26 HTM Corners First Solve by Sebastiano Tronto

Scramble: L D2 L’ U2 B2 L’ F2 D2 L2 F2 U2 F’ D U L D2 U2 B R2 F2 R
Solution: D B’ D2 B2 L’ B’ L’ R2 F’ L B’ D’ L’ B F’ D R U R’ U2 D2 L U’ F U2 F2 (26 HTM)

Eplanation:
D B’ D2 B2 L’ B’ L’ R2 F’ L //Corners -2 moves, and 4 edges (10/10)
B’ D’ L’ B F’ D R //4 more edges, B U2 F2 to solve corners (7/17)
U R’ U2 D2 L U’ //Last 4 edges + centres (6/23)
F U2 F2 //Solve everything (3/26)

Comment:
First I have found a short corners solution:

U L’ B2 U’ //First layer corners (4/4)
U L2 U’ L’ U L’ U’ L2 //CLL, 2 moves cancel (6/10)

Then I went back and modified that solution adding inner layer moves to preserve/solve some edges; I found 2 possible solutions that solved 4 edges together with the corners wit only 2 more moves:

1. D F’ R2 B2 D’ B’ D’ U2 F’ D U2 B2
2. D B’ D2 B2 L’ B’ L’ R2 F’ L R2 B2

Disregarding centres, the second one left a double edge swap and a 4-cycle, so it seemed more promising. Leaving the last two moves undone for better continuation, I have found the solution. 2nd and 3rd step are both setup moves + inner layer move + anti-setup; the 4-cycle needs a single quarter slice move, the double swap a half slice move.

I have tried this approach different times, but this is my first sub-30.
Maybe the scramble is lucky, but I’m happy with this result.

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