The New Sudoku Players' Forum

by **ArkieTech** » Sun Aug 18, 2019 10:06 am

Code: Select all: *-----------* |...|..6|851| |.6.|.1.|...| |.1.|7.3|...| |---+---+---| |1..|...|7..| |2..|1.9|..6| |..9|...|..3| |---+---+---| |...|9.4|.3.| |...|.8.|.4.| |746|2..|...| *-----------*

by **SpAce** » Sun Aug 18, 2019 11:58 am

Code: Select all: .------------------.------------------.-----------------. | 39 2379 237 | 4 29 6 | 8 5 1 | | 49 6 25 | 58 1 28-5 | 3 7 49 | | 4589 1 58 | 7 a[59] 3 | a24[9] 6 249 | :------------------+------------------+-----------------: | 1 58 458 | 3 6 258 | 7 29 459 | | 2 357 3457 | 1 457 9 | 45 8 6 | | 6 578 9 | 58 2457 2578 | 145 12 3 | :------------------+------------------+-----------------: | 58 258 1 | 9 7-5 4 | 6 3 257 | | 359 2359 235 | 6 8 157 | 125 4 257 | | 7 4 6 | 2 3 b1(5) | b1(59) 19 8 | '------------------'------------------'-----------------'

M-Wing:

(59)r3c57 = (95)r9c76 => -5 r2c6,r7c5; btte

This is how it continues to reach stte, but I don't think it counts as a single move as written:

[(59)r3c57 = (95)r9c76] - (5=7)r7c5 - r56c5 = r6c6 - (7=58)r46c2 => +7 r7c5,r6c6; -58 r4c3,r7c2, -5 r2c6,r5c23,r8c2; stte

I guess this would, technically, but I really don't like the redundant backpedaling and subchaining. Basically it's the same thing in a longer form:

(58=7)r46c2 - r6c6 = r56c5 - (7=5)r7c5 - (59)r9c67 = (95)r3c75 - (5=7)r7c5 - r56c5 = r6c6 - (7=58)r46c2
=> +7 r7c5,r6c6; -58 r4c3,r7c2, -5 r2c6,r5c23,r8c2; stte

by **Cenoman** » Sun Aug 18, 2019 8:14 pm

Code: Select all: +-----------------------+---------------------+-------------------+ | 39 2379 237 | 4 29 6 | 8 5 1 | | 49 6 25 | 58 1 Cc258 | 3 7 49 | | 4589 1 58 | 7 59 3 | 249 6 249 | +-----------------------+---------------------+-------------------+ | 1 Bb58 b458 | 3 6 Cc258 | 7 Y29 Xa459 | | 2 357 3457 | 1 457 9 | 45 8 6 | | 6 Bb578 9 | 58 2457 Cc2578 | 145 12 3 | +-----------------------+---------------------+-------------------+ | 58 B258 1 | 9 57 4 | 6 3 A257 | | 359 2359 235 | 6 8 y157 | 125 4 y257 | | 7 4 6 | 2 3 zCc15 | 159 Z9-1 8 | +-----------------------+---------------------+-------------------+

Kraken AALS (24579)r478c9:
(4)r4c9 - (4=587)b4p238 - (7=2581)r2469c6
(2)r7c9 - (2=587)r467c2 - (7=2581)r2469c6
(27-1)r8c69 = (1)r9c6
(9)r4c9 - r4c8 = (9)r9c8
=> -1 r9c8; ste
(In AALS cells r478c9, candidates of any combination of three digits can't all be false, otherwise the three cells are left with two digits only, hence the derived 4-SIS 49r4c9==2r78c9 [SIS: Strong Inference Set, one element at least is True])

Added, matrices

Hidden Text: Show

Solution as presented, 7x7 TM

Code: Select all: 9r9c8 9r4c8 1r9c6 1r8c6 7r8c6 7r6c6 758b4p238 4r4c3 758r467c2 2r7c2 7r8c6 7r8c9 9r4c9 4r4c9 2r7c9 2r8c9 (AALS r478c9) => -1 r9c8; ste

...with AALS internal link, 8x8 TM

Code: Select all: 9r9c8 9r4c8 1r9c6 1r8c6 7r8c6 7r6c6 758b4p238 4r4c3 758r467c2 2r7c2 7r8c6 7r8c9 2r7c9 2r8c9 57r78c9 9r4c9 4r4c9 5r4c9 => -1 r9c8; ste

...with ALS's half-developed, 9x9 TM

Code: Select all: 9r9c8 9r4c8 1r9c6 1r8c6 7r8c6 7r6c6 7r6c2 58r46c2 5|8r4c3 4r4c3 5|8r7c2 2r7c2 7r8c6 7r8c9 2r7c9 2r8c9 57r78c9 9r4c9 4r4c9 5r4c9 => -1 r9c8; ste

