The New Sudoku Players' Forum

by **SteveG48** » Fri Jan 22, 2021 10:31 pm

Code: Select all: *-----------* |...|.2.|...| |..1|6..|38.| |..9|..8|6.1| |---+---+---| |3..|.7.|..8| |...|9.5|7..| |9..|.1.|..4| |---+---+---| |8.4|7..|9..| |.67|..9|8..| |...|.4.|...| *-----------*

by **pjb** » Sat Jan 23, 2021 2:43 am

Can't get it in 1. Here's 2 step
Swordfish of 3s (r169\c346) -3 r3c4, r7c6, r8c4 =>

Code: Select all: 567 8 356 | 135 2 137 | 4 57 9 2457 245 1 | 6 9 47 | 3 8 257 2457 2345 9 |b45 a35 8 | 6 257 1 ------------------------+----------------------+--------------------- 3 e125 256 |c24 7 246 |d12 9 8 1246 124 26 | 9 8 5 | 7 13 236 9 7 8 | 23 1 236 | 25 256 4 ------------------------+----------------------+--------------------- 8 f1235 4 | 7 6 12 | 9 13 h235 12 6 7 | 125 5-3 9 | 8 4 j23 125 9 235 | 8 4 123 |i125 67 67

(3=5)r3c5 - (5=4)r3c4 - (4=2*)r4c4 - (2=1^)r4c7 - (1|2*=5)r4c2 - (5)r7c2 = (5)r7c9 - (5|1^=2)r9c7 - (2=3)r8c9 => -3 r8c5; stte

Phil

Website · by **denis_berthier** » Sat Jan 23, 2021 5:25 am

After a trivial part:

Code: Select all: *********************************************************************************************** *** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = *** Using CLIPS 6.32-r779 *** download from: https://github.com/denis-berthier/CSP-Rules-V2.1 *********************************************************************************************** 12 singles 145 candidates, 665 csp-links and 665 links. Density = 6.37% whip[1]: r5n3{c9 .} ==> r6c8 ≠ 3 whip[1]: r6n5{c8 .} ==> r4c7 ≠ 5 whip[1]: r5n4{c2 .} ==> r4c2 ≠ 4 whip[1]: b8n5{r8c5 .} ==> r8c9 ≠ 5, r8c1 ≠ 5 hidden-pairs-in-a-row: r9{n6 n7}{c8 c9} ==> r9c9 ≠ 5, r9c9 ≠ 3, r9c9 ≠ 2, r9c8 ≠ 5, r9c8 ≠ 3, r9c8 ≠ 2, r9c8 ≠ 1 hidden-pairs-in-a-column: c8{n1 n3}{r5 r7} ==> r7c8 ≠ 5, r7c8 ≠ 2, r5c8 ≠ 6, r5c8 ≠ 2

we reach the following resolution state:

Code: Select all: 567 8 356 135 2 137 4 57 9 2457 245 1 6 9 47 3 8 257 2457 2345 9 345 35 8 6 257 1 3 125 256 24 7 246 12 9 8 1246 124 26 9 8 5 7 13 236 9 7 8 23 1 236 25 256 4 8 1235 4 7 6 123 9 13 235 12 6 7 1235 35 9 8 4 23 125 9 235 8 4 123 125 67 67

Then a few fishes:

Code: Select all: finned-x-wing-in-rows: n5{r7 r2}{c9 c2} ==> r3c2 ≠ 5 finned-x-wing-in-columns: n1{c8 c2}{r7 r5} ==> r5c1 ≠ 1 whip[1]: c1n1{r9 .} ==> r7c2 ≠ 1 finned-x-wing-in-columns: n3{c2 c5}{r3 r7} ==> r7c6 ≠ 3 swordfish-in-rows: n3{r1 r6 r9}{c3 c4 c6} ==> r8c4 ≠ 3, r3c4 ≠ 3 biv-chain-rc[3]: r8c9{n2 n3} - r7c8{n3 n1} - r7c6{n1 n2} ==> r7c9 ≠ 2, r8c4 ≠ 2 whip[1]: b8n2{r9c6 .} ==> r4c6 ≠ 2, r6c6 ≠ 2 finned-x-wing-in-rows: n2{r8 r2}{c9 c1} ==> r3c1 ≠ 2

lead to this state:

