The New Sudoku Players' Forum

by **mith** » Mon May 24, 2021 11:54 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 . | . . . | +-------+-------+-------+ ....3.1.4....1..5..9.2.6........53...5.....8...97........9.3.2..3..8....4.6.2....

by **pjb** » Tue May 25, 2021 1:13 am

Code: Select all: 2567 26 57 | 8 3 79 | 1 69 4 678 68 3 | 4 1 79 |d69-2 5 a29 1 9 4 | 2 5 6 | 78 37 38 ------------------------+----------------------+--------------------- 2678 2468 78 | 1 9 5 | 3 467 27 67 5 17 | 3 4 2 |c679 8 b179 3 124 9 | 7 6 8 | 25 14 125 ------------------------+----------------------+--------------------- 58 18 158 | 9 7 3 | 4 2 6 9 3 2 | 6 8 4 | 57 17 157 4 7 6 | 5 2 1 | 89 39 38

(2=9)r2c9 - (9)r5c9 = (9-6)r5c7 = (6-2)r2c7 => -2 r2c7; stte

Phil

by **Leren** » Tue May 25, 2021 8:26 am

Code: Select all: *----------------------------------------* | 2567 26 57 | 8 3 79 | 1 a69 4 | | 678 68 3 | 4 1 79 | 269 5 2-9 | | 1 9 4 | 2 5 6 | 78 37 38 | |---------------+--------+---------------| | 2678 2468 78 | 1 9 5 | 3 b467 27 | | 67 5 17 | 3 4 2 |c679 8 d179 | | 3 124 9 | 7 6 8 | 25 14 125 | |---------------+--------+---------------| | 58 18 158 | 9 7 3 | 4 2 6 | | 9 3 2 | 6 8 4 | 57 17 157 | | 4 7 6 | 5 2 1 | 89 39 38 | *----------------------------------------*

M (ith) Wing : (9=6) r1c8 - r4c8 = (6-9) r5c7 = (9) r5c9 => - 9 r2c9; stte

Leren

by **rjamil** » Tue May 25, 2021 4:10 pm

Code: Select all: +-----------------+----------+--------------------+ | 2567 26 57 | 8 3 79 | 1 69 4 | | 678 68 3 | 4 1 79 | (26)9 5 (2-9) | | 1 9 4 | 2 5 6 | 78 37 38 | +-----------------+----------+--------------------+ | 2678 2468 78 | 1 9 5 | 3 467 27 | | 67 5 17 | 3 4 2 | 7(6-9) 8 (9)-17 | | 3 124 9 | 7 6 8 | 25 14 125 | +-----------------+----------+--------------------+ | 58 18 158 | 9 7 3 | 4 2 6 | | 9 3 2 | 6 8 4 | 57 17 157 | | 4 7 6 | 5 2 1 | 89 39 38 | +-----------------+----------+--------------------+

Strong Wing: SL 6 @ r25c7 2 @ r2c79 9 @ r5c79 r25c9 => -17 @ r5c9 => -9 @ r5c7 r2c9; stte

R. Jamil

by **Cenoman** » Tue May 25, 2021 4:53 pm

Code: Select all: +----------------------+-----------------+--------------------+ | 2567 b26# 57 | 8 3 79 | 1 a69* 4 | | c678# 68* 3 | 4 1 79 | 269* 5 2-9 | | 1 9 4 | 2 5 6 | 78 37 38 | +----------------------+-----------------+--------------------+ | c2678# 2468* 78 | 1 9 5 | 3 467* 27 | | d67 5 d17 | 3 4 2 | 679 8 d179 | | 3 124 9 | 7 6 8 | 25 14 125 | +----------------------+-----------------+--------------------+ | 58 18 158 | 9 7 3 | 4 2 6 | | 9 3 2 | 6 8 4 | 57 17 157 | | 4 7 6 | 5 2 1 | 89 39 38 | +----------------------+-----------------+--------------------+

