The New Sudoku Players' Forum

by **P.O.** » Sat Dec 18, 2021 4:59 pm

Code: Select all: . 9 . . . . . 1 3 5 2 . . . . . . 4 . . 1 . . . 2 . . . 1 . . . 7 . . . . . 9 1 2 . . 5 . . . . 8 . 4 . . . . . . 5 6 . . 3 9 6 3 . . . 1 . . . . . 4 3 . 2 . . 1 .9.....1352......4..1...2...1...7.....912..5....8.4......56..3963...1.....43.2..1

by **jco** » Sat Dec 18, 2021 8:45 pm

I found a solution in 3 steps. After basics,

Code: Select all: .-----------------------------------------------------. | 478 9 678 | 2 48 56 | 5678 1 3 | | 5 2 3678 | 67 1 369 | 6789 6789 4 | | 3478 468 1 | 467 348 3569 | 2 6789 5678 | |-----------------+----------------+------------------| | 238 1 3568 |d69 359 7 |a368-9 4 268 | | 3478 468 9 | 1 2 c36 |b3678 5 678 | | 237 56 3567 | 8 359 4 | 1 2679 267 | |-----------------+----------------+------------------| | 1 7 2 | 5 6 8 | 4 3 9 | | 6 3 58 | 49 49 1 | 578 278 2578 | | 9 58 4 | 3 7 2 | 568 68 1 | '-----------------------------------------------------'

1. (3)r4c7 = r5c7 - (3=6)r5c6 - (6=9)r4c4 => -9 r4c7 [4 placements & 2 lc eliminations]
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Code: Select all: .------------------------------------------------. | 478 9 678 | 2 48 5 | 68 1 3 | | 5 2 c368 | 67 1 36 | 9 d678 4 | | 348 468 1 | 467 348 9 | 2 678 5 | |-----------------+--------------+---------------| | 238 1 3568 | 69 359 7 | 38 4 268 | | 3478 468 9 | 1 2 36 | 378 5 678 | | 237 56 3567 | 8 35 4 | 1 9 267 | |-----------------+--------------+---------------| | 1 7 2 | 5 6 8 | 4 3 9 | | 6 3 b58 | 49 49 1 | 578 2 78 | | 9 a58 4 | 3 7 2 | 568 6-8 1 | '------------------------------------------------'

2. (8)r9c2 = r8c3 - (8)r2c3 = (8)r2c8 => -8 r9c8 [2 placements]
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Code: Select all: .-----------------------------------------------. | 478 9 78 | 2 48 5 | 6 1 3 | | 5 2 a368 | 67 1 e3-6| 9 78 4 | | 348 b468 1 | 467 348 9 | 2 78 5 | |-----------------+--------------+--------------| | 238 1 3568 | 69 359 7 | 38 4 268 | | 3478 468 9 | 1 2 d36 | 378 5 678 | | 237 c56 3567 | 8 c35 4 | 1 9 267 | |-----------------+--------------+--------------| | 1 7 2 | 5 6 8 | 4 3 9 | | 6 3 58 | 49 49 1 | 578 2 78 | | 9 58 4 | 3 7 2 | 58 6 1 | '-----------------------------------------------'

3. (6)r2c3 = (6)r3c2 - (6=53)r6c25 - (3=6)r5c6 => -6 r2c6; ste

Thanks for the puzzle.

by **Cenoman** » Sat Dec 18, 2021 10:47 pm

Two steps:

Code: Select all: +----------------------+---------------------+-----------------------+ | 478 9 678 | 2 48 56 | 5678 1 3 | | 5 2 3678 | 67 1 369 | 6789 6789 4 | | 3478 468 1 | 467 348 3569 | 2 6789 5678 | +----------------------+---------------------+-----------------------+ | 238 1 3568 | c69 359 7 | a368-9 4 268 | | 3478 468 9 | 1 2 c36 | b3678 5 678 | | 237 56 3567 | 8 359 4 | 1 2679 267 | +----------------------+---------------------+-----------------------+ | 1 7 2 | 5 6 8 | 4 3 9 | | 6 3 58 | 49 49 1 | 578 278 2578 | | 9 58 4 | 3 7 2 | 568 68 1 | +----------------------+---------------------+-----------------------+

1. (3)r4c7 = r5c7 - (3=69)b5p16 =>-9r4c7; 6 placements & ls

Code: Select all: +----------------------+-------------------+--------------------+ | 478 9 678 | 2 48 5 | 68 1 3 | | 5 2 368 | 67 1 36 | 9 678 4 | | 348 f468 1 | g67-4 c348 9 | 2 g678 5 | +----------------------+-------------------+--------------------+ | 238 1 3568 | 69 359 7 | 38 4 268 | | 3478 468 9 | 1 2 36 | 378 5 678 | | 237 e56 3567 | 8 d35 4 | 1 9 267 | +----------------------+-------------------+--------------------+ | 1 7 2 | 5 6 8 | 4 3 9 | | 6 3 58 | a49 b49 1 | 578 2 78 | | 9 58 4 | 3 7 2 | 568 68 1 | +----------------------+-------------------+--------------------+

