Sudokuwiki.org's Weekly 'Unsolvable' Sudoku #642

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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....7..3.5..4..6....9..2...3......7..8.9..4.......1..5..2.3....7..5...8..6. - Sudoku.Coach

SE: 9.3

You may notice I did not publish an article for puzzle #641. This is because it was too hard for me and I couldn't solve it! Sorry to disappoint.

Finned Swordfish

(3)r3c3 = r3c8 - r7c8 = (3-7)r7c4 = r7c1 - r4c1 = (7)r6c3 => r6c3<>3

(7)r6c3 = r9c3 - r7c1 = (7-3)r7c4 = r7c8 - r9c9 = (3-7)r1c9 = (7)r46c9 => r6c8<>7


(2)r3c27 = [(2=5)r3c5 - (5)r3c2 = [(7)r3c6 = r9c6 - r7c4 = (7-8)r7c1 = [(8)r7c2 = r7c7 - r8c9 = r12c9 - (8=1)r3c7 - (1=8)r3c2] - (8)r6c2 = (8-7)r6c3 = r9c3 - r9c6 = (7)r3c6]] => r3c6<>2

Expect to see r3 ALS/AHS used a lot in this article. A large portion of this chain feels redundant but I couldn't reduce it any further. Originally found as a big Kraken X-Wing but it's easier to put into notation this way.

By the same token:


(5)r3c2 = [(5=2)r3c5 - (2)r3c27 = [(3)r3c3 = r3c8 - r1c9 = r9c9 - r9c4 = (3-7)r7c4 = (7-8)r7c1 = [(8)r7c2 = r7c7 - (8=1)r3c7 - (1=8)r3c2] - (8)r6c2 = (8-7)r6c3 = r9c3 - r7c1 = (7-3)r7c4 = r9c4 - r9c9 = r1c9 - r3c8 = (3)r3c3]] => r3c3<>5


(2)r1c5 = [(2)r1c12 = [(2)r5c7 = r6c78 - (2)r6c5 = [(2)r3c5 = r8c5 - r8c1 = (2)r9c2] - (2)r3c2 = (2-1)r1c2 = r3c2 - (1=3782)r3c3678]] => r1c7<>2

Almost ER with an Almost-Transport into an ALS.


(2)r2c4 = [(3)r9c4 = (3-7)r7c4 = [(13)(r9c49=r9c7) - (1)r3c567 = [(7)r9c4 = r1c4 - (7=825)r3c567 - (25)r3c2 = [(2)r9c2 = r1c2 - (59)(b1p2=b1p36) - (9=8)r2c4 - (8=7)r3c6 - r1c4 = (7)r9c4]]]] => r9c4<>2

Nice use of an ALS to tie up 2 Kraken candidates at once. I tried to extend this to eliminate 9r9c4 but it never worked out.


(7)r1c4 = [(7)r6c9 = (7-8)r6c3 = r6c2 - (8)r7c2 = [(7)r6c9 = r6c3 - r4c1 = (7-8)r7c1 = r7c7 - (8)r13c7 = [(68)(b3p36=b3p1) - (4)r1c7 = [(8)r7c1 = (8)r7c7 - (49)(r7c7=r59c7) - (13)(r9c7=r9c49) - (7)r9c4 = (7)r7c4] - (7)r7c1 = r4c1 - r6c3 = (7)r6c9]]] => r1c9<>7


Grouped Kraken AHS: (2=36895)b1p12369 - (5)r3c2 = [(25)(r3c578=r3c2) - (2)r9c2 = (2-7)r9c6 = r3c6 - r1c4 = (7)r1c8] => r1c8<>2


(9)r7c2 = [(9)r2c4 = [(3)r7c4 = r7c8 - r9c9 = (3-7)r9c4 = [(3)r7c4 = r7c8 - (3)r1c8 = [(7)r7c4 = r1c4 - (7=4)r1c8 - r1c5 = (4-9)r2c6 = r2c3 - r1c2 = (9-2)r9c2 = (2-7)r9c6 = (7)r7c4]]] => r7c4<>9

(7)r1c8 = r1c4 - (7=3)r7c4 - (37)(r7c8=r13c8) => r1c8<>4


This one had too much overlapping nonsense so I split it into 3 diagrams. It's all based on the AALS (123678)r1278c1. 3 is easy to discount so these diagrams use the ALS (12678)r1278c1. Left diagram is minus the Kraken candidates 8r12c1, middle is for 8r2c1, right is showing the Almost-AIC that is tied to 8r1c1. Unfortunately I couldn't find any simpler way to weakly link 8r1c1 to 8r7c2. 

