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The possibility of solving a 3x3 Rubik's Cube under 2 seconds - Optimizing block building

Chung To Kong

arXiv:2609.12946v1cs.GT

TL;DR

Block building is an important speedcubing skill, but the paper identifies optimal move-sequence construction as an open problem. It presents the AK-cubie method, which produces a human-readable 25-move solution compared with a 16-move Two-Phase solution that is not easy for people to understand.

  • Problem

    Determining an optimal block-building move sequence remains an open problem, despite block building being a significant limiting factor in speedcubing.

    Source: §I · p. 1

  • Method

    The AK-cubie method solves one cubie at a time, incrementally combining cubies until eight edges and four corners are solved to complete the first two layers.

    Source: §III · p. 5

  • Results

    The Two-Phase search produces a 16-move solution that is not easy for humans to understand, while the AK-cubie method produces a human-readable 25-move solution.

    Source: §II · pp. 1–2

  • Takeaways & Limitations

    The authors state that solutions of 30 moves or fewer have a strong likelihood of breaking the 2.76-second world record for advanced speedcubers approaching 15 turns per second.

    Source: §VI · p. 9

Abstract

from arXiv · show

Block building is an essential skill in speedcubing competitions. However, there is currently no systematic method to understand or analyze block-building techniques. Rewatching gameplay reveals only the outcome, not the underlying mechanism. This paper presents a systematic approach, the "AK-cubie method" (or "cubie method" for short), for constructing near-optimal block-building move sequences within a short computation time. Speedcubers can use the accompanying software to train their look-ahead and block-building skills. We hope this work will contribute to breaking the 2-second world record in the near future.

I. INTRODUCTION

Block building is a significant limiting factor in speedcubing, yet finding an optimal sequence remains an open problem. This paper addresses systematic block building for the 3×3 Rubik's Cube.

I. INTRODUCTION

  • Block building is a significant limiting factor in speedcubing, and determining an optimal block-building sequence remains an open problem.The paper addresses systematic block building for the 3×3 Rubik's Cube.Source: §I · p. 1
  • High turns per second, minimal pickup and ending times, zero idle time, and One-Look Last Layer algorithms [2] are identified as critical to surpassing the current world record.Source: §I · p. 1
  • The introduction provides a link to the AK-cubie method software for the 3×3 Rubik's Cube.Source: §I · p. 1

II. BACKGROUND

For the 2.76-second record, the background contrasts the Two-phase search’s 16-move sequence, described as hard for humans to understand, with AK-cubie’s 25-move human-readable solution.

II. BACKGROUND

  • The current 3×3 world record described here is 2.76 seconds, achieved by Teodor Zajder with a 29-move solution.Source: §II · p. 1
  • Two-Phase (Kociemba) search yields 16 moves but is not easy for humans to understand, whereas AK-cubie produces a human-readable 25-move solution with two cube rotations.Source: §II · pp. 1–2
  • The illustrated solve builds a 2×2×2 block in 6 moves, extends it to XXX-cross in 6, completes F2L in 4, then uses 12-move 1LLL.Source: §II · pp. 2–3
  • AK-cubie generates HTM, one-handed, and two-handed solutions, and the authors also tested it on the two preceding world records.Source: §II · p. 3

III. SCOPE OF WORK

The AK-cubie method models edge and corner cubies separately, then builds blocks by solving and combining cubies incrementally. It searches candidate starts and trims move sequences before presenting ergonomic solutions.

III. SCOPE OF WORK

  • The method represents edge and corner positions and orientations in four arrays, while disregarding centers because the core algorithm uses no wide moves or cube rotations.Its core move set consists of face turns and half-turns.Source: §III · p. 5
  • It solves cubies incrementally, combining them until eight edges and four corners are solved and the first two layers are complete.At most three moves are required to place any edge or corner cubie in its correct position and orientation.Source: §III · p. 5
  • When adding a cubie, the method preserves previously solved cubies by treating unaffected positions as “don't care” and testing the top 50 shortest sequences.The trimming value limits branching, and the program halts if memory usage becomes high.Source: §III · p. 6
  • The search begins with a 2×1 block and extends it to 2×2 and 2×3 blocks, evaluating all 24 possible 2×1 blocks.The 24 starts correspond to four F2L pairs and six bottom colors.Source: §III · p. 6
  • NISS, insertion, and cancellations between block building and 1LLL are used to further reduce move counts.Such reductions can be challenging because solvers often rely on a consistent 1LLL setup for muscle memory.Source: §III · p. 6
  • After finding a solution, the software modifies it for finger-friendly one- and two-handed solving and presents the 10 lowest-move options for selection.The full program completes within 300 seconds by default, with an adjustable time limit; computation time depends on hardware.Source: §III · pp. 6–7

IV. TEST RESULT

The test section records AK-cubie solutions in normal, one-hand, and two-hand formats, with examples reporting move counts from 25 to 36. Some one- and two-hand outputs also list cube rotations.

IV. TEST RESULT

  • 25 moves are reported for Normal (HTM), One-hand, and Two-hand solutions in one example.The One-hand solution lists +5 cube rotations, and the Two-hand solution lists +3.Source: §IV · p. 7
  • Recorded outputs include a 36-move Two-hand solution, a 36-move Normal (HTM) solution, and a 36-move One-hand solution.The One-hand output lists +5 cube rotations; the Two-hand output lists +1.Source: §IV · p. 7
  • 30 moves are reported for Normal (HTM), One-hand, and Two-hand solutions in another example.The One-hand solution lists +5 cube rotations, and the Two-hand solution lists +2.Source: §IV · p. 8
  • A further example reports 32 moves for Normal (HTM), One-hand, and Two-hand solutions.The One-hand solution lists +4 cube rotations, and the Two-hand solution lists +3.Source: §IV · p. 8
  • Another example reports 32 moves for Normal (HTM) and One-hand, and 33 moves for Two-hand.The One-hand solution lists +4 cube rotations.Source: §IV · p. 9

V. FUTURE DEVELOPMENT

The authors identify larger cubes and further search optimizations as directions for future development.

V. FUTURE DEVELOPMENT

  • The AK-cubie method is described as generalizing naturally to larger cubes.Source: §V · p. 9
  • Block building, or the XXX-cross, remains a key limiting factor in speedcubing.Source: §V · p. 9
  • Potential optimizations include parallel processing, branch-depth control, advanced search strategies, and AI-driven heuristics.Source: §V · p. 9

VI. CONCLUSION

The conclusion presents AK-cubie as a systematic way to construct effective, human-readable solutions. It suggests that solutions of 30 moves or fewer at about 15 TPS could break the 2.76-second record, while describing a solve under 2 seconds as achievable.

VI. CONCLUSION

  • The AK-cubie method systematically constructs effective, human-readable solutions.Source: §VI · p. 9
  • At typical speeds approaching 15 TPS, solutions of 30 moves or fewer have a strong likelihood of breaking the 2.76-second world record.Source: §VI · p. 9
  • The authors present solving the cube within 2 seconds as achievable and hope the software helps speedcubers develop block-building and XXX-cross techniques.Source: §VI · p. 9
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