...fully developed, 11x11 BTM

Code: Select all: 9r9c8 9r4c8 1r9c6 1r8c6 7r8c6 7r6c6 7r6c2 5r6c2 8r6c2 5r4c2 8r4c2 5r4c3 8r4c3 4r4c3 5r7c2 8r7c2 2r7c2 7r8c6 7r8c9 9r4c9 4r4c9 5r4c9 2r7c9 5r7c9 7r7c9 2r8c9 5r8c9 7r8c9 => -1 r9c8; ste

by **SCLT** » Sun Aug 18, 2019 8:34 pm

Code: Select all: +--------------------+------------------+-----------------+ | 39 2379 237 | 4 29 6 | 8 5 1 | | 49 6 25 | 58 1 258 | 3 7 49 | | 4589 1 58 | 7 59 3 | 249 6 249 | +--------------------+------------------+-----------------+ | 1 58 458 | 3 6 258 | 7 29 459 | | 2 357 3457 | 1 457 9 | *45 8 6 | | 6 578 9 | 58 2457 2578 | *145 12 3 | +--------------------+------------------+-----------------+ | 58 258 1 | 9 57 4 | 6 3 257 | | 359 2359 235 | 6 8 157 | 25-1 4 257 | | 7 4 6 | 2 3 15 | *159 *19 8 | +--------------------+------------------+-----------------+

Couldn't manage stte today, but there is this:

WXYZ-Wing: r569c7, r9c8 => -1r8c7 ; lclste

by **SpAce** » Mon Aug 19, 2019 7:15 am

Inspired by Cenoman's solution:

Code: Select all: .--------------------.------------------.------------------. | 39 2379 237 | 4 29 6 | 8 5 1 | | 49 6 25 | 58 1 a258 | 3 7 49 | | 4589 1 58 | 7 59 3 | 249 6 249 | :--------------------+------------------+------------------: | 1 b58 c458 | 3 6 a258 | 7 e(2)9 d459 | | 2 357 3457 | 1 457 9 | 45 8 6 | | 6 b578 9 | 58 2457 a2578 | 145 e(12) 3 | :--------------------+------------------+------------------: | 58 c258 1 | 9 c57 4 | 6 3 d257 | | 359 2359 235 | 6 8 157 | 125 4 257 | | 7 4 6 | 2 3 a[1]5 | 159 9-1 8 | '--------------------'------------------'------------------'

(1=5*,287)r9246c6 - (7=58)r64c2 - (*5|8=427)r4c3,r7c25 - (4|2|7=59)r74c9 - (9=21)r46c8 => -1 r9c8; stte

Or without memory, using the CoALS rule (758=42)r647c2,r4c3:

(1=5287)r9246c6 - (758)r647c2,r4c3|(7)r8c6 = (427)r4c3,r7c25 - (4|2|7=59)r74c9 - (9=21)r46c8 => -1 r9c8; stte

Or with an AAIC:

[(1=5287)r9246c6 - (758=42)r647c2,r4c3 - (4|2=59)r74c9 - (9=21)r46c8] = (7)r7c9 - (7=51)b8p29 => -1 r9c8; stte

10x10 TM: Show

by **SCLT** » Mon Aug 19, 2019 7:51 pm

Kraken column: 5c7 (lots of partially overlapping chains):

Code: Select all: 5r6c7: +--------------------+------------------+-----------------+ | 39 2379 237 | 4 29 6 | 8 5 1 | | 49 6 25 | 58 1 258 | 3 7 c49 | | 4589 1 58 | 7 e59 3 | d249 6 c249 | +--------------------+------------------+-----------------+ | 1 58 458 | 3 6 258 | 7 29 b459 | | 2 357 3457 | 1 e457 9 | bf45 8 6 | | 6 578 9 | 58 2457 2578 | a145 12 3 | +--------------------+------------------+-----------------+ | 58 258 1 | 9 e57 4 | 6 3 257 | | 359 2359 235 | 6 8 157 | 125 4 257 | | 7 4 6 | 2 3 15 | 159 19 8 | +--------------------+------------------+-----------------+ 5r8c7: +--------------------+------------------+----------------+ | 39 2379 237 | 4 29 6 | 8 5 1 | | 49 6 25 | 58 1 d258 | 3 7 49 | | 4589 1 58 | 7 h59 3 | g249 6 249 | +--------------------+------------------+----------------+ | 1 c58 458 | 3 6 d258 | 7 29 459 | | 2 357 3457 | 1 h457 9 | i45 8 6 | | 6 c578 9 | 58 2457 d2578 | 145 12 3 | +--------------------+------------------+----------------+ | 58 c258 1 | 9 h57 4 | 6 3 257 | | b359 b2359 b235 | 6 8 157 | a125 4 257 | | 7 4 6 | 2 3 e15 | f159 19 8 | +--------------------+------------------+----------------+

Code: Select all: 5r5c7 - 4r5c7 || 5r6c7 - (5=49)b6p34 - 9r23c9 = r3c7 - (9=574)r357c5 - 4r5c7 || 5r8c7 - (5=392)r8c123 - (2=587)r467c2 - (7=285)r246c6 - 5r9c6 ===== \\ || || || || || // || =========================================================== // || // 5r9c7 - 9r9c7 = r3c7 - (9=574)r357c5 - 4r5c7

-4 r5c7 ; stte

by **SpAce** » Mon Aug 19, 2019 10:01 pm

SCLT wrote:Kraken column: 5c7 (lots of partially overlapping chains):

And the corresponding matrix:

12x12 TM: Show

Doesn't necessarily make much sense to write it as a flat chain, but just for fun:

(4=579)r573c5 - r3c79 = (9)r2c9&r9c7* - (9)r4c9|(5)r9c7 = (45^)b6p34&(5287)r9246c6 - (7=582)r467c2 - (239=5)r8c123 - r8^6*9c7 = (5)r5c7
=> -4 r5c7; stte

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