Code: Select all: 567 8 356 135 2 137 4 57 9 2457 245 1 6 9 47 3 8 257 457 234 9 45 35 8 6 257 1 3 125 256 24 7 46 12 9 8 246 124 26 9 8 5 7 13 236 9 7 8 23 1 36 25 256 4 8 235 4 7 6 12 9 13 35 12 6 7 15 35 9 8 4 23 125 9 235 8 4 123 125 67 67

Finally, two short bivalue-chains[3] give the solution:

Code: Select all: biv-chain-rn[3]: r8n2{c1 c9} - r8n3{c9 c5} - r9n3{c6 c3} ==> r9c3 ≠ 2 whip[1]: c3n2{r5 .} ==> r4c2 ≠ 2, r5c1 ≠ 2, r5c2 ≠ 2 biv-chain[3]: r3c5{n3 n5} - b8n5{r8c5 r8c4} - c4n1{r8 r1} ==> r1c4 ≠ 3 stte

by **SteveG48** » Sat Jan 23, 2021 5:08 pm

Code: Select all: *-------------------------------------------------------------* | 567 8 c356 |bc135 2 b137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 h2345 9 |ai4-35 ai35 8 | 6 257 1 | *-------------------+---------------------+-------------------| | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | *-------------------+---------------------+-------------------| | 8 g1235 4 | 7 6 f123 | 9 f13 235 | | 12 6 7 |de1235 e35 9 | 8 4 23 | | 125 9 d235 | 8 4 e123 | 125 67 67 | *-------------------------------------------------------------*

(4=35)r3c45 - (3|5)r1c46 = (13)r1c34 - 3c9c3|1r8c4 = (352)b8p459 - (2=13)r7c68 - 3r7c2 = r3c2 - (3=54)r3c45 => -35 r3c4 ; stte

by **Cenoman** » Sat Jan 23, 2021 5:39 pm

Code: Select all: +----------------------+--------------------+--------------------+ | 567 8 h356 | g135 2 ga13-7 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 G2345 9 | 345 35 8 | 6 257 1 | +----------------------+--------------------+--------------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +----------------------+--------------------+--------------------+ | 8 F1235 4 | 7 6 D123 | 9 E13 235 | | 12 6 7 | 1235 35 9 | 8 4 23 | | 125 9 B235 | 8 4 C123 | 125 67 67 | +----------------------+--------------------+--------------------+

(1)r1c6 = [(3)r9c3 = (3-1)r9c6 *=* r7c6 - (1=3)r7c8 - r7c2 = (3)r3c2] - (3)r1c3 = (31)r1c46 => -7 r1c6; ste

by **rjamil** » Sat Jan 23, 2021 5:40 pm

Wish to inform that my solver is able to solve op puzzle:

