The New Sudoku Players' Forum

by **Yogi** » Thu Jul 06, 2023 10:22 pm

19..6...58....5...5.493.16......36..2.7.4.9.3.357.....341..95.....3....17...2..3.

Code: Select all: +---+---+---+ |19.|.6.|..5| |8..|..5|...| |5.4|93.|16.| +---+---+---+ |...|..3|6..| |2.7|.4.|9.3| |.35|7..|...| +---+---+---+ |341|..9|5..| |...|3..|..1| |7..|.2.|.3.| +---+---+---+

by **Hajime** » Fri Jul 07, 2023 11:07 am

The first XYZ wing at: {689} in b7e4,b7e9,c3e4 (-9)b7c3 => (-9)r8c3
e stands for element (or position). b7e4,b7e9,c3e4 = wing,hinge,wing
But then forcing chains/nets are needed.

by **totuan** » Sat Jul 08, 2023 8:56 am

Code: Select all: *-----------------------------------------------------------------------------* | 1 9 #23 |*248e 6 2478 |#23478 2478 5 | | 8 267 #23+6a |*124e *17e 5 |#2347 2479 2479 | | 5 27 4 | 9 3 278 | 1 6 278 | |-------------------------+-------------------------+-------------------------| | 49 18 89 | 1258d 1589 3 | 6 124578 2478 | | 2 168 7 | 1568 4 168 | 9 158 3 | | 469 3 5 | 7 189 1268c | 48+2b 1248 248 | |-------------------------+-------------------------+-------------------------| | 3 4 1 | 68f *78e 9 | 5 278 2678g | | 69j 2568 289-6 | 3 578 4678 | 478 4789 1 | | 7 568 89-6i | 14568 2 1468 | 48 3 4689h | *-----------------------------------------------------------------------------*

My path for this one – d’ont use XYZ-wing

- Look at * marked cells: if r12c4<>2 => XY chains: [(8=7)r7c5-(7=1)r2c5-(1=4)r2c4-(4=8)r1c4] => r7c4<>8
- UR(23)r12c37 => (6)r2c3=(2)r6c7
01: (6)r2c3==(2)r6c7-r6c6=r4c4-(2)r12c4=[(8=7)r7c5-(7=1)r2c5-(1=4)r2c4-(4=8)r1c4]-(8=6)r7c4-r7c9=(6-9)r9c9=r9c3-(9=6)r8c1 => r89c3<>6, some singles

Code: Select all: *-----------------------------------------------------------------------------* | 1 9 3 |*248 6 2478 | 2478 2478 5 | | 8 27 6 |*124 *17 5 | 3 2479 2479 | | 5 27 4 | 9 3 278 | 1 6 278 | |-------------------------+-------------------------+-------------------------| | 49 18 89 | 1258 1589 3 | 6 124578 2478 | | 2 168 7 |#16+58 4 #16+8 | 9 158 3 | | 469 3 5 | 7 189 1268 | 248 1248 248 | |-------------------------+-------------------------+-------------------------| | 3 4 1 | 6-8 *78 9 | 5 278 2678 | | 69 568 2 | 3 578 4678 | 478 4789 1 | | 7 568 89 |#16+458 2 #16+48 | 48 3 4689 | *-----------------------------------------------------------------------------*

UR(16)r59c46 => (8)r5c4,r9c46=(8)r5c6=(5)r5c4=(5)r9c4=(4)r9c46
If r12c4<>2 => XY chains: [(8=7)r7c5-(7=1)r2c5-(1=4)r2c4-(4=8)r1c4] => r7c4<>8
02: Present as diagram: => r7c4<>8, some singles

Code: Select all: (8)r5c4,r9c46* || (8)r5c6-r13c6=r1c4* || (5)r5c4-(5=1289)r4c2345-(2)r12c4==[(8=7)r7c5-(7=1)r2c5-(1=4)r2c4-(4=8)r1c4]* || (5)r9c4-(5=78)r78c5* || (4)r9c46-(489=6)r9c379-r7c9=r7c4*

From here, ER-7.1 and it’s easy to finish.

Code: Select all: *-----------------------------------------------------------* | 1 9 3 |a48 6 247-8 | 278 2478 5 | | 8 27 6 |b14 c17 5 | 3 247 9 | | 5 27 4 | 9 3 27-8 | 1 6 278 | |-------------------+-------------------+-------------------| | 49 1 8 | 2 59 3 | 6 57 47 | | 2 6 7 | 158 4 e18 | 9 158 3 | | 49 3 5 | 7 d189 6 | 28 128 248 | |-------------------+-------------------+-------------------| | 3 4 1 | 6 78 9 | 5 278 278 | | 6 58 2 | 3 578 478 | 478 9 1 | | 7 58 9 | 1458 2 148 | 48 3 6 | *-----------------------------------------------------------*