2. (4=9)r8c4 - r8c5 = (9-5)r4c5 = r6c5 - (5=6)r6c2 - r3c2 = (67)r3c48 => -4 r3c4; ste

Website · by **denis_berthier** » Sun Dec 19, 2021 5:43 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 478 9 678 ! 2 48 56 ! 5678 1 3 ! ! 5 2 3678 ! 67 1 369 ! 6789 6789 4 ! ! 3478 468 1 ! 467 348 3569 ! 2 6789 5678 ! +----------------+----------------+----------------+ ! 238 1 3568 ! 69 359 7 ! 3689 4 268 ! ! 3478 468 9 ! 1 2 36 ! 3678 5 678 ! ! 237 56 3567 ! 8 359 4 ! 1 2679 267 ! +----------------+----------------+----------------+ ! 1 7 2 ! 5 6 8 ! 4 3 9 ! ! 6 3 58 ! 49 49 1 ! 578 278 2578 ! ! 9 58 4 ! 3 7 2 ! 568 68 1 ! +----------------+----------------+----------------+

Two steps in Z6:
First step:

Code: Select all: biv-chain[3]: r4c4{n9 n6} - r5c6{n6 n3} - b6n3{r5c7 r4c7} ==> r4c7≠9 singles ==> r6c8=9, r2c7=9, r3c6=9, r1c6=5, r3c9=5, r8c8=2 whip[1]: c8n7{r3 .} ==> r1c7≠7 whip[1]: r1n7{c3 .} ==> r2c3≠7, r3c1≠7 whip[1]: c9n6{r6 .} ==> r4c7≠6, r5c7≠6

After that, there are many possibilities in Z6 for the 2nd and final step, e.g.:

Code: Select all: z-chain[6]: r2n8{c3 c8} - r1c7{n8 n6} - b1n6{r1c3 r3c2} - r6c2{n6 n5} - r6c5{n5 n3} - r3n3{c5 .} ==> r2c3≠3 with z-candidates = n6r2c3 n3r3c1 stte

OR:

Code: Select all: z-chain[6]: b2n3{r2c6 r3c5} - r6c5{n3 n5} - r6c2{n5 n6} - r3n6{c2 c8} - c8n7{r3 r2} - r2c4{n7 .} ==> r2c6≠6 with z-candidates = n6r3c4 n6r2c4 stte

OR:

Code: Select all: z-chain[6]: r3n7{c4 c8} - r3n6{c8 c2} - r6c2{n6 n5} - r6c5{n5 n3} - r3c5{n3 n8} - r1c5{n8 .} ==> r3c4≠4 with z-candidates = n6r3c4 n4r3c5 n4r1c5 stte

OR:

Code: Select all: z-chain[6]: b5n9{r4c4 r4c5} - c5n5{r4 r6} - r6c2{n5 n6} - r3n6{c2 c8} - c8n7{r3 r2} - r2c4{n7 .} ==> r4c4≠6 with z-candidates = n6r3c4 n6r2c4 stte

OR:

Code: Select all: z-chain[6]: r3n3{c1 c5} - r6c5{n3 n5} - r6c2{n5 n6} - b1n6{r3c2 r1c3} - r1c7{n6 n8} - r2n8{c8 .} ==> r2c3≠3 with z-candidates = n6r2c3 n8r2c3 stte

by **P.O.** » Sun Dec 19, 2021 5:14 pm

same first elimination as all the previous solutions then one of the various possibilities;

Code: Select all: after singles and intersections: 478 9 678 2 48 56 5678 1 3 5 2 3678 67 1 369 6789 6789 4 3478 468 1 467 348 3569 2 6789 5678 238 1 3568 c6+9 359 7 a±368×9 4 268 3478 468 9 1 2 b3+6 a+3678 5 678 237 56 3567 8 359 4 1 2679 267 1 7 2 5 6 8 4 3 9 6 3 58 49 49 1 578 278 2578 9 58 4 3 7 2 568 68 1 c7n3{r4 r5} - r5c6{n3 n6} - r4c4{n6 n9} => r4c7 <> 9 singles + intersections 478 9 678 2 b4+8 5 68 1 3 5 2 368 67 1 36 9 678 4 f3(48) f(48)6 1 ×467 c+348 9 2 678 5 238 1 3568 69 359 7 38 4 268 3478 468 9 1 2 36 378 5 678 237 e5+6 3567 8 d3+5 4 1 9 267 1 7 2 5 6 8 4 3 9 6 3 58 a±49 a+49 1 578 2 78 9 58 4 3 7 2 568 68 1 r8n4{c4 c5} - r1c5{n4 n8} - r3c5{n4n8 n3} - r6c5{n3 n5} - r6c2{n5 n6} - r3{c1c2}{n4n8} => r3c4 <> 4 ste.

Puzzle 14