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by **yzfwsf** » Sat Oct 05, 2024 9:13 am

Code: Select all: ...8...329...6......5....76.53......8...196......4....1.....4....27....8.........

This puzzle has MSLS but my solver can't find it, is there another solver that can find it?
After basic steps ,at this state puzzle have MSLS.

Code: Select all: +------------------------+-------------------------------+---------------------------+ | 7-4 1467 1467 | 8 579 1457 | 59(1) 3 2 | | 9 2378-1 78-1 | 235(1) 6 2357-1 | 58(-1) 458(1) 45(1) | | 23-4 12348 5 | -23(149) 239 1234 | 89(1) 7 6 | +------------------------+-------------------------------+---------------------------+ | 267(4) 5 3 | 26 278 2678 | 278(1) -28(149) -7(149) | | 8 247 47 | 235 1 9 | 6 245 3457 | | 267 19 19 | 2356 4 235678 | 23578 258 357 | +------------------------+-------------------------------+---------------------------+ | 1 36789 6789 | 2356(9) 2358-9 23568 | 4 2569 3579 | | 35(4) -3(469) 2 | 7 35(9) -35(146) | 35(1) -5(169) 8 | | 357-4 346789 46789 | -2356(14-9) 2358-9 1234568 | 2357-1 12569 13579 | +------------------------+-------------------------------+---------------------------+

by **Cenoman** » Sat Oct 05, 2024 9:32 pm

The puzzle (rated about 9.2) is solved in three steps:

Code: Select all: +--------------------------+------------------------------+--------------------------+ | 47 1467 1467 | 8 579 1457 | 159 3 2 | | 9 12378 178 | 1235 6 12357 | 158 1458 145 | | 234 12348 5 | 12349 239 1234 | 189 7 6 | +--------------------------+------------------------------+--------------------------+ | 2467 5 3 | 26 278 2678 | 1278 12489 1479 | | 8 247 47 | 235 1 9 | 6 245 3457 | | 267 19 19 | 2356 4 235678 | 23578 258 357 | +--------------------------+------------------------------+--------------------------+ | 1 36789 6789 | 23569 23589 23568 | 4 2569 3579 | | 345 3469 2 | 7 359 13456 | 135 1569 8 | | 3457 346789 46789 | 1234569 23589 1234568 | 12357 12569 13579 | +--------------------------+------------------------------+--------------------------+

1. (1)r2c789 = r13c7 - r4c7 = (19-4)r4c89 = r4c1 - (4=7)r5c3 - (7=4581)r2c3789 => -1 r2c246; lcls, 1 placement

Code: Select all: +--------------------------+--------------------------+--------------------------+ | 7-4 1467 1467 | 8 579 1457 | 59-1 3 2 | | 9 2378 178 | 235 6 2357 | 58-1 1458 145 | | 23-4 12348 5 | 14 239 1234 | 89-1 7 6 | +--------------------------+--------------------------+--------------------------+ | <2467 5 3 | <26 <278 <278 | <1278 149-28 149-7 | | 8 247 47 | 235 1 9 | 6 245 3457 | | 267 19 19 | 2356 4 23578 | 23578 258 357 | +--------------------------+--------------------------+--------------------------+ | 1 3678 678 | 9 2358 23568 | 4 256 357 | | <345 469-3 2 | 7 <35 146-35 | <135 169-5 8 | | 357-4 346789 46789 | 14 2358 1234568 | 2357-1 12569 13579 | +--------------------------+--------------------------+--------------------------+

2. MSLS r4c14567, r8c157:
8 cell Truths, 8 Links: 4c1, 1c8, 2678r4, 35r8
14 eliminations: -4r139c1, -1r1239c7, -2r4c8, -7r4c9, -8r4c8, -3r8c26, -5r8c68; lcls, 40 placements

PM 8x8 of the move:

Hidden Text: Show

Code: Select all: +-----------------+------------------+------------------+ | 7 6 14 | 8 5 14 | 9 3 2 | | 9 3 8 | 2 6 7 | 5 14 14 | | 2 14 5 | 14 9 3 | 8 7 6 | +-----------------+------------------+------------------+ | 4 5 3 | 6 7 8 | 2 19 19 | | 8 2 7 | 3 1 9 | 6 45 45 | | 6 19 19 | 5 4 2 | 3 8 7 | +-----------------+------------------+------------------+ | 1 7 6 | 9 8 5 | 4 2 3 | | 5 49 2 | 7 3 46 | 1 69 8 | | 3 8 49 | 14 2 146 | 7 569 59 | +-----------------+------------------+------------------+

3. Remote pair (14)[r1c3 = r1c6 - r3c4 = r9c4] => -4 r9c3; ste
or DP(1459)r2459c89 using single internal => +6r9c8; ste

@yzfwsf: is your expectation to see a MSLS yielding the same resolution state as the one at the end of my step #2 ?

