The New Sudoku Players' Forum

by **Leren** » Fri May 28, 2021 9:23 am

Code: Select all: *-----------* |...|.8.|.3.| |3..|1.4|..5| |...|...|6.4| |---+---+---| |...|..1|...| |..8|.6.|5..| |4..|3..|.2.| |---+---+---| |..1|..9|7..| |..3|...|86.| |25.|.7.|..1| *-----------* ....8..3.3..1.4..5......6.4.....1.....8.6.5..4..3...2...1..97....3...86.25..7...1

by **rjamil** » Fri May 28, 2021 11:26 am

Code: Select all: +---------------------+--------------------+-----------------+ | 1579 1279 4 | 25679 8 2567 | 129 3 79 | | 3 678 67 | 1 29 4 | 29 78 5 | | 15789 12789 2579 | 2579 2359 2357 | 6 1789 4 | +---------------------+--------------------+-----------------+ | 5679 23679 25679 | 245789 2459 1 | 34 479 68 | | 179 12379 8 | 2479 6 27 | 5 1479 379 | | 4 1679 5679 | 3 59 578 | 19 2 68 | +---------------------+--------------------+-----------------+ | 68 468 1 | 46-2 (234) 9 | 7 5 (23) | | 79 479 3 | (245) 1 (25) | 8 6 29 | | 2 5 69 | 68 7 368 | 34 49 1 | +---------------------+--------------------+-----------------+

WXYZ-Wing: 2345 @ r7c59 r8c46 => -2 @ r7c4; btte
(Hidden Pair: 23 @ r7c59 => -4 @ r7c5; stte)

R. Jamil

by **jco** » Fri May 28, 2021 12:25 pm

Code: Select all: .-----------------------------------------------------------. | 1579 1279 4 | 25679 8 2567 | 129 3 79 | | 3 678 67 | 1 29 4 | 29 78 5 | | 15789 12789 2579 | 2579 2359 2357 | 6 1789 4 | |---------------------+--------------------+----------------| | 5679 23679 25679 | 245789 c2459 1 |d34 479 68 | | 179 12379 8 | 2479 6 27 | 5 1479 379 | | 4 1679 5679 | 3 59 578 | 19 2 68 | |---------------------+--------------------+----------------| | 68 468 1 | 246 b234 9 | 7 5 23 | | 79 479 3 | 245 1 25 | 8 6 29 | | 2 5 69 | 68 7 a368 |e4-3 49 1 | '-----------------------------------------------------------'

L-wing (3)r9c6=(3-4)r7c5=r4c5-r4c7=(4)r9c7 => -3 r9c7; ste

by **SteveG48** » Fri May 28, 2021 1:53 pm

Code: Select all: *-----------------------------------------------------------------------------* | 1579 1279 4 | 25679 8 2567 | 129 3 79 | | 3 678 67 | 1 29 4 | 29 78 5 | | 15789 12789 2579 | 2579 2359 2357 | 6 1789 4 | *-------------------------+-------------------------+-------------------------| | 5679 23679 25679 | 245789 a2459 1 | 3-4 479 68 | | 179 12379 8 | 2479 6 27 | 5 1479 379 | | 4 1679 5679 | 3 59 578 | 19 2 68 | *-------------------------+-------------------------+-------------------------| |c68 c468 1 |c246 b234 9 | 7 5 c23 | | 79 479 3 | 245 1 25 | 8 6 29 | | 2 5 69 | 68 7 368 |d34 49 1 | *-----------------------------------------------------------------------------*

4r4c5 = r7c5 - (4=2683)r7c1249 - (3=4)r9c7 => -4 r4c7 ; stte

Website · by **denis_berthier** » Sat May 29, 2021 4:35 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 1579 1279 4 ! 25679 8 2567 ! 129 3 79 ! ! 3 26789 2679 ! 1 29 4 ! 29 789 5 ! ! 15789 12789 2579 ! 2579 2359 2357 ! 6 1789 4 ! +----------------------+----------------------+----------------------+ ! 5679 23679 25679 ! 245789 2459 1 ! 349 479 36789 ! ! 179 12379 8 ! 2479 6 27 ! 5 1479 379 ! ! 4 1679 5679 ! 3 59 578 ! 19 2 6789 ! +----------------------+----------------------+----------------------+ ! 68 468 1 ! 246 234 9 ! 7 5 23 ! ! 79 479 3 ! 245 1 25 ! 8 6 29 ! ! 2 5 69 ! 68 7 368 ! 349 49 1 ! +----------------------+----------------------+----------------------+

===> There are 11 W1-anti-backdoors:
n3r3c6 n4r4c7 n4r5c4 n3r7c5 n4r7c5 n2r7c9 n4r8c2 n9r8c9 n9r9c3 n3r9c7 n4r9c8
all of which give rise to 1-step solutions with at most whips[7].

The simplest 3 require only a bivalue-chains[3]:

Code: Select all: biv-chain[3]: c5n4{r4 r7} - b8n3{r7c5 r9c6} - c7n3{r9 r4} ==> r4c7 ≠ 4 stte

Code: Select all: biv-chain[3]: r9n3{c6 c7} - c7n4{r9 r4} - c5n4{r4 r7} ==> r7c5 ≠ 3 stte

Code: Select all: biv-chain[3]: r7n3{c9 c5} - c5n4{r7 r4} - c7n4{r4 r9} ==> r9c7 ≠ 3 stte

by **pjb** » Sat May 29, 2021 10:59 am

Code: Select all: 1579 1279 4 | 25679 8 2567 | 129 3 79 3 678 67 | 1 29 4 | 29 78 5 15789 12789 2579 | 2579 2359 2357 | 6 1789 4 ------------------------+-----------------------+--------------------- 5679 23679 25679 | 245789 b2459 1 |a34 479 68 179 12379 8 | 2479 6 27 | 5 1479 79-3 4 1679 5679 | 3 59 578 | 19 2 68 ------------------------+-----------------------+--------------------- 68 468 1 | 246 c234 9 | 7 5 d23 79 479 3 | 245 1 25 | 8 6 29 2 5 69 | 68 7 368 | 4-3 49 1

(3=4)r4c7 - (4)r4c5 = (4-3)r7c5 = (3)r7c9 => -3 r5c9, r9c7; stte

Phil

by **Cenoman** » Sat May 29, 2021 5:07 pm

Code: Select all: +--------------------------+-------------------------+---------------------+ | 1579 1279 4 | 25679 8 2567 | 129 3 79 | | 3 678 67 | 1 29 4 | 29 78 5 | | 15789 12789 2579 | 2579 2359 2357 | 6 1789 4 | +--------------------------+-------------------------+---------------------+ | 5679 23679 25679 | 25789-4 2459 1 | 34 479 68 | | 179 12379 8 | 279-4 6 27 | 5 1479 379 | | 4 1679 5679 | 3 59 578 | 19 2 68 | +--------------------------+-------------------------+---------------------+ | 68 a468* 1 |ca246* b234 9 | 7 5 b23 | | 79 a479* 3 |da245* 1 d25 | 8 6 29 | | 2 5 69 | 68 7 368 | 34 49 1 | +--------------------------+-------------------------+---------------------+

Almost X-wing:
[XW(4)r78\c24] = (4-32)r7c5 = r7c4 - (2=54)r8c46 => -4 r45c4; ste

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