The New Sudoku Players' Forum

by **mith** » Mon Apr 05, 2021 3:03 pm

Code: Select all: +-------+-------+-------+ | . . 3 | . . 1 | 4 . . | | . . . | . . . | . 1 . | | . . 5 | . . 9 | . . . | +-------+-------+-------+ | 2 . . | . 6 . | . . 5 | | 3 . . | 5 . 8 | . . 9 | | 7 . . | . 9 . | . . 3 | +-------+-------+-------+ | . . . | 2 . . | 3 . . | | . 8 . | . . . | . . . | | . . 4 | 6 . . | 2 . . | +-------+-------+-------+ ..3..14.........1...5..9...2...6...53..5.8..97...9...3...2..3...8.........46..2..

by **Cenoman** » Mon Apr 05, 2021 8:20 pm

Code: Select all: +---------------------+-------------------+--------------------+ | 689 69 3 | 78 27 1 | 4 5 267 | | 4 2 7 | 3 5 6 | 9 1 8 | | c168 b16 5 | 478 247 9 | 67 3 267 | +---------------------+-------------------+--------------------+ | 2 xAa149 y189* | 147 6 3 | z178* 4-7 5 | | 3 B146 B16* | 5 47 8 |zB167* 2 9 | | 7 5 168* | 14 9 2 | 168* 46 3 | +---------------------+-------------------+--------------------+ | 1569 7 169 | 2 18 45 | 3 89 146 | | d16 8 2 | 9 3 47 | 5 d67 1467 | | 159 3 4 | 6 18 57 | 2 89 17 | +---------------------+-------------------+--------------------+

Kraken cell (149)r4c2 + DP (168)r456c37 (using internals)
(1)r4c2 - r3c2 = r3c1 - (1=67)r8c18
(4)r4c2 - (4=167)r5c237
(9)r4c2 - r4c3=DP=(7)r45c7
---------------
=> -7 r4c8; ste

by **pjb** » Tue Apr 06, 2021 12:22 am

Code: Select all: 689 b69 3 | 78 27 1 | 4 5 267 4 2 7 | 3 5 6 | 9 1 8 aB168 A16 5 | 478 247B 9 | 67a 3 267A -------------------------+----------------------+--------------------- 2 149 189 | 147D 6 3 | 178 eE47eE 5 3 c146 d16 | 5 47C 8 |d167b 2 9 7 5 168 | 14D 9 2 | 168b 46c 3 -------------------------+----------------------+--------------------- 1569 7 169 | 2 18 45 | 3 89 146 C16 8 2 | 9 3 47 | 5 D67d 1467 159 3 4 | 6 18 57 | 2 89 17

Kraken row r3c1279:
(6)r3c1 - r1c2 = r5c2 - (6=7)r5c37 - (7)r4c8
(6-1)r3c2 = r3c1 - (1=6)r8c1 - (6=7)r8c8 - (7)r4c8
(6)r3c7 - r56c7 = r6c8 - (6=7)r8c8 - (7)r4c8
(6-2)r3c9 = (2-4)r3c5 = (4)r5c5 - (4=7)r46c4 - (7)r4c8 => -7 r4c8; stte

Phil

by **AnotherLife** » Wed Apr 07, 2021 1:00 pm

After the lcls steps, I found manually a simple two-step solution without forcing chains.
1. W-wing
(7=4)r5c5-r6c4=r6c8-(4=7)r4c8 => -7 r4c4, r5c7

Code: Select all: .----------------.--------------.---------------. | 689 69 3 | 78 27 1 | 4 5 267 | | 4 2 7 | 3 5 6 | 9 1 8 | | 168 16 5 | 478 247 9 | 67 3 267 | :----------------+--------------+---------------: | 2 149 189 | 14-7 6 3 | 178 d47 5 | | 3 146 16 | 5 a47 8 | 16-7 2 9 | | 7 5 168 | b14 9 2 | 168 c46 3 | :----------------+--------------+---------------: | 1569 7 169 | 2 18 45 | 3 89 146 | | 16 8 2 | 9 3 47 | 5 67 1467 | | 159 3 4 | 6 18 57 | 2 89 17 | '----------------'--------------'---------------'

2. After 5 singles and some other lcls steps, there is an XY-Wing:
(4=6)r7c9-(6=7)r8c8-(7=4)r8c6 => -4 r7c6, r8c9; sste

Code: Select all: .--------------.-------------.----------------. | 89 69 3 | 78 2 1 | 4 5 67 | | 4 2 7 | 3 5 6 | 9 1 8 | | 18 16 5 | 78 4 9 | 67 3 2 | :--------------+-------------+----------------: | 2 19 189 | 14 6 3 | 178 47 5 | | 3 4 16 | 5 7 8 | 16 2 9 | | 7 5 168 | 14 9 2 | 168 46 3 | :--------------+-------------+----------------: | 56 7 19 | 2 18 5-4 | 3 89 a46 | | 16 8 2 | 9 3 c47 | 5 b67 167-4 | | 159 3 4 | 6 18 57 | 2 89 17 | '--------------'-------------'----------------'

Actually, if we eliminate a digit or force a digit into a cell with a forcing chain (or a forcing net), we might need three of more chains, so is it better than a two-step solution with two chains described by standard patterns?

by **jco** » Wed Apr 07, 2021 1:38 pm

Hello AnotherLife,

AnotherLife wrote:(...)
Actually, if we eliminate a digit or force a digit into a cell with a forcing chain (or a forcing net), we might need three of more chains, so is it better than a two-step solution with two chains described by standard patterns?

I like the puzzle section because I can see a variety of solutions found by the players as they use their knowledge and creativity to propose interesting solutions different from the ones already posted. Many times I started studying the details of techniques previously unknown to me because I noticed the beauty, elegance and effectiveness of those techniques used by advanced players to solve puzzles.

Regards,
jco

by **Hajime** » Sun Apr 11, 2021 4:56 pm

Just 2 XY-chains, one of length 3 and one of length 5:

Solution Path:

Hidden Text: Show

Summary used Methods

Hidden Text: Show

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