(8)r6c2 = r6c3 - (8=3)r3c3 - (3)r1c1 = [(8)r6c2 = (8-7)r6c3 = r4c1 - (7=268)r178c1 - (8)r2c1 = [(8)r7c7 = (8-12)r3c7 = [(8)r6c2 = (8-7)r6c3 = r4c1 - (7=2681)r1278c1 - r2c9 = (12)r23c8 - (12=5)r6c8 - r8c8 = (5-8)r8c9 = r2c9 - r3c7 = (8)r7c7]]] => r7c2<>8


(1)r3c7 = [(8=3)r3c3 - r5c3 = (3-1)r5c1 = [(8)r7c7 = r7c1 - r8c13 = (8-5)r8c9 = r8c8 - (5)r6c8 = [(8)r7c7 = (8-7)r7c1 = (7-1)r4c1 = r2c1 - r2c9 = r23c8 - (1=2)r6c8 - r56c7 = (2)r3c7]]] => r3c7<>8

(8)r6c2 = (8-7)r6c3 = r9c3 - r9c6 = (7-8)r3c6 = (8)r3c23 => r1c2<>8

AALS-Ring: (8=512)r3c257 - (12=73)r13c8 - r7c8 = (3-7)r7c4 = r7c1 - r9c3 = (7-8)r6c3 = (8)r6c2- => r6c3<>56
Shame this doesn't result in more eliminations.

Kraken Column: (8)r3c23 = r3c6 - r4c6 = (8-5)r4c4 = [(8)r3c23 = (8-7)r3c6 = r3c8 - r1c8 = (7-5)r1c4 = r5c4 - r5c3 = (5)r1c3] => r1c3<>8

Kraken Row: (5=2)r3c5 - (2=1)r3c7 - (1)r9c7 = [(5=2)r3c5 - (2=173)b3p278 - r7c8 = r7c4 - r9c4 = (3-1)r9c9 = r9c4 - (1=2895)r2458c4] => r1c4, r46c5<>5

Kraken AALS: (2)r3c2 = [(2=1)r3c7 - (1=497)r9c237 - (7=8)r6c3 - r6c2 = (8)r3c2] => r3c2<>2


Kraken X-Wing tie ALS AIC: (3)r9c9 = r1c9 - (3=1274)b3p2578 - (4)r2c6 = [(4)c36\r89 = (4)r5c3 - (4)r5c7 = [(4)r79c7 = r1c7 - (4=1273)b3p2578 - r1c9 = (3)r9c9]] => r9c9<>4

(1=3)r9c9 - r9c4 = (3-7)r7c4 = r7c1 - r4c1 = (7)r4c9 => r4c9<>1


(5=2)r3c5 - (2=1)r3c7 - (1)r9c7 = [(5)r1c3 = r5c3 - r5c4 = (5-8)r4c4 = r4c6 - (8)r3c6 = [(5=1273)r3c5678 - r1c9 = (3-1)r9c9 = r9c4 - (37)(b8p7 = b8p19) - (7=8)r3c6 - r4c6 = (8-5)r3c3 = r5c4 - r5c3 = (5)r1c3]] => r1c5, r3c2<>5

This places 5r3c5.

(7)r6c9 = (7-8)r6c3 = r6c2 - (8=12)r3c27 - r3c8 = (2)r6c8 - (578)(r6c8 = r6c239) => r6c9<>16

(4=1)r2c8 - r2c1 = (1-8)r3c2 = r6c2 - (8=7)r6c3 - (7=5)r6c9 - r8c9 = (5)r8c8 => r8c8<>4

(1=3)r9c9 - r9c4 = (3-7)r7c4 = r7c1 - r4c1 = r4c9 - (7=5)r6c9 - r8c9 = (5)r8c8 => r8c8<>1


Kraken AALS: (1=3)r9c9 - (3=4698)r7c2578 - (8)r8c9 = [(1=4576)r4568c9 - (6=21)r36c7 - r9c7 = (1)r89c9] => r2c9<>1

This isn't a hugely complex move but I made the image full sized because I love the colours.


Almost W-Wing Transport: (1)r5c9 = [(3)r5c1 = r1c1 - r1c9 = (3-1)r9c9 = r8c9 - r8c45 = (1-7)r9c4 = [(8=7)r6c3 - r9c3 = r9c6 - (7=8)r3c6] - (8=3)r3c3 - r1c1 = (3)r5c1] => r5c1<>1

This move also gives us the virtual strong link 3r5c1 = 1r5c9, or 3r5c1 = 3r9c9.