Hidden Text: Show

Code: Select all: ....2......16..38...9..86.13...7...8...9.57..9...1...48.47..9...67..98......4....#Steve Stumble 1-22-2021 +---+---+---+ |...|.2.|...| |..1|6..|38.| |..9|..8|6.1| +---+---+---+ |3..|.7.|..8| |...|9.5|7..| |9..|.1.|..4| +---+---+---+ |8.4|7..|9..| |.67|..9|8..| |...|.4.|...| +---+---+---+ +-------------------+------------------+--------------------+ | 4567 34578 3568 | 1345 2 1347 | 45 4579 579 | | 2457 2457 1 | 6 59 47 | 3 8 2579 | | 2457 23457 9 | 345 35 8 | 6 2457 1 | +-------------------+------------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 12569 8 | | 1246 1248 268 | 9 368 5 | 7 1236 236 | | 9 2578 2568 | 238 1 236 | 25 2356 4 | +-------------------+------------------+--------------------+ | 8 1235 4 | 7 356 1236 | 9 12356 2356 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 1236 | 125 123567 23567 | +-------------------+------------------+--------------------+ 1st) Hidden single: 4 @ r1c7 from values 45 Column 7 wise +-------------------+------------------+--------------------+ | 567 3578 3568 | 135 2 137 | 4 579 579 | | 2457 2457 1 | 6 59 47 | 3 8 2579 | | 2457 23457 9 | 345 35 8 | 6 257 1 | +-------------------+------------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 12569 8 | | 1246 1248 268 | 9 368 5 | 7 1236 236 | | 9 2578 2568 | 238 1 236 | 25 2356 4 | +-------------------+------------------+--------------------+ | 8 1235 4 | 7 356 1236 | 9 12356 2356 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 1236 | 125 123567 23567 | +-------------------+------------------+--------------------+ 2nd) Hidden single: 9 @ r2c5 from values 59 Column 5 wise +-------------------+------------------+--------------------+ | 567 3578 3568 | 135 2 137 | 4 579 579 | | 2457 2457 1 | 6 9 47 | 3 8 257 | | 2457 23457 9 | 345 35 8 | 6 257 1 | +-------------------+------------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 12569 8 | | 1246 1248 268 | 9 368 5 | 7 1236 236 | | 9 2578 2568 | 238 1 236 | 25 2356 4 | +-------------------+------------------+--------------------+ | 8 1235 4 | 7 356 1236 | 9 12356 2356 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 1236 | 125 123567 23567 | +-------------------+------------------+--------------------+ 3rd) Hidden single: 9 @ r1c9 from values 579 Column 9 wise +-------------------+------------------+--------------------+ | 567 3578 3568 | 135 2 137 | 4 57 9 | | 2457 2457 1 | 6 9 47 | 3 8 257 | | 2457 23457 9 | 345 35 8 | 6 257 1 | +-------------------+------------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 12569 8 | | 1246 1248 268 | 9 368 5 | 7 1236 236 | | 9 2578 2568 | 238 1 236 | 25 2356 4 | +-------------------+------------------+--------------------+ | 8 1235 4 | 7 356 1236 | 9 12356 2356 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 1236 | 125 123567 23567 | +-------------------+------------------+--------------------+ 4th) Hidden single: 9 @ r4c8 from values 12569 Row 4 wise +-------------------+------------------+--------------------+ | 567 3578 3568 | 135 2 137 | 4 57 9 | | 2457 2457 1 | 6 9 47 | 3 8 257 | | 2457 23457 9 | 345 35 8 | 6 257 1 | +-------------------+------------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 9 8 | | 1246 1248 268 | 9 368 5 | 7 1236 236 | | 9 2578 2568 | 238 1 236 | 25 2356 4 | +-------------------+------------------+--------------------+ | 8 1235 4 | 7 356 1236 | 9 12356 2356 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 1236 | 125 123567 23567 | +-------------------+------------------+--------------------+ 5th) Hidden single: 8 @ r5c5 from values 368 Column 5 wise +-------------------+------------------+--------------------+ | 567 3578 3568 | 135 2 137 | 4 57 9 | | 2457 2457 1 | 6 9 47 | 3 8 257 | | 2457 23457 9 | 345 35 8 | 6 257 1 | +-------------------+------------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 2578 2568 | 23 1 236 | 25 2356 4 | +-------------------+------------------+--------------------+ | 8 1235 4 | 7 356 1236 | 9 12356 2356 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 1236 | 125 123567 23567 | +-------------------+------------------+--------------------+ 6th) Hidden single: 7 @ r6c2 from values 2578 Row 6 wise +-------------------+------------------+--------------------+ | 567 358 3568 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-------------------+------------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 2568 | 23 1 236 | 25 2356 4 | +-------------------+------------------+--------------------+ | 8 1235 4 | 7 356 1236 | 9 12356 2356 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 1236 | 125 123567 23567 | +-------------------+------------------+--------------------+ 7th) Hidden single: 8 @ r1c2 from values 358 Column 2 wise +-------------------+------------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-------------------+------------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 2568 | 23 1 236 | 25 2356 4 | +-------------------+------------------+--------------------+ | 8 1235 4 | 7 356 1236 | 9 12356 2356 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 1236 | 125 123567 23567 | +-------------------+------------------+--------------------+ 8th) Hidden single: 8 @ r6c3 from values 2568 Row 6 wise +------------------+------------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +------------------+------------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 2356 4 | +------------------+------------------+--------------------+ | 8 1235 4 | 7 356 1236 | 9 12356 2356 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 1236 | 125 123567 23567 | +------------------+------------------+--------------------+ 9th) Hidden single: 6 @ r7c5 from values 356 Column 5 wise +------------------+----------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +------------------+----------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 2356 4 | +------------------+----------------+--------------------+ | 8 1235 4 | 7 6 123 | 9 1235 235 | | 125 6 7 | 1235 35 9 | 8 12345 235 | | 125 12359 235 | 12358 4 123 | 125 123567 23567 | +------------------+----------------+--------------------+ 10th) Hidden single: 4 @ r8c8 from values 12345 Row 8 wise +------------------+----------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +------------------+----------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 2356 4 | +------------------+----------------+--------------------+ | 8 1235 4 | 7 6 123 | 9 1235 235 | | 125 6 7 | 1235 35 9 | 8 4 235 | | 125 12359 235 | 12358 4 123 | 125 123567 23567 | +------------------+----------------+--------------------+ 11th) Hidden single: 9 @ r9c2 from values 12359 Row 9 wise +-----------------+----------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-----------------+----------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 2356 4 | +-----------------+----------------+--------------------+ | 8 1235 4 | 7 6 123 | 9 1235 235 | | 125 6 7 | 1235 35 9 | 8 4 235 | | 125 9 235 | 12358 4 123 | 125 123567 23567 | +-----------------+----------------+--------------------+ 12th) Hidden single: 8 @ r9c4 from values 12358 Row 9 wise +-----------------+---------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-----------------+---------------+--------------------+ | 3 1245 256 | 24 7 246 | 125 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 2356 4 | +-----------------+---------------+--------------------+ | 8 1235 4 | 7 6 123 | 9 1235 235 | | 125 6 7 | 1235 35 9 | 8 4 235 | | 125 9 235 | 8 4 123 | 125 123567 23567 | +-----------------+---------------+--------------------+ 12) Locked candidate Type 1 (Pointing): 5 @ r4c123 => -5 @ r4c456789 +-----------------+---------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-----------------+---------------+--------------------+ | 3 1245 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 2356 4 | +-----------------+---------------+--------------------+ | 8 1235 4 | 7 6 123 | 9 1235 235 | | 125 6 7 | 1235 35 9 | 8 4 235 | | 125 9 235 | 8 4 123 | 125 123567 23567 | +-----------------+---------------+--------------------+ 12) Locked candidate Type 1 (Pointing): 4 @ r4c456 => -4 @ r4c123789 +-----------------+---------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-----------------+---------------+--------------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 2356 4 | +-----------------+---------------+--------------------+ | 8 1235 4 | 7 6 123 | 9 1235 235 | | 125 6 7 | 1235 35 9 | 8 4 235 | | 125 9 235 | 8 4 123 | 125 123567 23567 | +-----------------+---------------+--------------------+ 12) Locked candidate Type 2 (Claiming): 3 @ r5c789 => -3 @ r46c789 +-----------------+---------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-----------------+---------------+--------------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +-----------------+---------------+--------------------+ | 8 1235 4 | 7 6 123 | 9 1235 235 | | 125 6 7 | 1235 35 9 | 8 4 235 | | 125 9 235 | 8 4 123 | 125 123567 23567 | +-----------------+---------------+--------------------+ 12) Locked candidate Type 1 (Pointing): 5 @ r8c456 => -5 @ r8c123789 +-----------------+---------------+--------------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-----------------+---------------+--------------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +-----------------+---------------+--------------------+ | 8 1235 4 | 7 6 123 | 9 1235 235 | | 12 6 7 | 1235 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 123567 23567 | +-----------------+---------------+--------------------+ 12) Hidden pair: Row 9 wise 67 @ r9c8 r9c9 => -1235 @ r9c8 -235 @ r9c9 +-----------------+---------------+----------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-----------------+---------------+----------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 1236 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +-----------------+---------------+----------------+ | 8 1235 4 | 7 6 123 | 9 1235 235 | | 12 6 7 | 1235 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +-----------------+---------------+----------------+ 12) Hidden pair: Column 8 wise 13 @ r5c8 r7c8 => -26 @ r5c8 -25 @ r7c8 +-----------------+---------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 345 35 8 | 6 257 1 | +-----------------+---------------+---------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +-----------------+---------------+---------------+ | 8 1235 4 | 7 6 123 | 9 13 235 | | 12 6 7 | 1235 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +-----------------+---------------+---------------+ 12) Sword Fish: Row wise 3 @ r169c346 +-----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 2345 9 | 45 35 8 | 6 257 1 | +-----------------+--------------+---------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +-----------------+--------------+---------------+ | 8 1235 4 | 7 6 12 | 9 13 235 | | 12 6 7 | 125 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +-----------------+--------------+---------------+ 12) Grouped Skyscraper: Rows 2 7 wise Base 5 @ r2c9 r7c9 Cover 5 @ r2c12 r7c2 => -5 @ r13c2 +-----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 234 9 | 45 35 8 | 6 257 1 | +-----------------+--------------+---------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +-----------------+--------------+---------------+ | 8 1235 4 | 7 6 12 | 9 13 235 | | 12 6 7 | 125 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +-----------------+--------------+---------------+ 12) Grouped Skyscraper: Columns 1 8 wise Base 1 @ r5c1 r5c8 Cover 1 @ r89c1 r7c8 => -1 @ r7c23 +----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 234 9 | 45 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 235 | | 12 6 7 | 125 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 12) Locked candidate Type 1 (Pointing): 1 @ r789c1 => -1 @ r123456c1 +----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 234 9 | 45 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 235 | | 12 6 7 | 125 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 12) Grouped W-Wing Type 1 Grid: 12 @ r4c7 r7c6 SL Column 8 between 1 @ r456c8 and 1 @ r7c8 => -2 @ r4c6 r7c7 +----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 234 9 | 45 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 256 | 24 7 46 | 12 9 8 | | 246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 235 | | 12 6 7 | 125 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 12) XY-Wing Type 2: 123 @ r7c68 r8c9 => -2 @ r7c79 r8c456 +----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 234 9 | 45 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 256 | 24 7 46 | 12 9 8 | | 246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 12) Locked candidate Type 2 (Claiming): 2 @ r456c4 => -2 @ r456c56 +----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 234 9 | 45 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 256 | 24 7 46 | 12 9 8 | | 246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 36 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 12) Grouped Skyscraper: Rows 2 8 wise Base 2 @ r2c9 r8c9 Cover 2 @ r2c12 r8c1 => -2 @ r13c1 +----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 457 234 9 | 45 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 256 | 24 7 46 | 12 9 8 | | 246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 36 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 12) XYZ-Wing: 135 @ r18c4 r3c5 => -5 @ r23c4 +----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 457 234 9 | 4 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 256 | 24 7 46 | 12 9 8 | | 246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 36 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 13th) Naked single: 4 @ r3c4 +----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 256 | 2 7 46 | 12 9 8 | | 246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 36 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 14th) Hidden single: 4 @ r4c6 from values 46 Row 4 wise +----------------+--------------+---------------+ | 567 8 356 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 256 | 2 7 4 | 12 9 8 | | 246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 36 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 15th) Hidden single: 6 @ r4c3 from values 256 Row 4 wise +----------------+--------------+---------------+ | 567 8 35 | 135 2 137 | 4 57 9 | | 2457 245 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 125 6 | 2 7 4 | 12 9 8 | | 24 124 2 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 36 | 25 256 4 | +----------------+--------------+---------------+ | 8 235 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 16th) Hidden single: 5 @ r4c2 from values 125 Row 4 wise +----------------+--------------+---------------+ | 567 8 35 | 135 2 137 | 4 57 9 | | 2457 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +----------------+--------------+---------------+ | 3 5 6 | 2 7 4 | 12 9 8 | | 24 124 2 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 36 | 25 256 4 | +----------------+--------------+---------------+ | 8 23 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 125 67 67 | +----------------+--------------+---------------+ 17th) Hidden single: 1 @ r4c7 from values 12 Row 4 wise +----------------+--------------+--------------+ | 567 8 35 | 135 2 137 | 4 57 9 | | 2457 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +----------------+--------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 24 124 2 | 9 8 5 | 7 3 236 | | 9 7 8 | 23 1 36 | 25 256 4 | +----------------+--------------+--------------+ | 8 23 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 25 67 67 | +----------------+--------------+--------------+ 18th) Naked single: 2 @ r4c4 +----------------+--------------+--------------+ | 567 8 35 | 135 2 137 | 4 57 9 | | 2457 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +----------------+--------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 24 124 2 | 9 8 5 | 7 3 236 | | 9 7 8 | 3 1 36 | 25 256 4 | +----------------+--------------+--------------+ | 8 23 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 25 67 67 | +----------------+--------------+--------------+ 19th) Hidden single: 1 @ r5c2 from values 124 Row 5 wise +---------------+--------------+--------------+ | 567 8 35 | 135 2 137 | 4 57 9 | | 2457 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +---------------+--------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 24 1 2 | 9 8 5 | 7 3 236 | | 9 7 8 | 3 1 36 | 25 256 4 | +---------------+--------------+--------------+ | 8 23 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 25 67 67 | +---------------+--------------+--------------+ 20th) Hidden single: 4 @ r5c1 from values 24 Row 5 wise +--------------+--------------+--------------+ | 567 8 35 | 135 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +--------------+--------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 236 | | 9 7 8 | 3 1 36 | 25 256 4 | +--------------+--------------+--------------+ | 8 23 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 235 | 8 4 123 | 25 67 67 | +--------------+--------------+--------------+ 21st) Naked single: 2 @ r5c3 +-------------+--------------+--------------+ | 567 8 35 | 135 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +-------------+--------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 36 | | 9 7 8 | 3 1 36 | 25 256 4 | +-------------+--------------+--------------+ | 8 23 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 25 67 67 | +-------------+--------------+--------------+ 22nd) Hidden single: 6 @ r5c9 from values 36 Row 5 wise +-------------+--------------+--------------+ | 567 8 35 | 135 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +-------------+--------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 36 | 25 25 4 | +-------------+--------------+--------------+ | 8 23 4 | 7 6 12 | 9 13 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 25 67 7 | +-------------+--------------+--------------+ 23rd) Naked single: 3 @ r5c8 +-------------+--------------+--------------+ | 567 8 35 | 135 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +-------------+--------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 36 | 25 25 4 | +-------------+--------------+--------------+ | 8 23 4 | 7 6 12 | 9 1 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 25 67 7 | +-------------+--------------+--------------+ 24th) Hidden single: 6 @ r1c1 from values 567 Row 1 wise +-------------+--------------+--------------+ | 6 8 35 | 135 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +-------------+--------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 36 | 25 25 4 | +-------------+--------------+--------------+ | 8 23 4 | 7 6 12 | 9 1 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 25 67 7 | +-------------+--------------+--------------+ 25th) Hidden single: 6 @ r6c6 from values 36 Row 6 wise +-------------+--------------+--------------+ | 6 8 35 | 135 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +-------------+--------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 25 25 4 | +-------------+--------------+--------------+ | 8 23 4 | 7 6 12 | 9 1 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 25 67 7 | +-------------+--------------+--------------+ 26th) Naked single: 3 @ r6c4 +-------------+-------------+--------------+ | 6 8 35 | 15 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +-------------+-------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 25 25 4 | +-------------+-------------+--------------+ | 8 23 4 | 7 6 12 | 9 1 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 25 67 7 | +-------------+-------------+--------------+ 27th) Naked single: 1 @ r7c8 +-------------+-------------+--------------+ | 6 8 35 | 15 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 257 | | 57 23 9 | 4 35 