The New Sudoku Players' Forum

by **Leren** » Fri Jun 11, 2021 8:23 am

Code: Select all: *-----------* |..2|..4|..5| |.1.|.9.|.38| |6..|.5.|...| |---+---+---| |..9|.2.|.17| |.3.|.8.|2..| |..5|1..|8..| |---+---+---| |..3|..2|...| |9..|.4.|.7.| |..7|9..|.54| *-----------* ..2..4..5.1..9..386...5......9.2..17.3..8.2....51..8....3..2...9...4..7...79...54

by **P.O.** » Fri Jun 11, 2021 9:36 am

Code: Select all: 3 79 2 8 167 4 1679 69 5 5 1 4 2 9 67 67 3 8 6 79 8 37 5 137 4 2 19 48 468 9 346 2 36 5 1 7 147 3 16 4567 8 5679 2 469 69 247 2467 5 1 67 679 8 469 3 14 456 3 567 167 2 169 8 169 9 568 16 56 4 1568 3 7 2 128 268 7 9 3 168 16 5 4 after singles: depth: 2 candidate: 6 from cell (((5 3 4) (1 6))) ((6 0) ((5 8 6) (4 6 9)) ((5 9 6) (6 9))) ((6 0) (6 8 6) (4 6 9)) ((4 1) ((6 1 4) (2 4 7)) ((6 2 4) (2 4 6 7))) ((6 2) (4 2 4) (4 6 8))

by **Cenoman** » Fri Jun 11, 2021 10:25 am

Code: Select all: +-------------------+----------------------+---------------------+ | 3 79 2 | 8 167 4 | 1679 69 5 | | 5 1 4 | 2 9 67 | 67 3 8 | | 6 79 8 | 37 5 137 | 4 2 19 | +-------------------+----------------------+---------------------+ | 48 a468 9 | b346 2 b36 | 5 1 7 | | 147 3 1-6 | c4567 8 5679 | 2 d469 d69 | | 247 246 5 | 1 67 679 | 8 469 3 | +-------------------+----------------------+---------------------+ | 14 456 3 | 567 167 2 | 169 8 169 | | 9 568 16 | 56 4 1568 | 3 7 2 | | 128 268 7 | 9 3 168 | 16 5 4 | +-------------------+----------------------+---------------------+

(6)r4c2 = (6-34)r4c46 = r5c4 - (4=96)r5c89 => -6 r5c3; ste

Edit: corrected typo and grid (once more spotted by JCO, thks !)

by **jco** » Fri Jun 11, 2021 10:54 pm

Code: Select all: .---------------------------------------------------. | 3 79 2 | 8 167 4 | 1679 69 5 | | 5 1 4 | 2 9 67 | 67 3 8 | | 6 79 8 | 37 5 137 | 4 2 19 | |---------------+-----------------+-----------------| |b48 a(46)8 9 | 346 2 36 | 5 1 7 | | 147 3 1-6| 4567 8 5679 | 2 y(46)9 z69 | |(4)27 (4)26 5 | 1 67 679 | 8 (4)69 3 | |---------------+-----------------+-----------------| |b14 456 3 | 567 167 2 | 169 8 169 | | 9 568 c16 | 56 4 1568 | 3 7 2 | | 128 268 7 | 9 3 168 | 16 5 4 | '---------------------------------------------------'

Kraken with Grouped W-wing (46)r5c8,r4c2 SL(4)r6c128
(8)r4c2 - (8=41)r47c1 - (1=6)r8c3
||
(9)r5c8 - (9=6)r5c9
||
W-wing
---------------
=> -6 r5c3; ste

by **pjb** » Sun Jun 13, 2021 4:24 am

Code: Select all: 3 79 2 | 8 167 4 | 1679 69 5 5 1 4 | 2 9 67 | 67 3 8 6 79 8 | 37 5 137 | 4 2 19 ------------------------+----------------------+--------------------- 48 b468 9 |c346 2 c36 | 5 1 7 f47-1 3 a16 | 4567 8 5679 | 2 469 69 e247 246 5 | 1 d67 679 | 8 469 3 ------------------------+----------------------+--------------------- g14 456 3 | 567 167 2 | 169 8 169 9 568 6-1 | 56 4 1568 | 3 7 2 g128 268 7 | 9 3 168 | 16 5 4

