The New Sudoku Players' Forum

by **eleven** » Fri Dec 31, 2021 10:22 am

Code: Select all: +-------------------+ | . 1 7 . . . . . . | | 6 . . 3 . . . . . | | . . . 2 . . 8 7 . | | . . 3 . . 7 . . 4 | | . 5 . . . . . . 9 | | 1 . . . . . . 2 . | | 7 8 . 6 . . 5 . . | | . . . . . 4 . . . | | . . . . . 5 3 . 2 | +-------------------+

by **totuan** » Fri Dec 31, 2021 2:27 pm

Code: Select all: *--------------------------------------------------------------------* | 23458 1 7 |#458 #4568 *68 | 24 9 36 | | 6 249 2489 | 3 7 *89 | 24 1 5 | | 3459 349 459 | 2 14569 169 | 8 7 36 | |----------------------+----------------------+----------------------| | 289 269 3 | 89 268 7 | 1 5 4 | | 248 5 2468 | 148 12468 1268 | 7 3 9 | | 1 7 4-9 |#459 #45 3 | 6 2 8 | |----------------------+----------------------+----------------------| | 7 8 %29 | 6 3 %29 | 5 4 1 | | 235 236 1256 | 18 128 4 | 9 68 7 | | 49 469 1469 | 7 189 5 | 3 68 2 | *--------------------------------------------------------------------*

My path for this one:
01: UR(45)r16c45: (9)r6c4==(6|8)r1c45-(6|8=9)r12c6-r7c6=r7c3 => r6c3<>9, some singles

Code: Select all: *-----------------------------------------------------------* | 2348 1 7 | 5 46 68 | 24 9 36 | | 6 249 289 | 3 7 89 | 24 1 5 | | 3459 349 59 | 2 1469 169 | 8 7 36 | |-------------------+-------------------+-------------------| | 29 29-6 3 | 8 #26 7 | 1 5 4 | | 28 5 *268 | 4 126 126 | 7 3 9 | | 1 7 4 | 9 5 3 | 6 2 8 | |-------------------+-------------------+-------------------| | 7 8 29 | 6 3 29 | 5 4 1 | | 235 236 *256 | 1 *28 4 | 9 *68 7 | | 49 469 1 | 7 89 5 | 3 68 2 | *-----------------------------------------------------------*

02: (6)r5c3=r8c3-(6=8)r8c8-(8=2)r8c5-(2=6)r4c5 => r4c2<>6, stte

Thanks for the puzzle and HAPPY NEW YEAR 2022 to all!
totuan

by **P.O.** » Fri Dec 31, 2021 5:14 pm

Code: Select all: after singles and intersections and algorithms have replaced humans: 23458 1 7 d(45)8 d(45)68 c+68 e2-4 9 36 6 249 f248+9 3 7 b+89 e2+4 1 5 3459 349 h4+59 2 14569 169 8 7 36 l-289 l-269 3 89 l+268 7 1 5 4 k+248 5 j246+8 148 12468 1×268 7 3 9 1 7 g+49 459 45 3 6 2 8 7 8 b+29 6 3 a±2+9 5 4 1 235 236 i(16)25 18 1×28 4 9 68 7 49 469 i(16)49 7 189 5 3 68 2 /- r7c3{n9 n2} r7c6{n2 n9} - r2c6{n9 n8} - r1c6{n8 n6} - r1{c4c5}{n4n5} - c7n4{r1 r2} - r2c3{n2n4n8 n9} - r6c3{n9 n4} - r3c3{n4n9 n5} - c3{r8r9}{n1n6} - r5c3{n2n4n6 n8} - r5c1{n4n8 n2} - r4n2{c1c2 c5} => r5c6 r8c5 <> 2 ste.

Happy new year to all.

by **jco** » Sat Jan 01, 2022 2:47 am

After basics

Code: Select all: .---------------------------------------------------------------------. | 23458 1 7 | 458 4568 68 | 24 9 36 | | 6 D249 bD(49)(28)| 3 7 cC89 | 24 1 5 | |E3459 E349 E459 | 2 14569 169 | 8 7 36 | |-----------------------+----------------------+----------------------| | 289 269 3 | 89 268 7 | 1 5 4 | | 248 5 2468 | 148 12468 1268 | 7 3 9 | | 1 7 4-9 | 459 45 3 | 6 2 8 | |-----------------------+----------------------+----------------------| | 7 8 eaA29 | 6 3 dB29 | 5 4 1 | | 235 236 1256 | 18 128 4 | 9 68 7 | | 49 469 1469 | 7 189 5 | 3 68 2 | '---------------------------------------------------------------------'

