(T), Bottom (B), Left (L), Right (R), Front (F), and Posterior (P), with + for clockwise, – for anticlockwise, and 2 for 180-degree turns. Another notation appeared in the 1982 "The Ideal Solution" book for Rubik's Revenge. Horizontal planes were noted as tables, with table 1 or T1 starting at the top. Vertical front to back planes were noted as books, with book 1 or B1 starting from the left. Vertical left to right planes were noted as windows, with window 1 or W1 starting at the front. Using the front face as a reference view, table moves were left or right, book moves were up or down, and window moves were clockwise or anticlockwise. Period of move sequences The repetition of any given move sequence on a cube which is initially in solved state will eventually return the cube back to its solved state: the smallest number of iterations required is the period of the sequence. For example, the 180-degree turn of any side has period 2 (e.g. {U2}2); the 90-degree turn of any side has period 4 (e.g. {R}4). The maximum period for a move sequence is 1260: for example, allowing for full rotations, {F x}1260 or {R y}1260 or {U z}1260; not allowing for rotations, {D R' U2 M}1260, or {B E L' F2}1260, or {S' U' B D2}1260; only allowing for clockwise quarter turns, {U R S U L}1260, or {F L E B L}1260, or {R U R D S}1260; only allowing for lateral clockwise quarter turns, {F B L F B R F U}1260, or {U D R U D L U F}1260, or {R L D R L U R F}1260. Optimal solutions Although there are a significant number of possible permutations for Rubik's Cube, a number of solutions have been developed which allow solving the cube in well under 100 moves. Many general solutions for the Cube have been discovered independently. David Singmaster first published his solution in the book Notes on Rubik's "Magic Cube" in 1981. This solution involves solving the Cube layer by layer, in which one layer (designated the top) is solved first, followed by the middle layer, and then the final and bottom layer. After sufficient practice, solving the Cube layer by layer can be done in under one minute. Other general solutions include "corners first" methods or combinations of several other methods. In 1982, David Singmaster and