RKT Cancel Algorithms

These won’t help you solve a puzzle for the first time

You do not need to learn RKT cancel algs to solve any puzzle. RKT can and should be done completely intuitively unless you are already speedsolving at a high level and wish to improve this step.

• See Notation and Commutator notation first.
• Single letters represent “Big 3D” moves. (R = RO, U = UO, etc.)

RKT Cancel Algorithms

4⁴ edge swap parity

Image	Description	RKT Cancel Algorithm
	UF and UR edges swapped	[f' l': [[r' U' l': D2], Iy2]]

F2L triggers

Image	Description	2RKT Cancel Algorithm
	Made Insert	R {1-2}Ozx2 U' R' {1-2}Ozx2 U
	Split Insert	{1-2}Ozx2 R U {1-2}Ozx2 R' U'
	Double Sexy	R U R' U' {1-2}Ozx2 R U R' U' {1-2}Ozx2

EOLL

Image	Name	RKT Cancel Algorithm
	Dots	F (R U R' U') F' 2Oy2 Fw (R U R' U') Fw'
	L	F ({1-2}Ozx2 U R {1-2}Ozx2 U' R') F'
	Line	F (R U {1-2}Ozx2 R' U' {1-2}Ozx2) F'

OCLL

Image	Name	RKT Cancel Algorithm
	Sune	R U R' {1-2}Ozx2 U R {1-2}Ozx2 U2 R'
	Antisune	R U2 {1-2}Ozx2 R' U' {1-2}Ozx2 R U' R'
	H	R U2 R' U' {1-2}Ozx2 R U R' U' {1-2}Ozx2 R U' R'
	U	(R U R' U R U2 R') Iy (R U2 R' U' R U' R') Iy'
	T	(R U R' U R U2 R') Iy' (R U2 R' U' R U' R') Iy
	L	(R U R' U R U2 R') Iy2 (R U2 R' U' R U' R') Iy2
	Pi	R U2 {1-2}Ozx2 R2 U' R2 U' R2 {1-2}Ozx2 U2 R

CPLL

To avoid RKT parity

• solve your RKT debt.
• if you have an adjacent corner swap, put the solved LL corner in IUFL and do the respective A-perm.
• if you have a diagonal corner swap,
  • if the IUFR corner belongs in IUBR, do a Iy.
  • so now the IUFR corner belongs in IUFL.
  • do Na-perm.

Image	Name	RKT Cancel Algorithm
	Aa	(Ix) R' U {1-2}Oz R' D2 R {1-2}Oz' U' R' D2 {1-2}Oz' R2
	Ab	(Ix) R2 {1-2}Oz D2 R U {1-2}Oz R' D2 R {1-2}Oz' U' R
	Na	R U' L U2 R' U L' {1-2}Oy2 R U' L U2 R' U L'
TODO	Nb

EPLL

Image	Name	RKT Cancel Algorithm
	Ub	R2 U R U {1-2}Ozx2 R' U' R' U' R' {1-2}Ozx2 U R'
	Ua	R U' {1-2}Ozx2 R U R U R {1-2}Ozx2 U' R' U' R2
	Z	(R U' R U R U R U' R' U' R2) Iy2 (R2 U R U R' U' R' U' R' U R') Iy2 alternate: M2 U' M U2 M' Iy2 M U2 M' U M2
	H	M2 U' M2 U2 M Iy2 M' U2 M Iy2 M U M2 alternate: R2 U2 R U2 {1-2}Ozx2 R2 U2 R2 {1-2}Ozx2 U2 R U2 R2

2RKT Cancel Algorithms

Image	Description	2RKT Cancel Algorithm
	Double Sexy Move	R U {1-2}Ozx2 R' U' {1-2}Azx2 R U {1-2}Ozx2 R' U' {1-2}Azx2

OCLL

Image	Name	RKT Cancel Algorithm
	H	R U2 {1-2}Azx2 R' U' {1-2}Ozx2 R U {1-2}Azx2 R' U' {1-2}Ozx2 R U' R'
	U	(R U R' {1-2}Azx2 U R {1-2}Azx2 U2 R') Iy (R U2 {1-2}Azx2 R' U' {1-2}Azx2 R U' R') Iy'
	T	(R U R' {1-2}Azx2U R {1-2}Azx2 U2 R') Iy' (R U2 {1-2}Azx2 R' U' {1-2}Azx2 R U' R') Iy
	L	(R U R' {1-2}Azx2 U R {1-2}Azx2 U2 R') Iy2 (R U2 {1-2}Azx2 R' U' {1-2}Azx2 R U' R') Iy2

EPLL

Image	Name	RKT Cancel Algorithm
	Z	(R U' {1-2}Azx2R U R U R {1-2}Azx2 U' R' U' R2) Iy2 (R2 U R U {1-2}Azx2 R' U' R' U' R' {1-2}Azx2 U R') Iy2