# Triforce

 Triforce method Information about the method Proposer(s): Trangium Proposed: 2021 Alt Names: none Variants: unnamed No. Steps: 7 No. Algs: 174 Avg Moves: ~135 STM Purpose(s): Speedsolving Novelty Lack of Parity

Triforce method is a 4x4 speedsolving and novelty method proposed by trangium for the August 2021 Method Development Competition. Its motivation is to avoid OLL parity while still being viable for speedsolving.

## Overview

1. U/D centers + 1x2x4 block (~24 moves): Solve a 1x2x4 block in dL and the first 2 centers. There are several options on how to split up this step into multiple substeps. One may choose to solve the block first, 2 centers first, center-block-center, or even freestyle.
2. Solve dM quads (~21 moves): Expand the 1x2x4 block into a 3x2x4 block while preserving the centers. After this step, R, U, and u moves will preserve the block.
3. Pair 5 U/D edges + Half Centers (~32 moves): Here, "half centers" means reducing the centers such that they can be solved with R2 and u moves. The best general approach is to get to half centers while pairing up 1-2 U/D edges, then pairing the rest of the U/D edges by setting up to u moves. Although one can't pair up E-slice edges, the fact that the centers aren't fully solved makes edge pairing more efficient overall. At some point towards the end of this step, place an E-slice edge pair in DR using an R2. This is to set up for the next step, EOLE.
4. EOLE (~7 moves, 24 algs): Use one of 24 algs to place all E-slice edges in the E slice while orienting all the U/D edges. Since one only has to recognize EO of five U/D edges, all of which are visible, recognition is extremely fast.
5. L6W (~10 moves, 14 algs): Solve the six E-slice wings. It is recommended to first solve the dFR or dBR wings, then proceed with one of 14 algs. Recognition can be tricky, but since there are so few cases, it is definitely viable.
6. L6C (~22-24 moves, 42-122 algs): Solve the 6 remaining corners without disturbing the EO or belt. The recommended approach is to first solve the 2 bottom corners (DCAL, intuitive or 80 algs), then solve the 4 top corners (CxLL, 42 algs). A y rotation should be done before starting the next step.
7. 5e5x (~19 moves): Use the m' U2 m trigger, along with U and u moves, to solve the remaining 5 edges and 5 centers simultaneously. PLL parity may happen here, but that can be fixed with (R2 u2)3 at the start of 5e5x. The key insight here is that m' U2 m cycles 3 edges and rotates the F center 180 degrees. This step can be completely intuitive but benefits from learning at least a few algs to deal with bad cases. See the full detailed method doc for how to solve 5e5x efficiently.

## Pros

• No OLL parity, leading to an efficiency gain of at least 10 moves over Yau
• Edge pairing is less restricted
• Good ergonomics for the majority of the solve: mostly <R, r, 3r, U, u>

## Cons

• The 1x2x4 step can be difficult
• A lot needs to be planned in inspection
• A few steps have awkward movesets
• Not that many algs will transfer from CFOP, so one will have to learn lots of new algs exclusively for Triforce

## Neutral Points

• No 3x3x3 stage, so one's 3x3x3 abilities won't transfer to 4x4x4. This can be a pro or a con depending on one's 3x3x3 skill.
• Many algorithmic steps, which could be a pro or a con depending on the solver
• Many variants, which means that a solver can choose which variant they prefer, but also means that further developments could quickly render certain variants obsolete

## Progression

 Step Beginner Triforce Intermediate Triforce Full Triforce EOLE 0 algs Orient edges as they are paired 12 algs Force an E-slice edge in BR 24 algs Full EOLE L6W 2 algs Solve both dFR and dBR first, leading to L4W 8 algs Always solve dBR first 14 algs Full L5W DCAL 0 algs Intuitively using R2 U* R2 and CFOP inserts 0-17 algs Learn algs for bad intuitive cases 80 algs Full DCAL CxLL 9 algs 2-look: Orient then permute corners 9-20 algs Learn some easy CxLLs 42 algs Full CxLL 5e5x 1 alg Parity alg only 3-11 algs Learn from top to bottom on the algsheet 14 algs Learn all the listed triggers Total 12 algs 32-68 algs 174 algs