# YruRU

 YruRU method Information about the method Proposer(s): Yash Mehta Proposed: 2020 Alt Names: none Variants: Briggs No. Steps: 5 No. Algs: 11 - 84 for LL; 0 - 40+ for EO Avg Moves: 45 - 55 Purpose(s): One-Handed Solving

YruRU (pronounced Why-Roo-Roo) is a 3x3x3 method designed specifically for One-Handed Solving. It is a CP-first method that relies on reduced move-sets to ensure great ergonomics for OH turning. The name YruRU is said to stand for Yash's r-u-R-U reduction, but can also be interpreted as "Why Roux?", a dig on Roux, which is widely regarded as the optimal OH speedsolving method known. While it is considered by some critics to be similar to other CP-first methods such as Briggs or 2GR now deemed infeasible for speed-solving, YruRU has a significantly different approach to Corner Permutation, first block and edge orientation.

## Overview

1. CP-line: First, a 1x1x3 block is solved in the bottom-left of the cube (for left-handed OH solvers), while simultaneously solving corner permutation. We get a CP-skip once every 6 solves. This step takes 4-6 moves on average, and following this step the entire cube is solved using <r, u, R, U>.
2. pEO-extension: In this step, the 1x1x3 line is extended to form a 1x2x3 block, while simultaneously orienting 2-3 of the remaining edges and ensuring one of the oriented edges ends up in DB. This is done to ensure that the following step can be executed with minimal pause for recognition. While completely intuitive, it can be broken into 18 cases after achieving a "setup configuration" and solved using 5-move algorithms. Since CP-line takes very few moves, it is usually possible to inspect up to and influence the setup configuration. This step takes 7-9 moves on average, and following this step, the entire cube is solved using <r, R, U>.
3. EO-BF: A step reminiscent of LEOR type methods, this step attempts to achieve a solved edge orientation, followed by solving of the DB and DF edges. However, due to the partial edge orientation already done, the case-count is severely restricted, and the orienting of the DB edge allows for very quick recognition of the EO case. Thus, the biggest drawback of LEOR-type is addressed effectively. While completely intuitive, the EO can be broken into ~40 cases with 5-7 move algorithms. The final two moves of the algorithm are flexible, which allows for easy influence of BF. This step takes 9-11 moves on average, and following this step, the entire cube is solved using <R, U>.
4. F2L: This is identical to solving a block in ZZ, however there is a choice of two bottom colours. This step takes ~15 moves in a speed-solve, although given extremely simple look-ahead and the most ergonomic OH move-set possible, it is easy to execute it at very high TPS.
5. LL: There are 84 possible cases for LL called 2GLLs. The recognition of these cases is substantially easier than ZBLL recognition due to the knowledge of solved CP; in fact it is arguably simpler than PLL recognition. The algorithms are on average 13 moves long, and are 2-gen, leading to very high TPS.

## Algorithms

2GLL algorithms are widely available online.

The idea to do EO is, as soon as the FB+pEO is done, intuit the number of bad edges present on the cube. Since all bad edges will be in the field of view, the accuracy of doing this will be near perfect given the small discrete set {0 (2%), 2 (36%), 4 (53%), 6 (9%)}. Then, identify the case and do the algorithm. The recognition speed should be comparable to OLL. Here is an exhaustive list of cases to be memorised, however all these are completely intuitive.

Note, the last two moves can be any one of U r, U' r, U r', U' r'

DF is bad: set up the other edge to one of these positions:

• UR: r U' R' U r
• RD: r U' R U r
• RB: r U' R2 U r

DF is good, both bad edges in U layer:

• UF-UB: r U' r U' R' U r
• UF-UR: r U R' U r (mirror for UB-UR)

DF is good, one bad edge in U layer:

• UF-RD: r U R U r (mirror for UB-RD)
• UF-RB: r U R2 U r (mirror for UB-RF)
• UF-RF: R' r U R U r (mirror for UB-RB)

If DF is good and both bad edges are in R layer: bring one of them to UF/UB:

• RB-RD: R' U r U R2 U r (mirror for RD-RF)
• RF-RB: R U r U R U r

All other cases' optimal solutions are 1 move setups to these (i.e. using R/U moves).

DF is bad: all (except one special case) optimal solutions are 0-3 move setups to staircase (UL-UF-RF) [or to arrow (UL-UF-UR) which basically sets up to staircase]:

• Staircase: r U r
• Arrow: R' r U r
• UF-UL-RD: R r U r
• UF-UL-RB: R2 r U r
• UF-UB-RF: R U R' r U r
• UF-UB-RD: R2 U R' r U r
• UF-UB-RB: R' U R' r U r
• UF-RF-RD: R U r U r
• UF-RB-RD: R2 U r U r
• RF-RB-RD: R U R U r U r
• Special case - UF-RF-RB: r U2 R2 U r

DF is good: make DF/DB bad using r U2 r or r2, then convert to staircase (or arrow)

• UF-UR-UB-UL: r U2 r' U2 r U r
• UF-UB-RF-RB: r U2 r U' r U r
• UF-UB-RB-RD: r U2 r U2 r U r (mirror for UF-UB-RF-RD)
• UF-UR-RF-RD: r2 U' R' U' r' U r (mirror for UB-UR-RB-RD)
• UF-UL-RF-RB: r2 U r U2 r2 U r
• UF-RF-RD-RB: r2 U' r U2 r2 U r
• UF-UR-UB-RF: r U' r' U2 r U r (mirror for UF-UR-UB-RB)
• UF-UR-UB-RD: R r U2 r U' r U r

All other cases' optimal (or 1 move over optimal) solutions are 1 move setups to these (i.e. using R-U moves)

Here, I will denote the case using good edges instead of bad edges: If DF is bad, simply put the two good edges in UR and DR using <R, U> moves, and do r' U' r2 U r

DF is bad, Both good edges in U layer:

• UF-UR: R2 U' r' U' r2 U r
• UL-UR: R2 U2 r' U' r2 U r

DF is bad, One good edge in U layer:

• UF-RF: R' U' r' U' r2 U r (mirror for UB-RB)
• UF-RD: U' r' U' r2 U r

DF is bad, Both good edges in R layer:

• RF-RB: R r' U' r2 U r
• RF-RD: R U R' U' r' U' r2 U r (mirror for RB-RD)

DF is good: Put the only other good edge in UR:

• UR: r U2 r U' r' U' r2 U r

## Pros

• Move set gets progressively ergonomic over the solve.
• Fairly low move-count compared to CFOP with similar number of algorithms.
• Extremely high TPS possible, especially for the latter parts of the solve.

## Cons

• CP-line is a difficult concept to master.
• The EO step usually requires a pause for recognition for most solvers.
• u moves are not very ergonomic for One-Handed solving.

## Walkthrough Solves

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

y' // Inspection

F' U' F U2 S' // CP-Line

r2 E R U' // Setup

u' R u' U r // FB+pEO

R r U2 r U' r U' r // EO

R U r2 // BF

U R2 U2 R2 // Square

U2 R' U' R U R' // F2L

U2 R' U2 R2 U2 R2 U' R2 U' R2 U R // 2GLL

Scramble: D' L F' U' R' L D R D2 F2 R2 D2 F2 L' U2 D2 L' B D2

x' // Inspection

r' U' f' U' F // CP-line

r U u R' u2 R' U // Setup

u R' u U r // FB+pEO

R U' r' U' r2 U' r // EO

U r2 // BF

U R U' R' U R2 // Square

U2 R' U2 R U2 R' U R U2 R' // F2L + cancelled moves

U2 R' U' R U' R' U2 R U' // 2GLL