Failed first version

Hidden Text: Show

If so, it is possible to combine steps #1, #2:
In the resolution state at the start of step #2, note that the only difference within MSLS cells is the candidate 9r8c5.
At the start of step #1, the resolution state is an almost MSLS:
[(1)r2c789 = r13c7 - r4c7 = (19-4)r4c89 = r4c1 - (4=7)r5c3 - (7=4581)r2c3789] - r2c4 = (14-9)r39c4 = r7c4 - (9)r8c5 = [MSLS] => the MSLS is True, and all its eliminations can be done.
Matrix of the move (MBM 15x15):

Code: Select all: 2r4c1 4r4c1 6r4c1 7r4c1 | 2r4c4 6r4c4 | 2r4c5 7r4c5 8r4c5 | 2r4c6 7r4c6 8r4c6 | 2r4c7 7r4c7 8r4c7 1r4c7 | 1r8c7 3r8c7 5r8c7 | 4r8c1 3r8c1 5r8c1 | 3r8c5 5r8c5 | 9r8c5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 9r7c4 9r39c4 14r39c4 1r2c4 1r2c789 1r13c7 1r4c7 19r4c89 4r4c89 4r4c1 4r5c3 7r5c3 1r2c3789 4587r2c3789

The matrix is of the type MBM (Mixed Block Matrix) with the MSLS PM 8x8 at its left-up part, and a TM 7x7 at its right-bottom part.
The first ten columns can be brought at the position of col #1, producing then the corresponding eliminations:
- for col # to #8: the 14 MSLS eliminations (-4r139c1, -1r1239c7, -2r4c8, -7r4c9, -8r4c8, -3r8c26, -5r8c68)
- for col # & #10: -9 b8p278, -23 r3c4, -2356r9c4
Note: -4 r1c1 & -1r1c7 are the effective eliminations yielding step #3 resolution state.

Added.
Silly me ! How could I missed that ? :oops:

I bothered to append additional truths and links to my step#2 MSLS, and didn't see that my first 12 rows brought an answer to the challenge:

Code: Select all: 2r4c1 4r4c1 6r4c1 7r4c1 2r4c4 6r4c4 2r4c5 7r4c5 8r4c5 2r4c6 7r4c6 8r4c6 2r4c7 7r4c7 8r4c7 1r4c7 1r8c7 3r8c7 5r8c7 4r8c1 3r8c1 5r8c1 3r8c5 5r8c5 9r8c5 9r7c4 9r3c4 9r9c4 4r3c4 4r9c4 1r3c4 1r9c4 1r2c4 1r13c7 1r2c789

12 Truths: 4n14567, 8n157, 149c4, 1b3
12 Links: 4c1, 1c7, 2678r4, 35r8, 9b8, 39n4, 1r2
24 eliminations: -4 r139c1, -28r4c8, -7 r4c9, -1 r29c7, -3 r8c26, -5 r8c68, -9 b8p278, - 23 r3c4, -2356r9c4, -1 r2c236; ste

Rank 0 logic, but not exactly a MSLS (4 Truths are not cell-truths). It has inspired me another presentation of the logic. See my post below.

by **yzfwsf** » Sat Oct 05, 2024 9:42 pm

Cenoman wrote:@yzfwsf: is your expectation to see a MSLS yielding the same resolution state as the one at the end of my step #2 ?

Yes, but the resolution state at the beginning is different.

by **blue** » Sun Oct 06, 2024 6:09 pm

yzfwsf wrote:This puzzle has MSLS but my solver can't find it, is there another solver that can find it?

This isn't from a public domain solver, but here's one:

Code: Select all: +-----------------------+---------------------------+-------------------------+ | 7-4 1467 1467 | 8 579 1457 | (159) 3 2 | | 9 2378-1 78-1 | (1235) 6 2357-1 | (58-1) (1458) (145) | | 23-4 12348 5 | 149-23 239 1234 | (189) 7 6 | +-----------------------+---------------------------+-------------------------+ | (2467) 5 3 | (26) 278 2678 | (1278) 149-28 149-7 | | 8 (247) (47) | (235) 1 9 | 6 (245) (3457) | | (267) 19 19 | (2356) 4 235678 | (23578) (258) (357) | +-----------------------+---------------------------+-------------------------+ | 1 36789 6789 | (23569) 2358-9 23568 | 4 2569 3579 | | (345) 469-3 2 | 7 (359) 146-35 | (135) 169-5 8 | | 357-4 346789 46789 | 14-23569 2358-9 1234568 | 2357-1 12569 13579 | +-----------------------+---------------------------+-------------------------+ 23 Truths = {468N1 5N2 5N3 24567N4 8N5 123468N7 256N8 256N9} 23 Links = {1r2 4r5 35r8 4c1 2356c4 1c7 4589b3 267b4 23578b6 9b8} 24 Eliminations --> r9c4<>23569, r2c2367<>1, r139c1<>4, r8c26<>3, r8c68<>5, r79c5<>9, r3c4<>23, r4c8<>28, r4c9<>7, r9c7<>1,

The cell list is: b3p14567, b4p1567, b6p156789, r24567c4, r8c157
After that and "basics", a "4c34" skyscraper reduces it to singles:
(Added: This is also Cenoman's final state.)

