Sudokuwiki.org's Weekly 'Unsolvable' Sudoku #644

In this post I'll be tackling the weekly "Unsolvable" puzzle from SudokuWiki. This week's puzzle was provided by Richard Kröger.

Puzzle string: .1...3..2..86..5..4......1...3..8.7.6...4.1...5.9.......2.....3....7.4...9...5.8. - Sudoku.Coach

SE: 9.2

Again I failed to come up with a solution for #643 in time - thankfully this week's puzzle is far easier than the previous lot...

(9=27)r35c6 - r6c6 = r5c13 - (7=9)r5c3 => r3c3<>9

Kraken Finned X-Wing: [(9)r3c7 = [(9)c17\r14b1 = r7c7 - r8c89 = (9)r8c6]] - (9=27)r35c6 - r6c6 = r6c13 - (7=9)r5c3 => r1c3<>9

Extending the previous AIC through an Almost-Finned-X-Wing to eliminate another 9. This already gives us a hidden single, which is promising.

(7)r3c34 = [(3)r3c7 = r6c7 - r6c5 = (3-7)r5c4 = r1c4 - (7=561)r138c3 - r8c9 = (1-7)r9c9 = (7)r23c9] => r3c7<>7

[(1)r7c6 = [(1)r9c9 = r8c9 - c36\68 = (1-4)r9c3 = (4)r7c2]] - (4)r7c6 = (4-7)r2c6 = [(7)r2c9 = r2c12 - (7=561)r138c3 - r8c9 = (1)r9c9] => r9c9<>7

An ALS-AIC tied with a double-Kraken X-Wing. I was very pleased to see that YZF Sudoku cannot eliminate 7r9c9, even with forcing chains.

AIC-tie-AIC: [(1=35687)b7p14567 - (7=124)b4p127 - r6c3 = (4)r9c3] = (8)r6c1 - (8)r6c9 = [(1=6)r9c9 - (6=4)r6c9 - r6c3 = (4)r9c3] => r9c3<>1

(7)r9c1 = [(7)r2c9 = [(7=561)r138c3 - (1=3)r9c1 - r8c12 = r8c4 - r5c4 = r5c8 - (3=94)r2c89 - r2c6 = (4-7)r1c4 = (7)r1c13]] => r2c1<>7

(4)r9c3 = r7c2 - r7c6 = (4-1)r2c6 = r2c5 - (1)r6c5 = [((4)r9c3 = r7c2 - r4c2 = (4-7)r6c3 = [(4)r9c3 = r7c2 - r4c2 = r6c3 - (4=2368)r6c5789 - r6c1 = (8-7)r5c2 = r6c1 - (47)(b7p17 = b7p29)]] => r9c3<>6

Quite ugly in notation and in the diagram because of all the overlapping links... but it's a pretty simple ALS/AHS AIC with 2 Kraken candidates.

(69)(r4c9 = r4c57) - (6)r9c5 = r9c79 - (6)b9p256 = [[[(1=2)r8c6 - (2=591)b9p256] - (1)r8c3 = (1-4)r6c3 = r9c3 - r7c2 = (4)r4c2] = (69-12)r8c6 = [(4)r4c2 = (4-6)r7c2 = r8c23 - (6=9)r8c6 - (9)r8c9 = [[(68)r7c2 = [[(6)r8c3 = (6-8)r8c2 = r5c2 - (8=5)r5c9 - (5=1)r8c9] - (1)r8c3 = (1-4)r6c3 = (4)r9c3]] - (4)r7c2 = (4)r4c2]]] => r4c9<>4

Yuck yuck yuck. This started as a fairly easy Kraken cell r8c6. 1 & 2 form an almost-Sue-de-Coq with b9p256, giving lots of potential eliminations to transport off of. The closest mutual elimination of this SdC and the extra 6s from the AALS was 4r4c9: great. The 6 in the kraken cell trivially leads to -r8c23 = (6-4)r7c2 = (4)r4c2: brilliant. All this happens in the left half of the image.

9 was a huge pain and I eventually devised this almost-AIC solution to wrangle all the branches towards (1)r8c3 = (4)r4c2. It's at this point that there are so many greyed out Kraken candidates that the beauty of an AIC has been lost and what I'm doing comes closer and closer to forcing logic. With classical AIC you're examining the pure logic of the grid and eliminations are incidental results of the connected strong link nodes. In this gross chain there's so much bending and engineering that it could never be anything *but* this specific elimination. Oh well, it's an "unsolvable" puzzle, if you want to solve it you're going to have to get your hands dirty. I don't think I care at this point. This elimination gives us 2 singles, let's continue...

Kraken Row: (9)r2c1 = (9-7)r1c1 = [(1)r4c4 = (1-4)r7c4 = (4-7)r1c4 = r1rc3 - (7=1)r6c3] - (1=2)r4c1 => r2c1<>2

(12)(r2c2 = r2c56) - (4)r2c6 = (4-7)r1c4 = (7)r1c13 => r2c2<>7

Kraken Cell: [(9)r4c6 = r4c9 - (9=6)r8c9 - r9c79 = r9c5 - (69)(r4c5 = r4c97)] = (15-69)r8c9 = [(1)r6c3 = r8c3 - (1=5)r8c9 - (5=8)r5c9 - (8=7)r5c2 - (7=1)r6c3] - (1=2)r4c1 => r4c7<>2