency Kit – 1979 (unknown month)
Steps: First layer edges, first layer corners, second layer edges, orient then permute last layer edges, permute then orient last layer corners.
Sweenen, John: The Hungarian Magic Cube - A Solution – 1979 (unknown month)
First layer edges, first layer corners, three second layer edges, permute then orient last layer corners, final second layer edge, permute then orient last layer edges.
Nelson, Roy: The Hungarian Cube - Nov-79
First layer, second layer, orient last layer corners, permute last layer corners, orient last layer edges, permute last layer edges.
An early version of Keyhole appears in 1981.
This is from the September 1981 issue of Cubism For Fun.
Marko Eekelen published a 1981 book titled Het Geheim Van De Wonderbaarlijke Kubus (English: How to Solve the Cube Puzzle). The method follows the below steps:
1. Edges of the first layer.
2. Three edges of the second layer.
3. All corners of the first layer. This uses the empty edge slot of the second layer as the keyhole.
4. Last edge of the second layer.
5. Last layer typical of other Layer By Layer methods at the time.
The September 1981 issue of Cubism For Fun provides an upgrade to Eekelen's method.
This one is more like the current basic keyhole methods.
1. Layer minus one corner.
2. Three edges of the second layer.
3. Last corner of the first layer.
4. Last edge of the second layer.
5. Last layer.
Keyhole also appears in March 1981 in Pierre Julien's Le Cube Hongrois.
It is also mentioned in the Blibliography of Notes on Rubik's 'Magic Cube'.