Snyder Method

The Snyder Method, invented by Anthony Snyder in 1982, is both a fewest moves and a speedsolving method for the 3x3x3 cube. It is based on blockbuilding and can be compared to Petrus and the Heise Method
Contents
The steps
 1. Form a 2x2x2 block, optionally an Xcross.
 2. Use any variety of methods to solve the rest of F2L, except for one slot.
 3. Solve the final pair and insert it while simultaneously orienting and placing a minimum of one last layer edge. (Anthony has since added optional starts using a 1x2x3 or a 2x2x3, also with or without the cross.)
 4. Orient and permute all the last layer edges, plus one corner.
 5. Solve the last three corners.
Claimed advantages
A salient characteristic of the Snyder Method is to orient and permute each piece at each stage simultaneously. Anthony claims several advantages for this:
 Simultaneous orientation and permutation helps to visualize piece relationships, useful to intuitive solving.
 There is a mathematical advantage.
Furthermore, all such lastlayer algorithms will be a subset of 1LLL, making the Snyder Method a possible candidate as an intermediate method for 1LLL.
Though there are many cases to first solving the LLE+1C, the more common cases can generally be solved in 610 turns, making it quite turn efficient.
Although the Snyder Method closely resembles the Petrus Method in its F2L approach, its lastlayer method differs considerably. This lastlayer method was independently proposed in 2005 by Kenneth Gustavsson, who called it "Fish & Chips."
A word about algorithms
Anthony found almost all of his algorithms independently and without computer aid, and claims that his method is one of the most efficient based primarily on humangenerated algorithms. Anthony explained this as follows: "In the 80's there was a general stereotype that using a computer was cheating, plus [I] enjoyed thinking up [my] own algorithms." However, he plans to upgrade his method using a computer in the near future.
Variations
The Snyder Method allows a number of variations to be applied wherever convenient.
 when a 2x2x3 block is not immediately apparent he will start with either a 1x2x3 or a 2x2x2, then immediately finish the 2x2x3 block with a second look, or, he puts together several CE pairs as in Heise, then assembles those into a F2L minus one CE
 two or more CE may be solved simultaneously to complete the F2L faster
 the LL may be solved in 1 look rather than 2, using either a shortestmove algorithm, combination, or substitution
In the early 80's, Anthony developed a complete set of fewestmove solutions for the CE pair cases and for the last three corners cases. However, he relied more extensively on the use of combinations and exchanges to efficiently put in the LL edges + corner. He makes up for this with a large selection of approximate directsolves on the entire LL, claiming to switch to this mode about 20% of the time.
This method requires 12 looks for the block+cross start, then up to 1 look each for the 13 CE pairs, then 12 looks for the last layer. Though there are a lot of looks, an attentive solver can be quite efficient, and average around 40 turns. Though a beginner will likely take a lot more than this, and a pro taking their time may get his/her average down to about 36. Many of the shorter algorithms were added throughout the 80's and 90's, and the library of LL direct solves were mostly added in the 00's.
Publication
In 1981 he printed his simple solution, a 7 algorithm system that is easy to learn. It was entitled, "Tony Snyder's Simplest Solution to Solve a Rubik's Cube", and though he personally only taught a handful of people this technique, a classmate took a copy and passed it out to students in a number of schools. He has not yet put to print his advanced technique.
Note: Having complete sets of short algorithms was very unusual in the 1980s (combining 2 algs in 1look was a common solution). Kenneth Gustavsson suggested the same LLmethod ('Fish & Chips') in 2005 but with VHF2L and the rest in two clearly defined steps, EP + 1 corner (36 cases, the 'fish' step) and then L3C (22 cases, the 'chips' step), this makes a 2look ZBLL, often a little more effective than COLL/EPLL.
Example solves
Here are some of Anthony's solves.
 The Snyder Method
 A newer demo, easier to see
 5 solves using Snyder Method 2, showing how fast it is despite his handicaps.
See also
If you have edges oriented when starting the last layer you can often do using only Sune, double Sune (or inverse and/or mirrors), JPLL a/b or UPLL a/b for the first look. Here are a couple of examples that show how this is done:
Scramble Solution F U F' L2 B' U' B U L2 F U' F' U AUF to UPLL a on the left side, (L3C 3twist). L' U R U' B2 U' B2 U B2 R' L U' AUF JPLL b, (L3C 'Anti Niklas') B' F R2 U' R2 U R2 U F' U' B U' JPLL b, (L3C Niklas) R2 F2 R2 U R' F2 R U' R2 F2 R U R U left side double Antisune (L' U2 L U...) R' F U2 F U L' U L F U' F U F R U2 left side double Antisune (again!) B L2 F' D F' D' F2 L2 B' U' y JPLL a (setup L' before the y for 1LLL) L U2 L D' B2 D L' U2 L D' B2 D L2 U' y2 left Antisune.
Sometimes more than one of these solutions are possible. Working like this solves the step in an easy 2:5 times, maybe more. It is effective, fast and OHfriendly, but recogniton for the sune/doublesune cases is horrible without loads of practice. For the cases where two opposite edges needs to be swapped COLL is a recommended alternative and for the cases with edges correct, one or two look L4C.
External links
 Speedsolving.com: Tony Snyder solves the cube
 Speedsolving.com: Reconstructions
 Speedsolving.com: Five more reconstructions
 blog.naver.com (korean, 3LLE+1C): [1] [2] [3] [4]