5-link oddagon (6)r24, c28, b3 having three guardians (#)
(9=6)r1c8 - r1c2 == r24c1 - (6=179)r5c139 => -9 r2c9; ste

by **jco** » Wed May 26, 2021 12:33 pm

Code: Select all: .-------------------------------------------------. | 2567 26 57 | 8 3 79 | 1 c(69) 4 | | 678 68 3 | 4 1 79 | b2(6)9 5 d2(9) | | 1 9 4 | 2 5 6 | 78 37 38 | |-----------------+----------+--------------------| | 2678 2468 78 | 1 9 5 | 3 467 27 | | 67 5 17 | 3 4 2 |a(6)7-9 8 e17(9)| | 3 124 9 | 7 6 8 | 25 14 125 | |-----------------+----------+--------------------| | 58 18 158 | 9 7 3 | 4 2 6 | | 9 3 2 | 6 8 4 | 57 17 157 | | 4 7 6 | 5 2 1 | 89 39 38 | '-------------------------------------------------'

S(plit)-Wing (6)r5c7=r2c7-(6=9)r1c8-r2c9=(9)r5c9 => -9 r5c7; ste

Website · by **denis_berthier** » Wed Jun 02, 2021 5:14 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 2567 26 57 ! 8 3 79 ! 1 69 4 ! ! 678 68 3 ! 4 1 79 ! 269 5 29 ! ! 1 9 4 ! 2 5 6 ! 78 37 378 ! +----------------+----------------+----------------+ ! 2678 2468 78 ! 1 9 5 ! 3 467 27 ! ! 67 5 17 ! 3 4 2 ! 679 8 179 ! ! 3 124 9 ! 7 6 8 ! 25 14 125 ! +----------------+----------------+----------------+ ! 58 18 158 ! 9 7 3 ! 4 2 6 ! ! 9 3 2 ! 6 8 4 ! 57 17 157 ! ! 4 7 6 ! 5 2 1 ! 89 39 389 ! +----------------+----------------+----------------+

===> There are 24 W1-anti-backdoors:
n5r1c3 n7r1c6 n9r1c8 n7r2c1 n9r2c6 n2r2c7 n6r2c7 n9r2c9 n8r3c7 n7r3c8 n3r3c9 n4r4c2 n6r4c8 n6r5c1 n9r5c7 n5r6c7 n4r6c8 n5r7c1 n7r8c7 n1r8c8 n5r8c9 n9r9c7 n3r9c8 n8r9c9

most of which lead to a 1-step solution with whips.

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

Code: Select all: biv-chain[3]: r2c9{n2 n9} - b6n9{r5c9 r5c7} - c7n6{r5 r2} ==> r2c7 ≠ 2 stte

Code: Select all: biv-chain[3]: r1c8{n9 n6} - b6n6{r4c8 r5c7} - b6n9{r5c7 r5c9} ==> r2c9 ≠ 9 stte

by **RSW** » Thu Jun 10, 2021 7:56 am

Code: Select all: +---------------+--------+-------------+ | 2567 26 57 | 8 3 79 | 1 69 4 | | 678 68 3 | 4 1 79 |c269 5 2-9 | | 1 9 4 | 2 5 6 | 78 37 38 | +---------------+--------+-------------+ | 2678 2468 78 | 1 9 5 | 3 467 27 | | 67 5 17 | 3 4 2 |b679 8 a179 | | 3 124 9 | 7 6 8 | 25 14 125 | +---------------+--------+-------------+ | 58 18 158 | 9 7 3 | 4 2 6 | | 9 3 2 | 6 8 4 | 57 17 157 | | 4 7 6 | 5 2 1 | 89 39 38 | +---------------+--------+-------------+

(9)r5c9=(9-6)r5c7=(6-2)r2c7=(2)r2c9 => -9r2c9; ste
Trying to write what is a digit forcing chain as an AIC.
I'd appreciate it if someone could check my notation and correct or improve it.

by **eleven** » Thu Jun 10, 2021 10:56 pm

RSW wrote:I'd appreciate it if someone could check my notation and correct or improve it.

It's fine for sure. People like it, if you add blanks before and after the '=' or '-' sign between cells (i was told).

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