Thistlethwaite's algorithm

Thistlethwaite method Information about the method Proposer(s): Morwen Thistlethwaite Proposed: 1981 Alt Names: none Variants: Human Thistlethwaite No. Steps: 4 No. Algs: 2,048 + 1,082,565 + 29,400 + 663,552 (number of states in each phase) Avg Moves: 31.3 Purpose(s): Computer algorithms Fewest Moves

A computer cube solving algorithm, based on reducing the cube to subgroups.

Phases

1. Reduction to G₁ = <U,D,L,R,F2,B2> (also known as Edge Orientation)
2. Reduction to G₂ = <U,D,L2,R2,F2,B2> (also known as Domino Reduction)
3. Reduction to G₃ = <U2,D2,L2,R2,F2,B2> (also known as Half Turn Reduction)
4. Final Solve
   Permutation of all pieces using only 180 degree faces turns

Thistlethwaite's original subgroups were G0 = <U,D,L,R,F,B>, G₁ = <U2,D2,L,R,F,B>, G₂ = <U2,D2,L,R,F2,B2>, G₃ = <U2,D2,L2,R2,F2,B2> and G4 = {1}. Phase 1 took at most 7 moves, phase 2 took at most 13 moves, phase 3 took at most 15 moves, phase 4 took at most 17 moves in HTM, resulting in at most 52 move long solution.

A popular belief is that the God's number for phase 4 is 15. While that is true for the <U2,D2,R2,L2,F2,B2> move set, when using the <U,D,R,L,F,B> move set instead, it actually becomes 13. Meaning that the solution length found by Thistlethwaite's algorithm in phase 4 ≥ the solution length found by Feather's algorithm in phase 2.

See also

• Human Thistlethwaite
• Kociemba
• God's Algorithm
• Puzzle theory
• Rubik's Cube Group
• Edge Orientation
• Domino Reduction
• Half Turn Reduction
• Feather's algorithm

External links

• Jaap's Thistlethwaite page
• Wikipedia: Morwen Thistlethwaite
• Wikipedia: Thistlethwaite's algorithm