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by **urhegyi** » Sun Jul 25, 2021 8:23 pm

I'm missing some technique to avoid brute force here. Anyone has an idea which one?

Code: Select all: 9...5...4.3....6....2....1....53....5..4.1..7....79....1....2....6....3.4...8...5

by **Leren** » Sun Jul 25, 2021 8:50 pm

Code: Select all: *--------------------------------------------------------------------------------* | 9 *678 *178 |#1236-78 5 #236-78 |*378 *278 4 | |*178 3 45 | 12789 1249 2478 | 6 5789-2 *289 | |*678 45 2 | 36789 469 34678 | 5789-3 1 *389 | |--------------------------+--------------------------+--------------------------| |#126-78 246789 14789 | 5 3 268 | 1489 24689 #126-89 | | 5 2689 389 | 4 26 1 | 389 2689 7 | |#1236-8 2468 1348 | 268 7 9 | 13458 24568 #1236-8 | |--------------------------+--------------------------+--------------------------| |*378 1 5789-3 | 3679 469 34567 | 2 4789-6 *689 | |*278 5789-2 6 | 1279 1249 2457 | 4789-1 3 *189 | | 4 *279 *379 |#1236-79 8 #236-7 |*179 *679 5 | *--------------------------------------------------------------------------------*

There is an SK Loop in cells marked * and # with 19 eliminations as marked. I don't think it gets you much further though.

Leren

<edit> I had a further trick up my sleeve - SK Loop Scenario Testing. This is a variety of Targeted T&E which tests which of the SK Loop * cell candidates must be false. I get the following:

Code: Select all: *-------------------------------------------------------------* | 9 *678 *78-1 | 1236 5 236 |*78-3 *278 4 | |*178 3 45 | 12789 1249 2478 | 6 5789 *89-2 | |*78-6 45 2 | 36789 469 34678 | 5789 1 *389 | |---------------------+------------------+--------------------| | 126 246789 14789 | 5 3 268 | 1489 24689 126 | | 5 2689 389 | 4 26 1 | 389 2689 7 | | 1236 2468 1348 | 268 7 9 | 13458 24568 1236 | |---------------------+------------------+--------------------| |*78-3 1 5789 | 3679 469 34567 | 2 4789 *689 | |*278 5789 6 | 1279 1249 2457 | 4789 3 *89-1 | | 4 *79-2 *379 | 1236 8 236 |*179 *79-6 5 | *-------------------------------------------------------------*

Which, after basics, leads you to here, which is solvable with standard methods :

Code: Select all: *-----------------------------------------------* | 9 6 78 | 1 5 3 | 78 2 4 | | 1 3 45 | 2789 249 2478 | 6 5789 89 | | 78 45 2 | 6789 469 4678 | 5789 1 3 | |----------------+---------------+--------------| | 6 24789 14789 | 5 3 28 | 489 489 12 | | 5 289 89 | 4 26 1 | 3 689 7 | | 3 248 148 | 268 7 9 | 458 4568 12 | |----------------+---------------+--------------| | 78 1 5789 | 3 49 457 | 2 4789 6 | | 2 5789 6 | 79 1 457 | 4789 3 89 | | 4 79 3 | 26 8 26 | 1 79 5 | *-----------------------------------------------*

Leren

Website · by **denis_berthier** » Mon Jul 26, 2021 5:57 am

.
SER = 10.4
BpB classification: p = 2

I find the same sk-loop as Leren, with 21 eliminations instead of 19 (because I don't apply Pairs before it).

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 9 678 178 ! 123678 5 23678 ! 378 278 4 ! ! 178 3 14578 ! 12789 1249 2478 ! 6 25789 289 ! ! 678 45678 2 ! 36789 469 34678 ! 35789 1 389 ! +----------------------+----------------------+----------------------+ ! 12678 246789 14789 ! 5 3 268 ! 1489 24689 12689 ! ! 5 2689 389 ! 4 26 1 ! 389 2689 7 ! ! 12368 2468 1348 ! 268 7 9 ! 13458 24568 12368 ! +----------------------+----------------------+----------------------+ ! 378 1 35789 ! 3679 469 34567 ! 2 46789 689 ! ! 278 25789 6 ! 1279 1249 2457 ! 14789 3 189 ! ! 4 279 379 ! 123679 8 2367 ! 179 679 5 ! +----------------------+----------------------+----------------------+

Code: Select all: belt[4] (= sk-loop) made of 4 crosses: cross in block b1 with center r1c1 horizontal outer candidates: 7 8 vertical outer candidates: 7 8 inner candidates: 1 6 cross in block b3 with center r1c9 horizontal outer candidates: 3 8 vertical outer candidates: 8 9 inner candidates: 2 3 cross in block b9 with center r9c9 horizontal outer candidates: 7 9 vertical outer candidates: 8 9 inner candidates: 1 6 cross in block b7 with center r9c1 horizontal outer candidates: 7 9 vertical outer candidates: 7 8 inner candidates: 2 3 ==> eliminations in rows: r9c6 ≠ 7, r9c4 ≠ 9, r9c4 ≠ 7, r1c6 ≠ 8, r1c6 ≠ 7, r1c4 ≠ 8, r1c4 ≠ 7 ==> eliminations in columns: r6c9 ≠ 8, r6c1 ≠ 8, r4c9 ≠ 9, r4c9 ≠ 8, r4c1 ≠ 8, r4c1 ≠ 7 ==> eliminations in blocks: r8c7 ≠ 1, r8c2 ≠ 2, r7c8 ≠ 6, r7c3 ≠ 3, r3c7 ≠ 3, r3c2 ≠ 6, r2c8 ≠ 2, r2c3 ≠ 1

Code: Select all: +----------------------+----------------------+----------------------+ ! 9 678 178 ! 1236 5 236 ! 378 278 4 ! ! 178 3 4578 ! 12789 1249 2478 ! 6 5789 289 ! ! 678 4578 2 ! 36789 469 34678 ! 5789 1 389 ! +----------------------+----------------------+----------------------+ ! 126 246789 14789 ! 5 3 268 ! 1489 24689 126 ! ! 5 2689 389 ! 4 26 1 ! 389 2689 7 ! ! 1236 2468 1348 ! 268 7 9 ! 13458 24568 1236 ! +----------------------+----------------------+----------------------+ ! 378 1 5789 ! 3679 469 34567 ! 2 4789 689 ! ! 278 5789 6 ! 1279 1249 2457 ! 4789 3 189 ! ! 4 279 379 ! 1236 8 236 ! 179 679 5 ! +----------------------+----------------------+----------------------+

hidden-pairs-in-a-block: b1{n4 n5}{r2c3 r3c2} ==> r3c2 ≠ 8, r3c2 ≠ 7, r2c3 ≠ 8, r2c3 ≠ 7

At this point, the puzzle is in T&E(W1, 1) = B1B = gB. It is therefore solvable by g-braids.

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trying to avoid brute force

trying to avoid brute force

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Re: trying to avoid brute force