Code: Select all: +--------------+--------------+------------+ | 7 6 1(4) | 8 5 1-4 | 9 3 2 | | 9 3 8 | 2 6 7 | 5 14 14 | | 2 1-4 5 | 1(4) 9 3 | 8 7 6 | +--------------+--------------+------------+ | 4 5 3 | 6 7 8 | 2 19 19 | | 8 2 7 | 3 1 9 | 6 45 45 | | 6 19 19 | 5 4 2 | 3 8 7 | +--------------+--------------+------------+ | 1 7 6 | 9 8 5 | 4 2 3 | | 5 49 2 | 7 3 46 | 1 69 8 | | 3 8 9(4) | 1(4) 2 146 | 7 569 59 | +--------------+--------------+------------+

by **yzfwsf** » Mon Oct 07, 2024 8:14 am

blue wrote:This isn't from a public domain solver, but here's one:

Awesome！

by **shye** » Mon Oct 07, 2024 5:39 pm

blue wrote:23 Truths = {468N1 5N2 5N3 24567N4 8N5 123468N7 256N8 256N9}
23 Links = {1r2 4r5 35r8 4c1 2356c4 1c7 4589b3 267b4 23578b6 9b8}
24 Eliminations --> r9c4<>23569, r2c2367<>1, r139c1<>4, r8c26<>3, r8c68<>5, r79c5<>9, r3c4<>23, r4c8<>28, r4c9<>7, r9c7<>1

great find! here's a multifish inversion that reduces the truth count to 11, makes it a bit more digestable i think:

base: 1b3, 149c4, 149r4, 1469r8
covers: 1r2, 1c7, 4c1, 9b8, r39c4, r4c89, r8c268

XSudo input: Show

by **yzfwsf** » Mon Oct 07, 2024 10:29 pm

shye wrote:great find! here's a multifish inversion that reduces the truth count to 11

Multifish [20,242] 30 Candidates,
10 Truths = {149R4 149C4 8N157 1B3}
10 Links = {1r2 35r8 1c7 4c1 39n4 4n8 4n9 9b8}
24 Eliminations --> r9c4<>23569, r2c2367<>1, r139c1<>4, r8c26<>3, r8c68<>5, r79c5<>9,
r3c4<>23, r4c8<>28, r4c9<>7, r9c7<>1,

by **blue** » Tue Oct 08, 2024 3:10 am

Like the last one, but with no "cannibal" eliminations:

10 Truths = {49R4 1C489 4C4 8N157 9B2}
10 Links = {1r2 35r8 4c1 9c5 39n4 4n8 4n9 1b9}
24 Eliminations --> r9c4<>23569, r2c2367<>1, r139c1<>4, r8c26<>3,
r8c68<>5, r79c5<>9, r3c4<>23, r4c8<>28, r4c9<>7, r9c7<>1,

by **Cenoman** » Tue Oct 08, 2024 9:35 pm

I have edited my post above. While correcting my failed first trial, I have found another way to present the same logic. I call that "AALS Kraken Loop" (same type as yzfwsf's 'Blossom Loop', but with an AALS as a stem)

Code: Select all: +--------------------------+------------------------------+--------------------------+ | 7-4 1467 1467 | 8 579 1457 | F159 3 2 | | 9 2378-1 78-1 | D1235 6 2357-1 | E58-1 E1458 E145 | | 23-4 12348 5 | C149-23 239 1234 | F189 7 6 | +--------------------------+------------------------------+--------------------------+ | b2467 5 3 | 26 278 2678 | d1278 c149-28 c149-7 | | 8 247 47 | 235 1 9 | 6 245 3457 | | 267 19 19 | 2356 4 235678 | 23578 258 357 | +--------------------------+------------------------------+--------------------------+ | 1 36789 6789 | B23569 2358-9 23568 | 4 2569 3579 | |za345 469-3 2 | 7 zA359 146-35 | z135 169-5 8 | | 357-4 346789 46789 | C14-23569 2358-9 1234568 | 2357-1 12569 13579 | +--------------------------+------------------------------+--------------------------+

AALS Kraken Loop (13459)r8c157
(4)r8c1 - r4c1 = (49-1)r4c89 = (1)r4c7
(9)r8c5 - r7c4 = (94-1)r39c4 = r2c4 - r2c789 = (1)r13c7
(351)r8c157
=> same 24 eliminations: -1 r29c7, -4 r139c1, -28r4c8, -7 r4c9, -9 b8p278, - 23 r3c4, -2356r9c4, -1 r2c236, -3 r8c26, -5 r8c68; lcls, 41 placements; then end as above.

by **yzfwsf** » Tue Oct 08, 2024 11:39 pm

Cenoman wrote:I have edited my post above. While correcting my failed first trial, I have found another way to present the same logic. I call that "AALS Kraken Loop" (same type as yzfwsf's 'Blossom Loop', but with an AALS as a stem)

I also found it manually, and now I plan to implement it in Blossom Loop.

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