8 | 6 257 1 | +-------------+-------------+--------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 25 25 4 | +-------------+-------------+--------------+ | 8 23 4 | 7 6 2 | 9 1 35 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 25 67 7 | +-------------+-------------+--------------+ 28th) Hidden single: 5 @ r7c9 from values 35 Row 7 wise +-------------+-------------+-------------+ | 6 8 35 | 15 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 27 | | 57 23 9 | 4 35 8 | 6 257 1 | +-------------+-------------+-------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 25 25 4 | +-------------+-------------+-------------+ | 8 23 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 2 67 7 | +-------------+-------------+-------------+ 29th) Hidden single: 5 @ r6c7 from values 25 Column 7 wise +-------------+-------------+------------+ | 6 8 35 | 15 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 27 | | 57 23 9 | 4 35 8 | 6 257 1 | +-------------+-------------+------------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +-------------+-------------+------------+ | 8 23 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 2 67 7 | +-------------+-------------+------------+ 30th) Naked single: 2 @ r6c8 +-------------+-------------+-----------+ | 6 8 35 | 15 2 137 | 4 57 9 | | 257 24 1 | 6 9 7 | 3 8 27 | | 57 23 9 | 4 35 8 | 6 57 1 | +-------------+-------------+-----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +-------------+-------------+-----------+ | 8 23 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 15 35 9 | 8 4 23 | | 125 9 35 | 8 4 123 | 2 67 7 | +-------------+-------------+-----------+ 31st) Hidden single: 2 @ r2c9 from values 27 Box 3 wise +-------------+-------------+----------+ | 6 8 35 | 15 2 137 | 4 57 9 | | 57 4 1 | 6 9 7 | 3 8 2 | | 57 23 9 | 4 35 8 | 6 57 1 | +-------------+-------------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +-------------+-------------+----------+ | 8 23 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 15 35 9 | 8 4 3 | | 125 9 35 | 8 4 123 | 2 67 7 | +-------------+-------------+----------+ 32nd) Hidden single: 2 @ r3c2 from values 23 Row 3 wise +------------+-------------+----------+ | 6 8 35 | 15 2 137 | 4 57 9 | | 57 4 1 | 6 9 7 | 3 8 2 | | 57 2 9 | 4 35 8 | 6 57 1 | +------------+-------------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +------------+-------------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 15 35 9 | 8 4 3 | | 125 9 35 | 8 4 123 | 2 67 7 | +------------+-------------+----------+ 33rd) Hidden single: 3 @ r1c3 from values 35 Box 1 wise +-----------+-------------+----------+ | 6 8 3 | 15 2 17 | 4 57 9 | | 57 4 1 | 6 9 7 | 3 8 2 | | 57 2 9 | 4 35 8 | 6 57 1 | +-----------+-------------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +-----------+-------------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 15 35 9 | 8 4 3 | | 125 9 5 | 8 4 123 | 2 67 7 | +-----------+-------------+----------+ 34th) Hidden single: 3 @ r3c5 from values 35 Row 3 wise +-----------+------------+----------+ | 6 8 3 | 15 2 17 | 4 57 9 | | 57 4 1 | 6 9 7 | 3 8 2 | | 57 2 9 | 4 3 8 | 6 57 1 | +-----------+------------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +-----------+------------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 15 5 9 | 8 4 3 | | 125 9 5 | 8 4 123 | 2 67 7 | +-----------+------------+----------+ 35th) Hidden single: 5 @ r1c4 from values 15 Box 2 wise +-----------+-----------+----------+ | 6 8 3 | 5 2 17 | 4 7 9 | | 57 4 1 | 6 9 7 | 3 8 2 | | 57 2 9 | 4 3 8 | 6 57 1 | +-----------+-----------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +-----------+-----------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 1 5 9 | 8 4 3 | | 125 9 5 | 8 4 123 | 2 67 7 | +-----------+-----------+----------+ 36th) Naked single: 3 @ r7c2 +-----------+-----------+----------+ | 6 8 3 | 5 2 17 | 4 7 9 | | 57 4 1 | 6 9 7 | 3 8 2 | | 57 2 9 | 4 3 8 | 6 57 1 | +-----------+-----------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +-----------+-----------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 1 5 9 | 8 4 3 | | 125 9 5 | 8 4 123 | 2 67 7 | +-----------+-----------+----------+ 37th) Hidden single: 5 @ r2c1 from values 57 Row 2 wise +----------+-----------+----------+ | 6 8 3 | 5 2 17 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 57 1 | +----------+-----------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +----------+-----------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 1 5 9 | 8 4 3 | | 12 9 5 | 8 4 123 | 2 67 7 | +----------+-----------+----------+ 38th) Naked single: 7 @ r3c1 +----------+-----------+----------+ | 6 8 3 | 5 2 17 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +----------+-----------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +----------+-----------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 1 5 9 | 8 4 3 | | 12 9 5 | 8 4 123 | 2 67 7 | +----------+-----------+----------+ 