Either (49) or (28) are false at r2c3, thus
[(9=2)r7c3 - (2*=8)r2c3 - (8=9)r2c6 - (9)r7c6 = (9)r7c3]
||
[(9)r7c3 = (9)r7c6 - (9)r2c6 = (9)r2c23 - (9=254)r3c123 - (4=*9)r2c3]
=> -9 r6c3;
---

Code: Select all: .--------------------------------------------. | 2348 1 7 | 5 46 68 | 24 9 36 | | 6 249 289 | 3 7 89 | 24 1 5 | | 3459 349 59 | 2 1469 169 | 8 7 36 | |----------------+--------------+------------| | 29 b269 3 | 8 a6-2 7 | 1 5 4 | | 28 5 268 | 4 126 126 | 7 3 9 | | 1 7 4 | 9 5 3 | 6 2 8 | |----------------+--------------+------------| | 7 8 29 | 6 3 29 | 5 4 1 | | 235 c236 d256 | 1 e28 4 | 9 e68 7 | | 49 c469 1 | 7 89 5 | 3 68 2 | '--------------------------------------------'

(6)r4c5 = r4c2 - r89c2 = r8c3 - (6=82)r8c85 => -2 r4c5; ste

Thanks for the puzzle.
Happy New Year to all!

by **RSW** » Sat Jan 01, 2022 11:43 am

Threes steps for me.

Code: Select all: +-----------------+------------------+----------+ | 23458 1 7 | 45-8 4568 68 | 24 9 36 | | 6 249 b2489 | 3 7 c89 | 24 1 5 | | 3459 349 459 | 2 14569 169 | 8 7 36 | +-----------------+------------------+----------+ | 29-8 269 3 |g89 268 7 | 1 5 4 | | 248 5 a2468 | 14-8 1246-8 126-8| 7 3 9 | | 1 7 de49 |f459 45 3 | 6 2 8 | +-----------------+------------------+----------+ | 7 8 d29 | 6 3 c29 | 5 4 1 | | 235 236 1256 | 18 128 4 | 9 68 7 | | 49 469 1469 | 7 189 5 | 3 68 2 | +-----------------+------------------+----------+

(8)r5c3 = (8)r2c3 - (8=92)r27c6* - (2=94)r67c3 - (9)r6c3 = (9)r6c4 - (9=8)r4c4 => -8r4c1 -8r1c4* -8r5c456

Code: Select all: +-----------------+------------------+----------+ | 23458 1 7 | #45 c#456 d68 | 24 9 36 | | 6 249 289-4 | 3 7 d89 | 24 1 5 | | 3459 349 59-4 | 2 14569 169 | 8 7 36 | +-----------------+------------------+----------+ | 29 269 3 | 89 268 7 | 1 5 4 | | 28-4 5 268-4 | 14 1246 126 | 7 3 9 | | 1 7 ae49 |b#59-4 #5-4 3 | 6 2 8 | +-----------------+------------------+----------+ | 7 8 e29 | 6 3 d29 | 5 4 1 | | 235 236 1256 | 18 128 4 | 9 68 7 | | 49 469 169-4 | 7 189 5 | 3 68 2 | +-----------------+------------------+----------+

UR(45)r16c45
(4=9)r6c3 - (9)r6c4 =UR= (6)r1c5 - (6=982)r127c6 - (2=94)r67c3 => -4r5c13 -4r239c3 -4r6c45

Code: Select all: +---------------+--------------+----------+ | 2348 1 7 | 5 46 68 | 24 9 36 | | 6 249 289 | 3 7 89 | 24 1 5 | | 3459 349 59 | 2 1469 169 | 8 7 36 | +---------------+--------------+----------+ | 29 29-6 3 | 8 a26 7 | 1 5 4 | | 28 5 268 | 4 126 126 | 7 3 9 | | 1 7 4 | 9 5 3 | 6 2 8 | +---------------+--------------+----------+ | 7 8 29 | 6 3 29 | 5 4 1 | | 235 236 256 | 1 a28 4 | 9 68 7 | |b49 b469 1 | 7 ab89 5 | 3 68 2 | +---------------+--------------+----------+

(6=289)r489c5 - (8=496)r9c125 => -6r4c2; stte

Thanks for the puzzle.
Happy New Year everyone.

Website · by **denis_berthier** » Sun Jan 02, 2022 5:42 am

.

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 23458 1 7 ! 458 4568 68 ! 24 9 36 ! ! 6 249 2489 ! 3 7 89 ! 24 1 5 ! ! 3459 349 459 ! 2 14569 169 ! 8 7 36 ! +-------------------+-------------------+-------------------+ ! 289 269 3 ! 89 268 7 ! 1 5 4 ! ! 248 5 2468 ! 148 12468 1268 ! 7 3 9 ! ! 1 7 49 ! 459 45 3 ! 6 2 8 ! +-------------------+-------------------+-------------------+ ! 7 8 29 ! 6 3 29 ! 5 4 1 ! ! 235 236 1256 ! 18 128 4 ! 9 68 7 ! ! 49 469 1469 ! 7 189 5 ! 3 68 2 ! +-------------------+-------------------+-------------------+ 121 candidates.