Ring: (1=8)r3c2 - r6c2 = (8-7)r6c3 = (7-1)r4c1 = (1)r2c1- => r4c1<>6


(1)r5c9 = [(1)r8c45 = r9c4 - (1)r5c4 = [(8=1)r3c2 - r2c1 = r4c1 - r5c2 = (1-9)r5c7 = r5c46 - (9)r4c56 = [(8=1)r3c2 - r2c1 = r4c1 - (1=68)r4c56]] - (8=7)r3c6 - (37)(r1c4 = r79c4) - (1)r9c4 = (1)r8c45] => r8c9<>1

This should be the last big move of the solve, it is significantly easier now.


Kraken ALS Transport: (4)r8c9 = [(7=58)r68c9 - r7c7 = (8-7)r7c1 = (7)r9c3] - (7)r6c3 = (7-1)r4c1 = r2c1 - (1=4)r2c8 => r12c9, r7c8<>4

ER

Sashimi Swordfish

AHS-AIC: (3)r3c3 = r3c8 - (3=9)r7c8 - (29)(r7c2 = r19c2) - (5)r1c2 = (5)r1c3 => r1c3<>3

Kraken Row: (8)r8c1 = [(8)r3c23 = (8-7)r3c6 = (7-2)r9c6 = r9c2 - (2=6)r8c1 - r8c56 = (6-4)r7c5 = r1c5 - r1c7 = (4-1)r2c8 = (1)r2c1] => r2c1<>8

the same with a little transport: (1)r2c1 - (1=8)r3c2 => r1c1<>8

Kraken Cell: (9)r1c2 = r7c2 - (9)r8c3 = [(4)r1c5 = (4-6)r7c5 = r7c12 - (6=4)r8c3 - r8c9 = r79c7 - r1c7 = (4)r1c5] => r1c5<>9

Ring: (2=4)r1c5 - r1c7 = (4-1)r2c8 = (1-2)r2c1 = (2)r2c46- => r1c4<>2, r2c1<>6

ALS-XZ: (8=12)b1p48 - (2=3798)r1279c4 => r3c6<>8

Hidden Pair

Kraken Cell: (9=8)r1c4 - (8)r1c7 = [(9=284)b2p124 - (4=6)r1c7 - (6=129)r356c7] => r5c4<>9

(9=64)r28c3 - r8c9 = r79c7 - r1c7 = (4-1)r2c8 = r2c1 - (1=7)r4c1 - r6c3 = (7)r9c3 => r9c3<>9

Kraken X-Wing: (9)r59\c67 = (9-2)r9c2 = (2)r1c2 - (59)(r1c2 = r1c34) => r2c6<>9

(9)r9c6 = [(9)r5c6 = r5c7 - r9c7 = (9-2)r9c2 = r9c6 - (2)r5c6 = [(8)r4c6 = (8-5)r4c4 = (5-2)r5c4 = (2-9)r5c7 = (9)r5c6]] => r4c6<>9

Kraken Finned Swordfish: (4)r7c5 = r1c5 - (4)r1c7 = [(9)c267\r579b8 = r1c2 - (9=8)r1c4 - (48)(r1c7 = r79c7) - (9)r79c7 = r5c7 - r5c6 = (9)r89c6] => r7c5<>9

(6=4)r7c5 - (4=2)r1c5 - (2=36)r15c1 => r7c1<>6

(9=378)r7c148 - r8c1 = (8-5)r8c9 = (5)r8c8 => r8c8<>9

Naked Triple

(6)r6c7 = r6c5 - (6=4)r7c5 - r1c5 = (4)r1c7 => r1c7<>6

(6=4)r7c5 - r89c6 = r2c6 - r2c8 = (4-9)r4c8 = (9)r4c5 => r4c5<>6

(6=4)r7c5 - r1c5 = (4-8)r2c6 = (8-6)r4c6 = (6)r4c2 => r7c2<>6

STTE

Definitely easier than #640, probably also easier than #639. Or perhaps I've gotten used to solving these horrid puzzles. This was an effort over 3 days, Sudoku.Coach says I took 4h07m but that doesn't include my time fiddling around in Xsudo. Puzzle #643 will be posted tomorrow, let's hope it's not another SE 9.4 monstrosity...





















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