The Possibility of Solving a 3x3 Rubik’s Cube under 3 Seconds
Rubik's cube was invented in 1974. Since then, speedcubers all over the world try their best to break the world record again and again. The newest record is 3.47 seconds. There are many factors that affect the timing including turns per second (tps), algorithm, finger trick, and hardware of the cube. In this paper, the lower bound of the cube solving time will be discussed using convex optimization. Extended analysis of the world records will be used to understand how to improve the timing. With the understanding of each part of the solving step, the paper suggests a list of speed improvement technique. Based on the analysis of the world record, there is a high possibility that the 3 seconds mark will be broken soon.
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[2] M. Park, "WR [6.82] OH Rubik's Cube 3x3 One handed World Record Single." (Online). Available: https://www.youtube.com/watch?v=LvFtz4QAP5g.
[3] J. Perm, "Why Are There 43,252,003,274,489,856,000 Rubik's Cube Combinations?." (Online). Available: https://www.youtube.com/watch?v=z2-d0x_qxSM.
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[7] "List of methods." (Online). Available: https://www.speedsolving.com/wiki/index.php/List_of_methods.
[8] B. Noris, "LEARNING FROM THE PROS," 2021. (Online). Available: https://basilio.dev/cubing/recons/.
[9] "Rubik's Cube solution with advanced Fridrich (CFOP) method." (Online). Available: https://ruwix.com/the-rubiks-cube/advanced-cfop-fridrich/.
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[11] J. Perm, "Rubik's Cube Move Notation." (Online). Available: https://jperm.net/3x3/moves.
[12] "What Are The Limits?." (Online). Available: https://www.cubeskills.com/blog/what-are-the-limits.
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[15] "Metric." (Online). Available: https://www.speedsolving.com/wiki/index.php/Metric.
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[17] "Finger tricks - How To Get Faster At Cubing." (Online). Available: https://ruwix.com/the-rubiks-cube/fingertricks/.
[18] "TNoodle." (Online). Available: https://github.com/thewca/tnoodle.
[19] "WCA Regulations." (Online). Available: https://www.worldcubeassociation.org/regulations/#article-4-scrambling.
[20] LaZer0MonKey, "Breakdown of Max Park's 6.82 One-Handed World Record Solve!." (Online). Available: https://www.youtube.com/watch?v=xlgmyzaWeeo.
[21] "RUR'U' vs RBR'B'." (Online). Available: https://youtu.be/Lh1IOekzB5U.
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[24] "The Fewest Move Count (FMC) Event." (Online). Available: https://ruwix.com/the-rubiks-cube/fmc-fewest-move-count-challenge-method-tips/.
[25] "FMC rankings, World Cube Association." (Online). Available: https://www.worldcubeassociation.org/results/rankings/333fm/single.
[26] "STACKMAT™ PRO TIMER." (Online). Available: https://www.speedstacks.com/store/retail/speed-stacks-stackmat-pro-timer/.
[27] "Capacitive Touch Sensors." (Online). Available: https://www.fujitsu.com/downloads/MICRO/fme/articles/fujitsu-whitepaper-capacitive-touch-sensors.pdf.
[28] "GAN356 i2." (Online). Available: https://www.gancube.com/gan356-i2.
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[31] "Pseudo block." (Online). Available: https://youtu.be/5cdHQvAaiV8.
[32] "PLL algorithm." (Online). Available: http://www.rubiksplace.com/speedcubing/PLL-algorithms/.
[33] "XCross." (Online). Available: https://www.speedsolving.com/wiki/index.php/XCross.
[34] "How To Solve the Cross FASTER [Cross Boot Camp]." (Online). Available: https://www.youtube.com/watch?v=VWwj_HaPpYI.
[35] "Color neutrality." (Online). Available: https://www.speedsolving.com/wiki/index.php/Color_neutrality.
[36] CubeHead, "Pseudoslotting : Full Tutorial + Example Solves." (Online). Available: https://www.youtube.com/watch?v=xjhjdIFddCk.
[37] J. Perm, "Advanced F2L: Edge Control." (Online). Available: https://www.youtube.com/watch?v=zB5-8HAfldM.
[38] "ZBLL." (Online). Available: https://www.speedsolving.com/wiki/index.php/ZBLL.
[39] W. X. Junshen Kevin Chen, Zhouheng Sun, "DeepCube: Transcribing Rubik’s Cube Moves with Action Recognition." (Online). Available: https://russellxie7.me/docs/cube.pdf.
[1] cyotheking, "WCA Competitor Tutorial." (Online). Available: https://youtu.be/dPL3eV-A0ww?t=97.
[2] M. Park, "WR [6.82] OH Rubik's Cube 3x3 One handed World Record Single." (Online). Available: https://www.youtube.com/watch?v=LvFtz4QAP5g.
[3] J. Perm, "Why Are There 43,252,003,274,489,856,000 Rubik's Cube Combinations?." (Online). Available: https://www.youtube.com/watch?v=z2-d0x_qxSM.
[4] "God's Number is 20." (Online). Available: http://www.cube20.org/.
[5] E. Shinder, "Mathematics of the Rubiks’ cube." (Online). Available: http://e-shinder.staff.shef.ac.uk/rubiks-cube.pdf.
[6] MoYu-Cube, "2018 MoYu World Record Prize Announcement," 2018. (Online). Available: https://www.facebook.com/moyumagiccube/posts/2018-moyu-world- record-prize-announcement-for-cubers-who-break-official-world-re/1580692178678403/.
