New 3^4 computer-assisted shortest solution (125 STM) using blockbuilding search program

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ajfarkas12

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Sep 24, 2025, 12:28:17 AMSep 24
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Hello all,

A quick note: STM = slice turn metric. See hypercubing.xyz/notation for a description of various turn metrics, and my 2022 post on the mailing list for my reasoning for using STM here.

For the last couple weeks I've been working on robodoan, an automated solver for 3^4 using incremental blockbuilding. Although it can't yet do a full solve, it's able to reliably compute a 60-75 STM solution to the first two layers in under 10 seconds on my laptop. For comparison, the previous shortest solution by Charles Doan (188 STM) completed F2L in 114 STM. It works by pairing blocks one at a time, brute-force searching ahead by up to 5 moves (usually ≤3) to pair blocks using some heuristics. To get short solutions, it tracks up to ~10,000 possible solutions at once and picks the best ones at each step. See the README for more details.

Attached is a 125 STM solve Luna Harran and I did in 4 stages:
  1. F2L (63 STM, automatic) - We generated 5 scrambles using MC4D, loaded them into robodoan, and manually reviewed several of the generated solutions. The shortest F2L solution was 61 STM, but it had a poor OLC. We found one that was 63 STM and had a decent OLC (orient last cell).
  2. OLC (21 STM, manual) - We solved OLC using 2 algorithm executions, including a slice RKT-canceled fat sune and a 6-move 4D OLC algorithm.
  3. 2cPLC (8 STM, manual) - We solved 2cPLC (permute last cell) using an adjacent 3-cycle that canceled into the last OLC algorithm.
  4. PLC (33 STM, computer-assisted) - We entered the final cube state into Cube Explorer to get a 3D solution and then manually found a decent RKT-cancel for it.
The MC4D log file shows 150 moves because MC4D does not allow 180-degree ridge turns and because there are several corner & edge twists that I didn't bother simplifying. To verify the move count, load the .hsc file in Hyperspeedcube.

I've lost motivation to continue working on the program for now, but in the future I'd like to come back to it and implement searching for OLC and PLC. I expect it'll then be capable of finding solutions less than 110 moves, possibly as low as 100.

I'd like to thank Luna Harran for her help with teaching me the grip-theoretic foundations of blockbuilding and with tuning the search parameters.

2025-09-24_computer_assisted_fmc_wr_125stm_andrew_farkas_and_luna_harran.log
2025-09-24_computer_assisted_fmc_wr_125stm_andrew_farkas_and_luna_harran.hsc

Rowan Fortier

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Sep 24, 2025, 12:28:30 AMSep 24
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GREAT JOB!!!!!!!!!!!

Ty Jones

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Sep 24, 2025, 12:50:58 AMSep 24
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Wow! Very impressive. Nice work!


Sep 23, 2025, 10:28 PM by rowan....@gmail.com:
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Roice Nelson

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Sep 24, 2025, 1:45:31 PMSep 24
to Rowan Fortier, hypercubing
I'd like to echo Rowan. Having participated in early days of the shortest competition, this is SO COOL to see and read about.

Maybe it can narrow intuition about the range of God's Number for the 3^4 too, even if we likely won't ever know that. The range is still wide for sure, but I'll throw out a guess after seeing these numbers. I'll bet it is 80 :D

Best,
Roice


Andrew Farkas

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Sep 24, 2025, 1:48:19 PMSep 24
to roi...@gmail.com, Rowan Fortier, hypercubing
Thank you! 80 is my new guess for God's Number as well, with a ±25 margin.



--

"Machines take me by surprise with great frequency." - Alan Turing

ajfarkas12

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Sep 26, 2025, 2:40:15 AMSep 26
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Whoops, I just realized I forgot to combine one of the slice moves. It's actually 124 STM. (I've attached the updated log file.)
2025-09-24_computer_assisted_fmc_wr_124stm_andrew_farkas_and_luna_harran.hsc

ajfarkas12

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Sep 26, 2025, 2:40:26 AMSep 26
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Whoops, I realized I forgot to cancel some of the slice moves in PLC so it's actually 122 STM. Attached are the updated log files.

On Wednesday, September 24, 2025 at 12:50:58 AM UTC-4 Ty Jones wrote:
2025-09-24_computer_assisted_fmc_wr_122stm_andrew_farkas_and_luna_harran.hsc
2025-09-24_computer_assisted_fmc_wr_122stm_andrew_farkas_and_luna_harran.log
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