The puzzle is in W4 but also in Z4:

Code: Select all: finned-x-wing-in-rows: n9{r7 r2}{c6 c3} ==> r3c3≠9 biv-chain[3]: r2c7{n4 n2} - r1n2{c7 c1} - b1n8{r1c1 r2c3} ==> r2c3≠4 z-chain[3]: r9c1{n4 n9} - c5n9{r9 r3} - r3n4{c5 .} ==> r1c1≠4 with z-candidates = n4r3c3 n4r3c2 n4r3c1 z-chain[3]: c4n4{r6 r1} - c4n5{r1 r6} - r6c5{n5 .} ==> r5c5≠4 with z-candidates = n4r5c4 n4r6c5 biv-chain[4]: r2c6{n8 n9} - r7n9{c6 c3} - r6n9{c3 c4} - c4n5{r6 r1} ==> r1c4≠8 biv-chain[4]: r2c6{n8 n9} - r7n9{c6 c3} - r6n9{c3 c4} - r4c4{n9 n8} ==> r5c6≠8 whip[1]: c6n8{r2 .} ==> r1c5≠8 biv-chain[4]: r6c3{n4 n9} - r7n9{c3 c6} - r2c6{n9 n8} - c3n8{r2 r5} ==> r5c3≠4 biv-chain[4]: c5n9{r3 r9} - r9c1{n9 n4} - r5n4{c1 c4} - r1c4{n4 n5} ==> r3c5≠5 whip[1]: r3n5{c3 .} ==> r1c1≠5 biv-chain[4]: c1n5{r8 r3} - r3c3{n5 n4} - r6c3{n4 n9} - r7c3{n9 n2} ==> r8c1≠2 biv-chain[4]: r9n1{c3 c5} - c4n1{r8 r5} - r5n4{c4 c1} - r9c1{n4 n9} ==> r9c3≠9 z-chain[4]: r7n9{c3 c6} - r2c6{n9 n8} - r2c3{n8 n2} - r7c3{n2 .} ==> r6c3≠9 with z-candidates = n9r2c3 n9r7c3 singles ==> r6c3=4, r3c3=5, r6c5=5, r6c4=9, r4c4=8, r8c4=1, r5c4=4, r1c4=5, r9c3=1, r8c1=5, r8c2=3 whip[1]: b7n2{r8c3 .} ==> r2c3≠2, r5c3≠2 naked-pairs-in-a-row: r2{c3 c6}{n8 n9} ==> r2c2≠9 x-wing-in-rows: n9{r2 r7}{c3 c6} ==> r3c6≠9 biv-chain[3]: r5c3{n6 n8} - r2n8{c3 c6} - r1c6{n8 n6} ==> r5c6≠6 whip[1]: c6n6{r3 .} ==> r1c5≠6, r3c5≠6 singles ==> r1c5=4, r1c7=2, r2c7=4, r2c2=2 biv-chain[3]: r4c2{n9 n6} - r5c3{n6 n8} - r2c3{n8 n9} ==> r3c2≠9 singles ==> r3c2=4, r9c1=4 biv-chain[3]: c5n6{r4 r5} - c3n6{r5 r8} - r8n2{c3 c5} ==> r4c5≠2 stte

In my approach, obtaining this rating is the basis for dealing with any additional requirement on the number of steps.
There is no 1- or 2- step solution with whips of reasonable length.
I therefore decided to try multi-step solutions with longer z-chains (I could have chosen whips, but as the original puzzle doesn't require whips, I thought it was more fun not to have them in the solution). z-chains are like oddagons, in that they have z-candidates but no t-candidate.

Code: Select all: *** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+O+SFin *** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1 (smart-solve-ntimes-with-fewer-steps 10 ".17......6..3........2..87...3..7..4.5......91......2.78.6..5.......4........53.2" )

gives 4 non-W1 steps in Z7 on the first try:

