The New Sudoku Players' Forum

by **mith** » Mon Apr 12, 2021 9:25 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 | +-------+-------+-------+ 3....1...4.....15..9...2...65...3.......5.......8...97...9...3..23.....8...4....6

by **RSW** » Mon Apr 12, 2021 10:42 pm

An ugly two step solution:

Code: Select all: +---------------+-----------+-------------+ | 3 678 2578 | 56 4 1 | 68 2678 9 | | 4 678 278 | 36 78 9 | 1 5 23 | | 578 9 1 | 356 78 2 | 368 678 4 | +---------------+-----------+-------------+ | 6 5 78 | 27 9 3 | 4 28 1 | | 789 1 789 | 27 5 4 | 368 268 23 | | 2 3 4 | 8 1 6 | 5 9 7 | +---------------+-----------+-------------+ | 1 4 6 | 9 2 8 | 7 3 5 | | 57 2 3 | 1 6 57 | 9 4 8 | | 5789 78 5789 | 4 3 57 | 2 1 6 | +---------------+-----------+-------------+

1. XYZ-wing: (678)r1c7, r3c8, r3c5 => -8r3c7
2. Nishio net: 6?r1c4 > (3r2c4, 5r1c3) > (2r2c9, 2r1c8) > -2r2c9 > ?r2c9 => -6r1c4; btte

Website · by **denis_berthier** » Tue Apr 13, 2021 5:11 am

.
Resolution state after Singles and whips[1]:

Code: Select all: +----------------+----------------+----------------+ ! 3 678 2578 ! 56 4 1 ! 68 2678 9 ! ! 4 678 278 ! 36 78 9 ! 1 5 23 ! ! 578 9 1 ! 356 78 2 ! 368 678 4 ! +----------------+----------------+----------------+ ! 6 5 78 ! 27 9 3 ! 4 28 1 ! ! 789 1 789 ! 27 5 4 ! 368 268 23 ! ! 2 3 4 ! 8 1 6 ! 5 9 7 ! +----------------+----------------+----------------+ ! 1 4 6 ! 9 2 8 ! 7 3 5 ! ! 57 2 3 ! 1 6 57 ! 9 4 8 ! ! 5789 78 5789 ! 4 3 57 ! 2 1 6 ! +----------------+----------------+----------------+

z-chain[6]: r4n2{c8 c4} - r4n7{c4 c3} - r1n7{c3 c2} - c2n6{r1 r2} - r2c4{n6 n3} - r2c9{n3 .} ==> r1c8 ≠ 2
stte

Note: a simplest-first solution can be found using only bivalue-chains of length <= 4

by **Leren** » Tue Apr 13, 2021 6:21 am

Code: Select all: *-------------------------------------------------* | 3 b678 2578b | 56 4 1 | 68 Aa268-7a 9 | | 4 D678 278 |C36 78 9 | 1 5 B23 | | 578 9 1 | 356 78 2 | 368 678 4 | |-----------------+------------+------------------| | 6 5 78 | 27 9 3 | 4 28 1 | | 789 1 789 | 27 5 4 | 368 268 23 | | 2 3 4 | 8 1 6 | 5 9 7 | |-----------------+------------+------------------| | 1 4 6 | 9 2 8 | 7 3 5 | | 57 2 3 | 1 6 57 | 9 4 8 | | 5789 78e 5789c | 4 3 57d | 2 1 6 | *-------------------------------------------------* Kraken Column 2 Digit 7: 7 r1c8 - 7 r1c2; 7 r1c8 - 2 r1c8 = (2-3) r2c9 = (3-6) r2c4 = 6 r2c2 -7 r2c2; 7 r1c8 - 2 r1c8 = (2-5) r1c3 = r9c3 - (5=7) r9c6 - 7 r9c2; => - 7 r1c8; stte

