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FMC Reconstruction 1

Here is an educational FMC reconstruction for an actual solve during a competition.

The scramble:

R' U' F D U2 L2 U2 B' D2 R2 F2 R2 B' L' D F' L D' L F2 R' U' F

The 30 move solution:

U2 R' U' L D B' D B U2 B' L' D L2 D' L D L2 F L F' D' B2 L U' L2 U D B' L B2


The method is block building + NISS.

We start with a 5 move X-Cross:

U2 R' U' L U2

And do not notice a good enough continuation within reasonable time, therefore, considered NISS.

The original problem is to find x, so that scramble * 5 move X-Cross * x = Identity

With NISS, we try to find y which solves the new scramble 5 move X-Cross inverse * scramble inverse.

Then y inverse will be the x, and the solution will be 5 move X-Cross * y inverse.

The NISS scramble (denote as A):

U2 L' U R U2 F' U R F2 L' D L' F D' L B R2 F2 R2 D2 B U2 L2 U2 D' F' U R

With this scramble, we may apply B2 L' B D' to solve 2x2x3 (with a D2 prescramble).

Then U' L2 U L' B2 solve all but last F2L (with a B D2 prescramble).

Then no promising continuation was found, therefore, we apply NISS second time.

With some intuition, realized D' B D' is a better prescramble with NISS.

The (secondary) NISS scramble (denote as B):

B2 L U' L2 U D B' L B2 + R' U' F D U2 L2 U2 B' D2 R2 F2 R2 B' L' D F' L D' L F2 R' U' F + U2 R' U' L U2 + D B' D

The solution (except for 3c) is:

L' D L2 D' L D L2 F L F' D'

Very luckily solving the F2L directly solve everything but 3 corners.

We produce the 28 move skeleton as:

U2 R' U' L U2 D B' D L' D L2 D' L D L2 F L F' D' B2 L U' L2 U D B' L B2

We are now already guaranteed (most likely) 28 + 8 = 36 move solution, although most likely better.

We luckily found an insertion at U2 R' U' L U2 D + insertion + B' D L' D L2 D' L D L2 F L F' D' B2 L U' L2 U D B' L B2, the insertion is U2 B' D B U2 B' D' B

The last 2 moves D' B cancels perfectly with B' D (4 move cancelled), which gives us:

U2 R' U' L U2 D U2 B' D B U2 B' L' D L2 D' L D L2 F L F' D' B2 L U' L2 U D B' L B2

Even better, notice U2 D U2 is actually redundant, and can be simplified as D!

Therefore, we can cancel 2 more moves, and get an incredible 6 move cancellation!

The final answer is: U2 R' U' L D B' D B U2 B' L' D L2 D' L D L2 F L F' D' B2 L U' L2 U D B' L B2

FMC Reconstruction 2

Here is another FMC reconstruction for a normal practice.

Scramble: R' U' F L D F2 D2 B U' F B2 R' L' D2 B2 R F2 B2 D2 R' D2 L B' U2 R' U' F

The 29 move solution: F' U2 F2 L' U R D' R F' R' F B R U' B U B D B L B' L' D' R' B R B R' B'


First we build blocks as:

  1. F' U2 F2 L' U for 2x2x2 block
  2. R D' R F' R' F for 2x2x3 block
  3. B R U' B U for F2L except last slot

Then we explored different strategies, but decided it's not a good enough case. So we applied NISS:

NISS scramble: U' B' U R' B' F' R F R' D R' U' L F2 U' R U2 B L' D2 R D2 B2 F2 R' B2 D2 L R B2 F' U B' D2 F2 D' L' F' U R

With the NISS scramble, we can do the last F2L with B R B' R' B' R

And the OLL is a 6-mover. We notice the bar and decided to apply via the mirror algorithm that preserves the bar:

D L B L' B' D'

And we end up with a PLL skip!! B' finishes the solve.

Now we simply clean up the solution as the original block + inverse of the solution after NISS.