(1=6)r5c3 - (6)r4c2 = (6)r4c46 - (6=7)r6c5 - (7)r6c1 = (7-1)r5c1 = (1)r79c1 => -1 r5c1, r8c3; stte

Phil

Website · by **denis_berthier** » Tue Jun 15, 2021 3:39 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 3 79 2 ! 8 167 4 ! 1679 69 5 ! ! 5 1 4 ! 2 9 67 ! 67 3 8 ! ! 6 79 8 ! 37 5 137 ! 4 2 19 ! +----------------+----------------+----------------+ ! 48 468 9 ! 346 2 36 ! 5 1 7 ! ! 147 3 16 ! 4567 8 5679 ! 2 469 69 ! ! 247 246 5 ! 1 67 679 ! 8 469 3 ! +----------------+----------------+----------------+ ! 14 456 3 ! 567 167 2 ! 169 8 169 ! ! 9 568 16 ! 56 4 1568 ! 3 7 2 ! ! 128 268 7 ! 9 3 168 ! 16 5 4 ! +----------------+----------------+----------------+

===> There are 16 W1-anti-backdoors:
n9r1c8 n6r4c2 n4r4c4 n1r5c1 n6r5c3 n4r5c8 n9r5c9 n7r6c1 n2r6c2 n6r6c5 n6r6c8 n9r7c7 n6r7c9 n1r8c3 n2r9c1 n1r9c7
10 of which give rise to a solution with whips[≤7]

The simplest is:

Code: Select all: z-chain[4]: r5n1{c3 c1} - c1n7{r5 r6} - r6c5{n7 n6} - b6n6{r6c8 .} ==> r5c3 ≠ 6 stte

[Edit, after being asked by a non-posting reader] The means for obtaining such results with CSP-Rules is by choosing some set of rules in the configuration file, with a maximum length for chains, e.g.

Code: Select all: (defglobal ?*all-chains-max-length* = 8) (bind ?*Bivalue-Chains* TRUE) (bind ?*Whips* TRUE) ; (bind ?*G-Whips* TRUE) (bind ?*z-Chains* TRUE) (bind ?*Typed-Bivalue-Chains* TRUE) (bind ?*Typed-z-Chains* TRUE) (bind ?*Typed-Whips* TRUE) ; (bind ?*Oddagons* TRUE)

and then typing the command:

Code: Select all: (find-sudoku-1-steppers-wrt-resolution-theory W1 "..2..4..5.1..9..386...5......9.2..17.3..8.2....51..8....3..2...9...4..7...79...54")

For this puzzle, the total computation time for all the 1-step solutions is 16s.
Details about this recent feature of SudoRules are available in the Basic User Manual on https://github.com/denis-berthier/CSP-Rules-V2.1
Make sure you have a recent update of CSP-Rules.

by **RSW** » Tue Jun 15, 2021 6:52 am

Code: Select all: +------------+---------------+--------------+ | 3 79 2 | 8 167 4 | 1679 69 5 | | 5 1 4 | 2 9 67 | 67 3 8 | | 6 79 8 | 37 5 137 | 4 2 19 | +------------+---------------+--------------+ | 48 468 9 | 346 2 36 | 5 1 7 | |e147 3 *1-6| 4567 8 5679 | 2 a469 a69 | |d247 246 5 | 1 c67 679 | 8 b469 3 | +------------+---------------+--------------+ | 14 456 3 | 567 167 2 | 169 8 169 | | 9 568 16 | 56 4 1568 | 3 7 2 | | 128 268 7 | 9 3 168 | 16 5 4 | +------------+---------------+--------------+

(6)r5c89 = r6c8 - (6=7)r6c5 - (7)r6c1 = (7-1)r5c1 = (1)r5c3 => -6r5c3; ste

Edit: Once again, thanks to JCO for correcting my notation.

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