(My) Rubik's Cube Solution

  • At the first sight, my (favourite) method to solve the Rubik's cube looks like a mix of (or it was inspired by) Adam's method, Roux method and Salvia's method. It solves the cube in parts, by maneuvering that the previously solved parts would not be disturbed, or would be disturbed only minimally (if unavoidable).

  • The method reuses algorithms for permuting (PLLC) and orienting (OLLC) the last layer corners as from the Corners First approach. However, it utilizes the fact that algorithms do not only preserve the first layer corners but also the two particular edges from the first and two from the second layer.
  • Hence the method starts by solving those four edges followed by the first layer corners making an incomplete First Two Layers (iF2L). It continues with the second layer corners, followed by the four remaining edges from the left and right layers. It ends up by solving the four middle edges (midges) from the vertical M-slice in a sandwich between the R and L layers.

  • The method builds the cube in eight steps as listed below, with a Java simulation showing the whole process in action:
    1. Left and right edges in D-layer together with the three adjacent centres
    2. Left and right edges in B-layer (together with the centre between them)
    3. All four corners in D-layer
    4. Positioning U-layer corners (PLLC)
    5. Orienting U-layer corners (OLLC)
    6. Four remaining edges in R and L layers, left/right pairwise
    7. Orienting M-layer edges (OMLE)
    8. Positioning M-layer edges (PMLE)

  • The solved portions are illustrated upon the 2nd, 3rd (two views), 5th and 6th step. For convenience, first three steps are worked out on the upper half of the cube, and only then we rotate the cube to get it really down into the first two layers:

  • First three steps are intuitive, as well as the sixth step.
  • A single algorithm (or its inverse) can be applied once or twice to cover all the OLLC cases (and similarly for PLLC, OMLE and PMLE cases) but we have also direct and optimized algs per each case. All together, minimum four algs are enough to be memorized for the whole method.
  • Algorithms for PMLE are short and intuitive (IMHO, no need to memorize them). Algs for OMLE are not long either (8 to 11 slice turns) and hopefully they can be also understood intuitively.
  • Two algorithms for PLLC are simple and ergonomic: we have more freedom compared to e.g. Beginner's method or other methods leaving the 3rd layer for last, since the incompletness of F2L (DF, DB, FR and FL edges are missing), and since the U-layer edges and corners are not yet oriented.
  • For OLLC we share the well known Sune™ algorithm by L. Petrus to twist three by three corners. However, twisting of e.g. two pairs of opposite corners can be done by a direct short alg, since the F2L was not completed before.
  • With a look-ahead experience and following the provided 11 (eleven) optimized algs (and their inverses), the cube can be solved in cca 55 face and slice turns. It could be reduced by half a dozen turns if PLLC and OLLC as well as OMLE and PMLE steps would be coupled together (resulting with more cases to be recognized and more algs to be memorized) - however, the challenge of intuitive approach would be completely lost.
  • Singmaster's notation etc.

    1. First two opposite edges

  • For (beginner's) convenience during the next two steps, keep the two just solved edges temporarily left, front and back on the equator. Left handed person will keep them on the right, front and back also on the equator.
  • The next two edges will be solved as in the upper layer, front and back, and corners in the 3rd step will be also solved in the upper layer. Then we will turn the cube upside-down and around, that the solved four edges and corners form the proclaimed incomplete First Two Layers.

  • 2. Second two opposite edges

    3. First four corners

  • For the next two steps turn the cube that previously solved corners go to the bottom. The optimized PLLC and OLLC algorithms (except for Sune™ and Antisune™) utilize the structure of incomplete F2L and require no (solved) edges in the F layer and M slice to take care about.
  • Now, the cube should be oriented that the four solved corners go to the bottom layer and that the four solved edges go left and right on the equator, into the first two layers. Whenever it would be necessary for PLLC or OLLC cases and their corresponding algs, turn the U layer around for preparation.

  • 4. PLLC on iF2L

    5. OLLC on iF2L

    6. (Two) pairs of left/right edges

    7. OMLE

    8. PMLE

  • M turns accumulated through the steps 6 to 8 should be compensated by the final, one-time M-slice alignment.
  • Observe that the fourth PMLE case does not require prep turns. To avoid cube rotations or M turns as preps for the first three cases, one can replace F turns in the algs by appropriate U, B or D turns. E.g., <B2> M performs similar clockwise 3-cycling, just leaving a different, fourth, fixed midge.

  • Closing notes

  • Provided algs were analysed and optimized thanks to J. Jelinek's command-line ACube solver. E.g., inputs: "@? @? @? @? @? @? @? @? @? @? @? @? @ULF @URB @UBL @UFR !!" and "@? @? @? @? @? @? @? @? @? @? @? @? @UBL @URB @UFR @ULF !!" result with the left-handed PLLC algorithms as above.
  • Hence, even in the pure Corners first method, two 3rd layer corners cannot be swapped more efficiently. Since these algs are also not invariant on the FL and FR edges, more complicated (and longer) PLLC algs are required when F2L are solved completely before.

  • Illustrated by Java animated AnimCube by courtesy of J. Jelinek

  • I. Penzar, Aug 13, 2013, ver. 1.03
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