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I used Shuang Chen's 4x4x4 solver for reduction to 3x3x3, and then the huge optimal solver of Cube Explorer 5.01

Spoiler: More details
Tom, one thing I'm curious about: How did you produce the scrambles? Looks like 3x3+reduction+random, but the 3x3 part is pretty long and the reduction part is pretty short. Doesn't look like Shuang Chen's solver, so I'm wondering...

I used Shuang Chen's 4x4x4 solver for reduction to 3x3x3, and then the huge optimal solver of Cube Explorer 5.01

**s**. With a script of my own in between.I slightly modified Shuang Chen's solver to feed our scrambles into it, to search more (multiplying the numbers like PHASE1_SOLUTIONS by 100 or 1000), and to print not just one solution but keep printing solutions that are not more than three moves longer than the shortest so far (counting in OBTM, as that's what that solver uses). I stopped it when I had around 1000 OBTM-short reductions (or rather, solutions containing them) for each scramble.

Then I used a (messy and quite possibly buggy) script of my own to extract the reductions (and 3x3 parts), minimize them for OBTM (some cancellations were possible) and BTM (much was possible, as Shuang Chen's solver doesn't use BTM), sort them by resulting move count and produce input files for Cube Explorer that looked like this:

This is the start of my input file for scramble 1 for BTM. Each line is a 3x3x3 part that I want Cube Explorer to optimize, and in the comment the already "optimized" reduction leading to that 3x3x3 part (gets shown in Cube Explorer as "Pattern Name"). Note that most of the time each reduction gets "tripled" because when the reduction for example ends in Bw2, you can append a B2 or F2 for free (doesn't change the BTM length as they just turn the Bw2 into 2B2 or 2F2 z2). This gives you three times as many 3x3x3 chances to try.

Then in a Cube Explorer clickfest, I tried the cubes from the shortest reductions first, and stopped searches when they couldn't lead to a shorter solution than I had already found at that point. Only tried the first few dozen or so for each scramble, gave up when I would've needed like 14 HTM to improve. Oh and for BTM I used the "Allow Slice Moves" option, which I somehow hadn't known existed.

Then I used a (messy and quite possibly buggy) script of my own to extract the reductions (and 3x3 parts), minimize them for OBTM (some cancellations were possible) and BTM (much was possible, as Shuang Chen's solver doesn't use BTM), sort them by resulting move count and produce input files for Cube Explorer that looked like this:

Code:

```
L U R' B U' F2 B D' U R F2 L2 U2 R' U2 R' D2 B2 // line4 BTM 22 redux: Dw Fw D' Lw2 B Uw Lw U2 Fw2 2U2 D' B2 U2 Lw D' R2 F Uw2 Rw2 D L2 Bw2
F2 L U R' B U' F2 B D' U R F2 L2 U2 R' U2 R' D2 B2 // line4 BTM 22 redux: Dw Fw D' Lw2 B Dw y Lw U2 Fw2 2U2 D' B2 U2 Lw D' R2 F Dw2 y2 Lw2 x2 D L2 2F2 z2
B2 L U R' B U' F2 B D' U R F2 L2 U2 R' U2 R' D2 B2 // line4 BTM 22 redux: Dw Fw D' Lw2 B Dw y Lw U2 Fw2 2U2 D' B2 U2 Lw D' R2 F Dw2 y2 Lw2 x2 D L2 2B2
B' L2 B' U2 D2 L2 F R2 B L U2 F D B' L' U R2 F' B' L' // line13 BTM 22 redux: R2 Dw2 Bw' U' Rw' 2B' S2 L' F2 Uw D B' L2 Uw L D2 2B2 Dw2 R' B' Rw2 Dw2
U2 B' L2 B' U2 D2 L2 F R2 B L U2 F D B' L' U R2 F' B' L' // line13 BTM 22 redux: R2 Dw2 Fw' z U' Lw' x' 2F' S' L' F2 Dw y D B' L2 Dw y L D2 2B2 Dw2 R' B' Lw2 x2 2U2 y2
D2 B' L2 B' U2 D2 L2 F R2 B L U2 F D B' L' U R2 F' B' L' // line13 BTM 22 redux: R2 Dw2 Fw' z U' Lw' x' 2F' S' L' F2 Dw y D B' L2 Dw y L D2 2B2 Dw2 R' B' Lw2 x2 2D2
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```

Then in a Cube Explorer clickfest, I tried the cubes from the shortest reductions first, and stopped searches when they couldn't lead to a shorter solution than I had already found at that point. Only tried the first few dozen or so for each scramble, gave up when I would've needed like 14 HTM to improve. Oh and for BTM I used the "Allow Slice Moves" option, which I somehow hadn't known existed.

Last edited: Jul 16, 2014