[7] "List of methods." (Online). Available: https://www.speedsolving.com/wiki/index.php/List_of_methods.
[8] B. Noris, "LEARNING FROM THE PROS," 2021. (Online). Available: https://basilio.dev/cubing/recons/.
[9] "Rubik's Cube solution with advanced Fridrich (CFOP) method." (Online). Available: https://ruwix.com/the-rubiks-cube/advanced-cfop-fridrich/.
[10] M. Coltheart, "Iconic memory." (Online). Available: https://royalsocietypublishing.org/doi/abs/10.1098/rstb.1983.0055.
[11] J. Perm, "Rubik's Cube Move Notation." (Online). Available: https://jperm.net/3x3/moves.
[12] "What Are The Limits?." (Online). Available: https://www.cubeskills.com/blog/what-are-the-limits.
[13] K. Gundersen, "Muscle memory and a new cellular model for muscle atrophy and hypertrophy," J Exp Biol, vol. 219, no. Pt 2, pp. 235-42, Jan 2016, doi: 10.1242/jeb.124495.
[14] LaZer0MonKey, "Breakdown of Yusheng Du's 3.47 World Record Solve!." (Online). Available: https://youtu.be/qT5Jan1sLQE?t=153.
[15] "Metric." (Online). Available: https://www.speedsolving.com/wiki/index.php/Metric.
[16] D. Blender, "Yusheng Du 3.47 World Record 3D Visualization." (Online). Available: https://www.youtube.com/watch?v=JDLlEAw5WRM.
[17] "Finger tricks - How To Get Faster At Cubing." (Online). Available: https://ruwix.com/the-rubiks-cube/fingertricks/.
[18] "TNoodle." (Online). Available: https://github.com/thewca/tnoodle.
[19] "WCA Regulations." (Online). Available: https://www.worldcubeassociation.org/regulations/#article-4-scrambling.
[20] LaZer0MonKey, "Breakdown of Max Park's 6.82 One-Handed World Record Solve!." (Online). Available: https://www.youtube.com/watch?v=xlgmyzaWeeo.
[21] "RUR'U' vs RBR'B'." (Online). Available: https://youtu.be/Lh1IOekzB5U.
[22] "Cube Explorer." (Online). Available: https://ruwix.com/the-rubiks-cube/herbert-kociemba-optimal-cube-solver-cube-explorer/.
[23] "UUUU vs U'U'U'U'." (Online). Available: https://youtu.be/OTDEKqwInYA.
[24] "The Fewest Move Count (FMC) Event." (Online). Available: https://ruwix.com/the-rubiks-cube/fmc-fewest-move-count-challenge-method-tips/.
[25] "FMC rankings, World Cube Association." (Online). Available: https://www.worldcubeassociation.org/results/rankings/333fm/single.
[26] "STACKMAT™ PRO TIMER." (Online). Available: https://www.speedstacks.com/store/retail/speed-stacks-stackmat-pro-timer/.
[27] "Capacitive Touch Sensors." (Online). Available: https://www.fujitsu.com/downloads/MICRO/fme/articles/fujitsu-whitepaper-capacitive-touch-sensors.pdf.
[28] "GAN356 i2." (Online). Available: https://www.gancube.com/gan356-i2.
[29] "Go Cube." (Online). Available: https://getgocube.com/.
[30] "LFCL 3x3 Rubik’s Cube Method." (Online). Available: https://docs.google.com/document/d/1nJ11uxsT96FJXnPQWd2n1eTPAWqkuxh3Wf_m1EevPck/edit.
[31] "Pseudo block." (Online). Available: https://youtu.be/5cdHQvAaiV8.
[32] "PLL algorithm." (Online). Available: http://www.rubiksplace.com/speedcubing/PLL-algorithms/.
[33] "XCross." (Online). Available: https://www.speedsolving.com/wiki/index.php/XCross.
[34] "How To Solve the Cross FASTER [Cross Boot Camp]." (Online). Available: https://www.youtube.com/watch?v=VWwj_HaPpYI.
[35] "Color neutrality." (Online). Available: https://www.speedsolving.com/wiki/index.php/Color_neutrality.
[36] CubeHead, "Pseudoslotting : Full Tutorial + Example Solves." (Online). Available: https://www.youtube.com/watch?v=xjhjdIFddCk.
[37] J. Perm, "Advanced F2L: Edge Control." (Online). Available: https://www.youtube.com/watch?v=zB5-8HAfldM.
[38] "ZBLL." (Online). Available: https://www.speedsolving.com/wiki/index.php/ZBLL.
[39] W. X. Junshen Kevin Chen, Zhouheng Sun, "DeepCube: Transcribing Rubik’s Cube Moves with Action Recognition." (Online). Available: https://russellxie7.me/docs/cube.pdf.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:80873", author = "Chung To Kong and Siu Ming Yiu", title = "The Possibility of Solving a 3x3 Rubik’s Cube under 3 Seconds", abstract = "Rubik's cube was invented in 1974. Since then, speedcubers all over the world try their best to break the world record again and again. The newest record is 3.47 seconds. There are many factors that affect the timing including turns per second (tps), algorithm, finger trick, and hardware of the cube. In this paper, the lower bound of the cube solving time will be discussed using convex optimization. Extended analysis of the world records will be used to understand how to improve the timing. With the understanding of each part of the solving step, the paper suggests a list of speed improvement technique. Based on the analysis of the world record, there is a high possibility that the 3 seconds mark will be broken soon. ", keywords = "Rubik’s cube, convex optimization, speed cubing, CFOP.", volume = "16", number = "7", pages = "43-9", }
