The New Sudoku Players' Forum

Website · by **denis_berthier** » Mon Jan 03, 2022 7:42 am

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Code: Select all: +-------+-------+-------+ ! . . 8 ! . 4 . ! 9 . . ! ! . 1 . ! . 9 . ! . 6 . ! ! 9 . . ! . 5 . ! . . 2 ! +-------+-------+-------+ ! . . . ! 9 . . ! . . . ! ! 5 2 1 ! . 3 . ! 4 9 8 ! ! . . . ! . . 5 ! . . . ! +-------+-------+-------+ ! 8 . . ! . 6 . ! . . 7 ! ! . 9 . ! . 2 . ! . 5 . ! ! . . 6 ! . 7 . ! 3 . . ! +-------+-------+-------+ ..8.4.9...1..9..6.9...5...2...9.....521.3.498.....5...8...6...7.9..2..5...6.7.3.. SER = 7.8

Intermediate between my previous two puzzles with the same pattern.

by **Cenoman** » Mon Jan 03, 2022 8:31 pm

Three steps:

Code: Select all: +-----------------------+-----------------------+-------------------------+ | 2367 3567 8 | 12367 4 12367 | 9 137 135 | | 2347 1 B25 | 2378 9 2378 |xA578 6 345 | | 9 3467 347 | 13678 5 13678 |xa178 13478 2 | +-----------------------+-----------------------+-------------------------+ | 3467 34678 347 | 9 18 24 | 12567 1237 1356 | | 5 2 1 | 67 3 67 | 4 9 8 | | 3467 34678 9 | 24 18 5 | 1267 1237 136 | +-----------------------+-----------------------+-------------------------+ | 8 345 C25 | 1345 6 9 | b12 124 7 | | 1347 9 347 | 1348 2 1348 | y168 5 146 | | D124 45 6 | 1458 7 148 | 3 z148-2 9 | +-----------------------+-----------------------+-------------------------+

1. Kraken AALS (Almost-almost NP)
(1)r3c7 - (1=2)r7c7
(5)r2c7 - (5=2)r2c3 - r7c3 = (2)r9c1
(78)r23c7 - r8c7 = (8)r9c8
=> -2 r9c8; 9 placements & ls

Code: Select all: +--------------------+-----------------------+-------------------------+ | 367 5 8 | 12367 4 12367 | 9 137 13 | | *347 1 2 | 378 9 378 | 578 6 *345 | | 9 67 34 | 13678 5 13678 | 178 13478 2 | +--------------------+-----------------------+-------------------------+ | 3467 678 34 | 9 18 24 | 12567 1237 1356 | | 5 2 1 | 67 3 67 | 4 9 8 | | *3467 678 9 | *24 18 5 | 1267 1237 136 | +--------------------+-----------------------+-------------------------+ | 8 3 5 | 1-4 6 9 | 12 124 7 | | 1 9 7 | *348 2 *348 | 68 5 *46 | | 2 4 6 | 5 7 18 | 3 18 9 | +--------------------+-----------------------+-------------------------+

2. Finned Swordfish: (4)r268\c149 fr8c6 => -4 r7c4; 18 placements & ls

Code: Select all: +-------------------+-----------------+-------------------+ | 7-6 5 8 | e26 4 12 | 9 37 13 | | 3 1 2 | 8 9 7 | 5 6 4 | | 9 a67 4 | 36 5 13 | 17 8 2 | +-------------------+-----------------+-------------------+ | 467 *678 3 | 9 *18 24 | *167 27 5 | | 5 2 1 | 7 3 6 | 4 9 8 | | 467 *678 9 | d24 *18 5 | *167 c237 b13 | +-------------------+-----------------+-------------------+ | 8 3 5 | 1 6 9 | 2 4 7 | | 1 9 7 | 34 2 34 | 8 5 6 | | 2 4 6 | 5 7 8 | 3 1 9 | +-------------------+-----------------+-------------------+

3. Bug-lite (168)r46c257 using externals (6)r3c2 == (1-3)r6c9 = (3-2)r6c8 = r6c4 - (2=6)r1c4 => -6 r1c1; ste

Happy New Year everybody !

by **DEFISE** » Tue Jan 04, 2022 11:27 am

Happy new year to all !