Code: Select all: 1) z-chain[7]: b8n9{r9c5 r7c6} - b8n2{r7c6 r8c5} - r4c5{n2 n6} - b4n6{r4c2 r5c3} - c3n8{r5 r2} - r2c6{n8 n9} - c5n9{r3 .} ==> r9c5≠8 with z-candidates = n8r4c5 n9r9c5 singles ==> r9c8=8, r8c8=6 2) biv-chain[5]: r4c4{n8 n9} - r6n9{c4 c3} - r7n9{c3 c6} - r2c6{n9 n8} - c3n8{r2 r5} ==> r5c5≠8, r5c4≠8, r5c6≠8, r4c1≠8 whip[1]: c6n8{r2 .} ==> r1c4≠8, r1c5≠8 3) z-chain[6]: c5n9{r3 r9} - r9n1{c5 c3} - c3n6{r9 r5} - r4n6{c2 c5} - r1c5{n6 n5} - r6c5{n5 .} ==> r3c5≠4 with z-candidates = n4r1c5 n4r6c5 whip[1]: r3n4{c3 .} ==> r1c1≠4, r2c2≠4, r2c3≠4 singles ==> r2c7=4, r1c7=2 4) z-chain[4]: r7n9{c3 c6} - r2n9{c6 c2} - r2n2{c2 c3} - r7c3{n2 .} ==> r6c3≠9, r9c3≠9, r3c3≠9 with z-candidates = n9r2c3 n9r7c3 stte

Happy New Year

by **eleven** » Sun Jan 02, 2022 10:01 am

Thanx for your solutions, and a happy new year to all.

I made it the same way as totuan, using the UR 45. Without 9r6c4 there is a type 3 UR, forcing a pair 68 in r1c456 and 9r2c6.

For a 1-step solution i needed a Kraken from r5c1:

Code: Select all: *------------------------------------------------------------------* | e23458 1 7 |f#45+8 f#45+68 f68 | 24 9 36 | | 6 249 2489 | 3 7 gc89 | 24 1 5 | | 3459 349 459 | 2 1456-9 c169 | 8 7 36 | |-----------------------+------------------------+-----------------| | 289 269 3 | 89 268 7 | 1 5 4 | | *248 5 2468 | 148 12468 a1268 | 7 3 9 | | 1 7 d49 | #45+9 #45 3 | 6 2 8 | |-----------------------+------------------------+-----------------| | 7 8 29 | 6 3 b29 | 5 4 1 | | 235 236 1256 | 18 128 4 | 9 68 7 | | 49 469 1469 | 7 189 5 | 3 68 2 | *------------------------------------------------------------------*

2r5c1 - r5c6 = (2-9)r7c6 = 9r23c6
4r5c1 - (4=9)r6c3 - 9r6c4 == 9r2c6
8r5c1 - r1c1 = r1c456 - (8=9)r2c6
=> -9r3c5

Website · by **denis_berthier** » Sun Jan 02, 2022 1:08 pm

eleven wrote:For a 1-step solution i needed a Kraken from r5c1:
Code: Select all
*------------------------------------------------------------------* | e23458 1 7 |f#45+8 f#45+68 f68 | 24 9 36 | | 6 249 2489 | 3 7 gc89 | 24 1 5 | | 3459 349 459 | 2 1456-9 c169 | 8 7 36 | |-----------------------+------------------------+-----------------| | 289 269 3 | 89 268 7 | 1 5 4 | | *248 5 2468 | 148 12468 a1268 | 7 3 9 | | 1 7 d49 | #45+9 #45 3 | 6 2 8 | |-----------------------+------------------------+-----------------| | 7 8 29 | 6 3 b29 | 5 4 1 | | 235 236 1256 | 18 128 4 | 9 68 7 | | 49 469 1469 | 7 189 5 | 3 68 2 | *------------------------------------------------------------------*

2r5c1 - r5c6 = (2-9)r7c6 = 9r23c6
4r5c1 - (4=9)r6c3 - 9r6c4 == 9r2c6
8r5c1 - r1c1 = r1c456 - (8=9)r2c6
=> -9r3c5

I hadn't looked for so large patterns, but the same elimination is obtained by a whip[11]:
whip[11]: c6n9{r3 r7} - r7c3{n9 n2} - c6n2{r7 r5} - c6n1{r5 r3} - c6n6{r3 r1} - c6n8{r1 r2} - r1n8{c5 c1} - r5c1{n8 n4} - r6c3{n4 n9} - b1n9{r3c3 r2c2} - b1n2{r2c2 .} ==> r3c5≠9

by **eleven** » Sun Jan 02, 2022 2:38 pm

In this chain you have to remember 4 digits on the way to reach a contradiction, which is rather hard without using a (simple) solver.
I found the kraken this way (using 9r2c6=9r6c4 from the UR):
9r23c6 = (92r75c6 & 94r6c43) - (2|4=8)r5c1 - r1c1 = r1c456 - (8=9)r2c6

Website · by **denis_berthier** » Mon Jan 03, 2022 7:38 am

Notice I didn't say the whip[11] solution was a reasonable one. I think such long chains are very difficult to find for a manual solver.
Of my 3 above solutions, the one I prefer is the simplest one, requiring only z-chains[4].
As usual, adding requirements on the number of steps introduces complexities that do not really belong to the puzzle.

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