Warning: include(header.php): failed to open stream: No such file or directory in /home3/makisumi/public_html/bld/misc.php on line 15

Warning: include(header.php): failed to open stream: No such file or directory in /home3/makisumi/public_html/bld/misc.php on line 15

Warning: include(): Failed opening 'header.php' for inclusion (include_path='.:/opt/php54/lib/php') in /home3/makisumi/public_html/bld/misc.php on line 15

Miscellaneous Blindfold Cubing Techniques

This is where I'll put the more advanced blindfold cubing techniques (including ones that I don't use). Many of these will probably be taken from the Blindfold Cubing Forum. Keep an eye on that forum for a discussion of the cutting-edge techniques and new ideas in blindfold cubing, both for 3x3 and for bigger cubes.

Menu

Damage Control Techniques
Pick-Up Cycling

Execution Techniques
All possible double transposition of corners involving both U and D
Breaking into a new cycle
Two-Step Corner Orientation

Damage Control Techniques

Pick-Up Cycling

If we finish reducing both corner and edge permutation and our memory indicates that we have an odd number of 2-cycles remaining, we have made an error memorizing or updating the permutation. In this situation, it is often the case that we have skipped over one piece in a particular cycle. This situation can easily be fixed with the following technique.

Say we have the cycle (ABCDEFG) and forget B. Since we believe that the cycle is (ACDEFG), we perform (ACD) and (AEF) to reduce this to (AG). Skipping over B actually leaves an additional cycle called "pick-up cycle," (BC), formed from the piece we forgot and the piece that directly follows it in the original cycle. Rather than reversing the two cycles we performed and starting from the beginning, we can solve fix our mistake with the double transposition (AG)(BC). If we forget two consecutive pieces, the pick-up cycle is formed from these two pieces and the piece directly following them in the original cycle.

The same rule applies no matter how many pieces we forget. For example, say we leave out B, E, F, and I in the cycle (ABCDEFGHIJ). Since we believe that this cycle is (ACDGHJ), we perform (ACD) and (AGH) to reduce this to (AJ). In reality, we must additionally perform the three pick-up cycles (BC), (EFG), and (IJ). Here, (IJ) must be performed after (AJ), which is the same as performing (AIJ).

This technique can also be used when we cannot recall one piece in a cycle. Rather than stopping while trying to remember this one piece, we can go on with the rest of the cycle and return to the pick-up cycle when we recall the forgotten piece. In the case that we forget a piece in an odd cycle, we can keep the excution easy by pairing off the pieces after the first one in the cycle. For example, say we forget B in the odd cycle (ABCDE). While (ACD) leaves a possibly difficult double transposition (AE)(BC), performing (ADE) will leave a simple 3-cycle (BCD). Memorizing cycles in pairs make the secord approach very natural; instead of talking about one forgotten piece, we deal with a pair of pieces of which one was forgotten.

Excution Techniques

All possible double transposition of corners involving both U and D

3 corners in one layer

CP(24)(37): (RB'R'B)*3 CP(34)(26): (U2'RU'R'U'RU'R')*2 (inverse of Joel van Noort's) CP(34)(15): (U2'L'ULUL'UL)*2 (mirror)

2 corners in U, 2 corners in D (diagonal/diagonal)

Case 1 = CP(26)(48): B'-(RUR'U')*3-B or B'-(URU'R')*3-B
Case 2 = CP(24)(68): L2-(X on F face)-L2

2 corners in U, 2 corners in D (adjacent/adjacent)

Case 3 = CP(12)(56): D2B2-(E permutation)-B2D2
Case 4 = CP(26)(37): B-(RUR'U')*3-B'

Case 5 = CP(16)(25): (X on F face)
Case 5' = CP(16)(47): (RU'R'U)*3(R'URU')*3

2 corners in U, 2 corners in D (adjacent/diagonal)

Case 6 = CP(25)(37): L2-(Q)-L2
Case 7 = CP(24)(56): L2DR2-(Q)-R2D'L2

Breaking into a new cycle

Anyone who uses the Pochmann method is already familiar with this concept for 2-cycles. This also works for and can be useful with 3-cycles.

Say we need to solve the cycles (AB)(CDEF). Doing (ABC) breaks into a second cycle and leaves us with (ADEFC). Note that C, which we used to break into the second cycle, must be attached to the end of the cycle. In 3-cycle methods, this allows us to avoid leaving 2-cycles unsolved in even cycles. In effect, we replace the double transposition (XY)(ZW) with two 3-cycles, (XYZ)(XWZ). This is especially useful for 4x4, where double transpositions are hard to set up.

Two-Step Corner Orientation

Corner orientation where the sum of the orientations of the U corners is not divisible by 3 has always caused me troubles. For this reason, I have tried to systemize the process by solving corner orientation in at most two algorithms.

There are four groups of algorithms.

Group 1

RUR'URU2'R'-U-R2U'R'U'RURURU'R-U (Sune, U, PLL U, U)
L'U'LU'L'U2L-U'-R'UR'U'R'U'R'URUR2-U' (Sune, U', PLL U, U')
FRUR'U'RUR'U'F'-RUR'U'RwR'URU'R'w or RU-R2U'R2'U'R2U2'R2U'-R'URU2'R'U

Group 2

The two usual commutators for corner orientation:
U'R'URU'R'U-L'-U'RUR'U'RU-L
L'-U'R'URU'R'U-L-U'RUR'U'RU

Group 3

A=(RU'R'UR'FRF')^2
B=(R'FRF'RU'R'U)^2

xyAy'x'
xyBy'x'

x'z'Azx
x'z'Bzx

Group 4

RU2'R'U2-RUR'U'-RU2'R'U2-RUR'U'
RU'-R'U2RU2'-R'URU'-R'U2RU2'-R'U
(RU'R'U-RU2'R'U2)^2
RU2'-R'URU'-R'U2RU2'-R'URU'-R'U2

We also have several cases to consider.

Case O: If the sum of the orientations of U corners is divisible by 3, solve each side separately with one algorithm from Group 1.

Case I: 1 incorrect corner on U, 1 incorrect corner on D
Use one of the two Group 2 algorithms.

Case II: 1 incorrect corner on one side, 2 incorrect corners on the other
This case can be solved easily intuitively with a set-up move and one of two algorithms rotating three corners.

Case III: 3 incorrect corners on either U or D
Flip the cube so that this side is on top. Use a Group 3 algorithm to fix this face. We then need to just check the orientation of the other three D corners besides DRF; this last orientation must make the sum of the D orientations divisible by 3, and then the D orientations can be solved by a Group 1 algorithm. If there is only one incorrect corner on the side without three incorrect corners, we bring this corner to DRF and solve the orientation in one step.

Case IV: 4 incorrect corners on either U or D
We proceed just as in Case III but with a Group 4 instead of a Group 3 algorithm.

Case V: 2 incorrect corners on both U and D

There are thirteen cases to consider.

Although I came up with this approach independently, I was not the first to explore this idea. Chris Krueger told me that Thom Barlow had described the same approach on his now-defunct site.


Warning: include(footer.php): failed to open stream: No such file or directory in /home3/makisumi/public_html/bld/misc.php on line 325

Warning: include(footer.php): failed to open stream: No such file or directory in /home3/makisumi/public_html/bld/misc.php on line 325

Warning: include(): Failed opening 'footer.php' for inclusion (include_path='.:/opt/php54/lib/php') in /home3/makisumi/public_html/bld/misc.php on line 325