In 3 steps too:

Singles: 9r6c3, 9r7c6, 9r9c9
Box/Line: 6r5b5 => -6r4c6 -6r6c4
Box/Line: 7r5b5 => -7r4c6 -7r6c4
Box/Line: 1c5b5 => -1r4c6 -1r6c4
Box/Line: 8c5b5 => -8r4c6 -8r6c4
Hidden pairs: 25c3r27 (not necessary for the rest)

whip[6]: c3n2{r2 r7}- b9n2{r7c7 r9c8}- b9n8{r9c8 r8c7}- r2c7{n8 n7}- r3c7{n7 n1}- r7c7{n1 .}
=> -5r2c3
Singles: 5r7c3, 4r9c2, 3r7c2, 7r8c3, 1r8c1, 2r9c1, 5r9c4, 5r1c2, 2r2c3

whip[3]: r2n4{c9 c1}- r6n4{c1 c4}- c6n4{r4 .} => -4r8c9
Single(s): 6r8c9, 8r8c7, 1r9c8, 2r7c7, 4r7c8, 1r7c4, 8r9c6, 8r2c4, 4r3c3, 3r4c3, 4r2c9, 5r2c7, 8r3c8, 5r4c9
Box/Line: 3r3b2 => -3r1c4 -3r1c6 -3r2c6
Singles: 7r2c6, 3r2c1, 6r5c6, 7r5c4

whip[4]: r1c8{n7 n3}- r1c9{n3 n1}- r1c6{n1 n2}- r4n2{c6 .} => -7r4c8
STTE
N.B: I checked by hand that the last two whips are z-chains if we take into account the initial hidden-pairs, but maybe also without these pairs.

by **eleven** » Tue Jan 04, 2022 11:56 am

Code: Select all: +----------------------+----------------------+----------------------+ | 2367 3567 8 | 12367 4 12367 | 9 137 135 | | 2347 1 25 | 2378 9 2378 | 578 6 345 | | 9 3467 347 | 13678 5 13678 | 178 13478 2 | +----------------------+----------------------+----------------------+ | 3467 34678 347 | 9 18 24 | 12567 1237 1356 | | 5 2 1 | 67 3 67 | 4 9 8 | | 3467 34678 9 | 24 18 5 | 1267 1237 136 | +----------------------+----------------------+----------------------+ | 8 345 b25 | 1345 6 9 |a12 124 7 | |d1347 9 347 | 1348 2 1348 | 68-1 5 46-1 | |c124 45 6 | 1458 7 148 | 3 1248 9 | +----------------------+----------------------+----------------------+

(1=2)r7c7 - r7c3 = (2-1)r9c1 = r8c1 => -1r8c79

Code: Select all: +----------------------+----------------------+----------------------+ | 2367 3567 8 | 12367 4 12367 | 9 137 135 | |a2347 1 25 | 2378 9 2378 | 578 6 b345 | | 9 3467 *347 | 13678 5 13678 | 178 13478 2 | +----------------------+----------------------+----------------------+ | 3467 34678 #347 | 9 18 #24 | 12567 1237 1356 | | 5 2 1 | 67 3 67 | 4 9 8 | | 3467 34678 9 | 24 18 5 | 1267 1237 136 | +----------------------+----------------------+----------------------+ | 8 345 d25 | 1345 6 9 |d12 d124 7 | | 1347 9 #347 | 1348 2 #1348 | 68 5 6-4 | | 124 c45 6 | 1458 7 *148 | 3 1248 9 | +----------------------+----------------------+----------------------+

x-wing 4 r48c36 with 2 fins:
4r3c3 - r2c1 = r2c9
4r9c6 - (4=5)r9c2 - (5=214)r7c378
=> -4r8c9