Leren

by **SteveG48** » Tue Apr 13, 2021 1:01 pm

Code: Select all: *-----------------------------------------------------------* | 3 678 2578 |b56 4 1 | 68 2678 9 | | 4 g678 m78-2 |a36 h78 9 | 1 5 aL23 | |d578 9 1 |c356 i78 2 | 368 j678 4 | *-------------------+-------------------+-------------------| | 6 5 78 | 27 9 3 | 4 j28 1 | | 789 1 789 | 27 5 4 | 368 j268 k23 | | 2 3 4 | 8 1 6 | 5 9 7 | *-------------------+-------------------+-------------------| | 1 4 6 | 9 2 8 | 7 3 5 | |e57 2 3 | 1 6 57 | 9 4 8 | | 5789 f78 5789 | 4 3 57 | 2 1 6 | *-----------------------------------------------------------*

[(2=36)r2c49 - (6=5)r1c4 - r3c4 = r3c1 - (5=7)r8c1 - (7=8)r9c2 - 8r2c2 == 8r2c5 - (8=7)r3c5 - (7=682)r345c8 - 2r5c9 = 2r2c9] = 8r2c3 => -2 r2c3 ; stte

by **Ngisa** » Tue Apr 13, 2021 5:11 pm

Two steps

Code: Select all: +----------------------+------------------+--------------------+ | 3 678 e278-5|a56 4 1 | 68 d2678 9 | | 4 678 278 |b36 78 9 | 1 5 c23 | | 578 9 1 | 356 78 2 | 368 678 4 | +----------------------+------------------+--------------------+ | 6 5 78 | 27 9 3 | 4 28 1 | | 789 1 789 | 27 5 4 | 368 268 23 | | 2 3 4 | 8 1 6 | 5 9 7 | +----------------------+------------------+--------------------+ | 1 4 6 | 9 2 8 | 7 3 5 | | 57 2 3 | 1 6 57 | 9 4 8 | | 5789 78 5789 | 4 3 57 | 2 1 6 | +----------------------+------------------+--------------------+

Step 1: (5=6)r1c4 - (6=3)r2c4 - (3=2)r2c9 - r1c8 = (2)r1c3 => - 5r1c3

Code: Select all: +-----------------+-----------------+---------------------+ | 3 67 28 | 5 4 1 | 68 26*7 9 | | 4 67 28 | 36 78 9 | 1 5 23 | | 5 9 1 | 36 78 2 | 36*8 7-6 4 | +-----------------+-----------------+---------------------+ | 6 5 7 | 2 9 3 | 4 8 1 | | 8 1 9 | 7 5 4 | 36 26 23 | | 2 3 4 | 8 1 6 | 5 9 7 | +-----------------+-----------------+---------------------+ | 1 4 6 | 9 2 8 | 7 3 5 | | 7 2 3 | 1 6 5 | 9 4 8 | | 9 8 5 | 4 3 7 | 2 1 6 | +-----------------+-----------------+---------------------+

Step 2: (BUG + 2) = (6)b3p27 => - 6r3c8; stte

Clement

by **jco** » Wed Apr 14, 2021 2:15 pm

Hello,

After basics

Code: Select all: .---------------------------------------------------. | 3 c678 zuAa2578 |v 56 4 1 |b68 2678 9 | | 4 d678 78-2 |ve36 78 9 | 1 5 wDe23 | | 578 9 1 | 356 78 2 | 368 678 4 | |--------------------+--------------+---------------| | 6 5 B78 | 27 9 3 | 4 B28 1 | | 789 1 789 | 27 5 4 | 368 268 C23 | | 2 3 4 | 8 1 6 | 5 9 7 | |--------------------+--------------+---------------| | 1 4 6 | 9 2 8 | 7 3 5 | | 57 2 3 | 1 6 57 | 9 4 8 | | 5789 78 5789 | 4 3 57 | 2 1 6 | '---------------------------------------------------'

1. Kraken Cell (2578)r1c3
(2)r1c3
(5)r1c3-(5=63)r12c4-(3=2)r2c9
(7)r1c3-(7=82)r4c38-r5c9=(2)r2c9
(8)r1c3-(8=6)r1c7-(6)r1c2=r2c2-(6=32)r2c49
--------------------------
=> -2 r2c3; ste

Regards,
jco

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