Message #4064

From: Marc Ringuette <>
Subject: 2x2x2x2: U2 parity
Date: Sat, 14 Jul 2018 10:47:26 -0700

Hi, Andy,

That 8 move U2 parity algorithm is so much better than the 18 move one
that I had come up with, thanks!  And it is easy to tweak to maximize
cancellations as below.

Your idea of coming up with a complete list of "PBL plus parity" algs,
to avoid ever inserting an explicit parity step, is pretty fancy.   In
lieu of the fancy approach, I think I’ll use this method when I’m trying
to minimize moves:

(1) Solve each subcube to "1 turn away from solved" counting parity of each.
(2) Mentally find the shortest solution to the full puzzle ignoring
parity.   It will be a trivial solution of <=4 moves.   Count parity of
that solution.
(3) If parity would be off, insert a variant of the parity algorithm
(either R2 F2 R2 U’ R2 F2 R2 U’, or R2 F2 R2 U R2 F2 R2 U, or U’ R2 F2
R2 U’ R2 F2 R2) on one of the subcubes now, cancelling the last move of
the parity algorithm with the first move of the computed solution
whenever possible.
(4) Finish the solution.


On 7/13/2018 8:11 PM, Andy F [4D_Cubing] wrote:
> … As for solving the U2 parity …
> (R2 F2 R2 U’)2
> On 7/12/2018 6:51 PM, Marc Ringuette
> <> [4D_Cubing] wrote:
>> 25 Alg for final U2 on R cube (18 moves)   1m16s