39th) Naked single: 2 @ r7c6 +----------+----------+----------+ | 6 8 3 | 5 2 17 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +----------+----------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +----------+----------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 1 5 9 | 8 4 3 | | 12 9 5 | 8 4 13 | 2 67 7 | +----------+----------+----------+ 40th) Naked single: 5 @ r3c8 +----------+----------+----------+ | 6 8 3 | 5 2 17 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +----------+----------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +----------+----------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 1 5 9 | 8 4 3 | | 12 9 5 | 8 4 13 | 2 67 7 | +----------+----------+----------+ 41st) Hidden single: 1 @ r1c6 from values 17 Row 1 wise +----------+---------+----------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +----------+---------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +----------+---------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 12 6 7 | 1 5 9 | 8 4 3 | | 12 9 5 | 8 4 3 | 2 67 7 | +----------+---------+----------+ 42nd) Hidden single: 2 @ r8c1 from values 12 Row 8 wise +---------+---------+----------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 67 7 | +---------+---------+----------+ 43rd) Naked single: 1 @ r8c4 +---------+---------+----------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 67 7 | +---------+---------+----------+ 44th) Naked single: 5 @ r8c5 +---------+---------+----------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 67 7 | +---------+---------+----------+ 45th) Naked single: 4 @ r2c2 +---------+---------+----------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 67 7 | +---------+---------+----------+ 46th) Naked single: 3 @ r8c9 +---------+---------+----------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 67 7 | +---------+---------+----------+ 47th) Naked single: 1 @ r9c1 +---------+---------+----------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+----------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+----------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 67 7 | +---------+---------+----------+ 48th) Naked single: 7 @ r1c8 +---------+---------+---------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+---------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+---------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 6 7 | +---------+---------+---------+ 49th) Naked single: 5 @ r9c3 +---------+---------+---------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+---------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+---------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 6 7 | +---------+---------+---------+ 50th) Naked single: 7 @ r2c6 +---------+---------+---------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+---------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+---------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 6 7 | +---------+---------+---------+ 51st) Naked single: 3 @ r9c6 +---------+---------+---------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+---------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+---------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 6 7 | +---------+---------+---------+ 52nd) Naked single: 2 @ r9c7 +---------+---------+---------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+---------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+---------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 6 7 | +---------+---------+---------+ 53rd) Naked single: 6 @ r9c8 +---------+---------+---------+ | 6 8 3 | 5 2 1 | 4 7 9 | | 5 4 1 | 6 9 7 | 3 8 2 | | 7 2 9 | 4 3 8 | 6 5 1 | +---------+---------+---------+ | 3 5 6 | 2 7 4 | 1 9 8 | | 4 1 2 | 9 8 5 | 7 3 6 | | 9 7 8 | 3 1 6 | 5 2 4 | +---------+---------+---------+ | 8 3 4 | 7 6 2 | 9 1 5 | | 2 6 7 | 1 5 9 | 8 4 3 | | 1 9 5 | 8 4 3 | 2 6 7 | +---------+---------+---------+ 54th) Naked single: 7 @ r9c9 1) 683521479541697382729438651356274198412985736978316524834762915267159843195843267 # S1 # C27 # P196 # N23 # H31 # G0 # D0 # 0.013000

R. Jamil

by **SteveG48** » Sat Jan 23, 2021 6:09 pm

Cenoman wrote:
Code: Select all
+----------------------+--------------------+--------------------+ | 567 8 h356 | g135 2 ga13-7 | 4 57 9 | | 2457 245 1 | 6 9 47 | 3 8 257 | | 2457 G2345 9 | 345 35 8 | 6 257 1 | +----------------------+--------------------+--------------------+ | 3 125 256 | 24 7 246 | 12 9 8 | | 1246 124 26 | 9 8 5 | 7 13 236 | | 9 7 8 | 23 1 236 | 25 256 4 | +----------------------+--------------------+--------------------+ | 8 F1235 4 | 7 6 D123 | 9 E13 235 | | 12 6 7 | 1235 35 9 | 8 4 23 | | 125 9 B235 | 8 4 C123 | 125 67 67 | +----------------------+--------------------+--------------------+

(1)r1c6 = [(3)r9c3 = (3-1)r9c6 *=* r7c6 - (1=3)r7c8 - r7c2 = (3)r3c2] - (3)r1c3 = (31)r1c46 => -7 r1c6; ste

Yikes! I love it.

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