03: (8=4)r1c4-(4=1)r2c4-r2c5=r6c5-(1=8)r5c6 => r13c6<>8, some singles

Code: Select all: *--------------------------------------------------* | 1 9 3 | 8 6 247 | 27 247 5 | | 8 27 6 | 14 17 5 | 3 247 9 | | 5 27 4 | 9 3 27 | 1 6 8 | |----------------+----------------+----------------| | 49 1 8 | 2 59 3 | 6 57 47 | | 2 6 7 | 15 4 a18 | 9 b158 3 | | 49 3 5 | 7 19-8 6 | 28 128 24 | |----------------+----------------+----------------| | 3 4 1 | 6 d78 9 | 5 c278 27 | | 6 58 2 | 3 578 47-8 | 478 9 1 | | 7 58 9 | 145 2 14-8 | 48 3 6 | *--------------------------------------------------*

04: 8’s abcd => r6c5,r89c6<>8, some singles

Code: Select all: *--------------------------------------------------* | 1 9 3 | 8 6 247 | 27 247 5 | | 8 27 6 | 14 17 5 | 3 247 9 | | 5 27 4 | 9 3 27 | 1 6 8 | |----------------+----------------+----------------| | 49 1 8 | 2 59 3 | 6 57 47 | | 2 6 7 | 15 4 8 | 9 15 3 | | 49 3 5 | 7 19 6 |a28 b128 4-2 | |----------------+----------------+----------------| | 3 4 1 | 6 78 9 | 5 278 c27 | | 6 58 2 | 3 578 47 | 478 9 1 | | 7 58 9 | 45 2 1 | 48 3 6 | *--------------------------------------------------*

05: (2=8)r6c7-r6c8=(8-2)r7c8=r7c9 => r6c9<>2, stte

Thanks for the puzzle!
totuan

by **Cenoman** » Sun Jul 09, 2023 10:05 am

FWIW a solution with AICs and only three kraken steps (steps 5, 6, 7, presented as almost wings)

Hidden Text: Show

1. (9=8)r4c3 - (8=69)b7p49 => -9 r8c3
2. (1=89)r4c23 - r9c3 = (9-6)r9c9 = r7c9 - (6=785)b8p125 - (5=891)r4c235 => -1 r4c48
3. (1=89)r4c23 - r9c3 = (9-6)r9c9 = r7c9 - (6=87)r7c45 - (7=1)r2c5 => -1 r4c5; 1 placement (+1r4c2)
4. (6)r6c6 = r6c1 - (6=9)r8c1 - r9c3 = (9-6)r9c9 = r7c9 -(6=8)r7c4 - r78c5 = (8)r46c5 => -8 r6c6
5. (2)[r4c4 = r6c6 - r6c7 = r1c7] = (2-3)r2c7 = r2c3 - (3=2)r1c3 => -2 r1c4
6. [(4=82)r69c7 - r6c6 = r4c4 - (2=4)r2c4] = (1)r2c4 - (1=7)r2c5 - r13c6 = r8c6 - (7=84)r89c7 => -4 r2c7
7. [(1)r9c6 = (1-6)r9c4 = (6)r5c4 - (6=81)r5c26] = (6)r7c4 - r7c9 = (6-9)r9c9 = r9c3 - (9=6)r8c1 - r6c1= (6)r6c6 => -1 r6c6

Hidden Text: Show

8. (36)r2c37 = r2c2 - r5c2 = r6c1 - (6=2)r6c6 - r4c4|r6c7 = (2r2c4&23r12c7) => -2 r2c37, -7 r2c7; lcls, 4 placements
9. (9)r2c9 = r2c8 - r8c8 = (9-6)r8c1 = r6c1 - (6=2)r6c6 - r4c4 = (2)r2c4* - (2=367)r2c237 => -2r2c9*, -7r2c9
10. (1)r6c8 = r6c5 - (1=7)r2c5 - (7=8)r7c5 - (8=6)r7c4 - (6=2784)r3467c9 => -4 r6c8
11. (4=895)r4c135 - (5=786)b8p125 - (6=2784)r3467c9 => -4 r4c8

Hidden Text: Show

12. (4=8)r9c7 - (8=9)r9c3 - r8c1 = (9)r8c8 => -4 r8c8; lcls, 8 placements
13. (4=7)r8c6 - r78c5 = (7-1)r2c5 = r2c4 - r9c4 = (1)r9c6 => -4 r9c6; lcls, 4 placements

Hidden Text: Show

14. (7=2)r1c7 - r6c7 = r6c9 - (2=7)r7c9 => -7 r8c7; ste

The New Sudoku Players' Forum

XYZ then . . . ?

XYZ then . . . ?

Re: XYZ then . . . ?

Re: XYZ then . . . ?

Re: XYZ then . . . ?