Code: Select all: +----------------------+----------------------+----------------------+ | 267 567 8 | 1267 4 1267 | 9 137 135 | | 237 1 a25 | 2378 9 2378 |b57 6 4 | | 9 3467 347 | 1367 5 1367 |b17 8 2 | +----------------------+----------------------+----------------------+ | 3467 34678 347 | 9 18 24 | 12567 1237 135 | | 5 2 1 | 67 3 67 | 4 9 8 | | 3467 34678 9 | 24 18 5 | 1267 1237 13 | +----------------------+----------------------+----------------------+ | 8 345 5-2 | 1345 6 9 |b12 124 7 | | 1347 9 347 | 134 2 134 | 8 5 6 | | 124 45 6 | 1458 7 148 | 3 124 9 | +----------------------+----------------------+----------------------+

(2=5)r2c3 - (5=712)r237c7 => -2r7c3

Code: Select all: +----------------+----------------+----------------+ | 67 5 8 | 26 4 b12 | 9 b37 b13 | | 3 1 2 | 8 9 7 | 5 6 4 | | 9 67 4 | 36 5 13 | 17 8 2 | +----------------+----------------+----------------+ | 467 678 3 | 9 18 4-2 | 167 a27 5 | | 5 2 1 | 7 3 6 | 4 9 8 | | 467 678 9 | 24 18 5 | 167 237 13 | +----------------+----------------+----------------+ | 8 3 5 | 1 6 9 | 2 4 7 | | 1 9 7 | 34 2 34 | 8 5 6 | | 2 4 6 | 5 7 8 | 3 1 9 | +----------------+----------------+----------------+

(2=7)r4c8 - (7=312)r1c896 => -2r4c6, stte

Website · by **denis_berthier** » Tue Jan 04, 2022 12:41 pm

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Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 2367 3567 8 ! 12367 4 12367 ! 9 137 135 ! ! 2347 1 23457 ! 2378 9 2378 ! 578 6 345 ! ! 9 3467 347 ! 13678 5 13678 ! 178 13478 2 ! +-------------------+-------------------+-------------------+ ! 3467 34678 347 ! 9 18 24 ! 12567 1237 1356 ! ! 5 2 1 ! 67 3 67 ! 4 9 8 ! ! 3467 34678 9 ! 24 18 5 ! 1267 1237 136 ! +-------------------+-------------------+-------------------+ ! 8 345 2345 ! 1345 6 9 ! 12 124 7 ! ! 1347 9 347 ! 1348 2 1348 ! 168 5 146 ! ! 124 45 6 ! 1458 7 148 ! 3 1248 9 ! +-------------------+-------------------+-------------------+

The puzzle is solvable in Z4 (and is therefore intermediate between the other two also wrt the W rating system).

Here is one solution in Z4, based on the simplest-first strategy: Show

As usual with the simplest-first strategy, other solutions in Z4 can probably be found, with fewer steps.

There is no 1- or 2-step whip solution in W8.

I therefore tried the fewer step algorithm in W6 (my philosophy being that an increase in length by 2 wrt to the rating is the limit of the reasonable).

whip[6]: r7n2{c8 c3} - c3n5{r7 r2} - c7n5{r2 r4} - c7n2{r4 r6} - c7n6{r6 r8} - b9n8{r8c7 .} ==> r9c8≠2
singles ==> r9c1=2, r2c3=2, r1c2=5, r9c2=4, r7c2=3, r7c3=5, r8c3=7, r8c1=1, r9c4=5

Code: Select all: +-------------------+-------------------+-------------------+ ! 367 5 8 ! 12367 4 12367 ! 9 137 13 ! ! 347 1 2 ! 378 9 378 ! 578 6 345 ! ! 9 67 34 ! 13678 5 13678 ! 178 13478 2 ! +-------------------+-------------------+-------------------+ ! 3467 678 34 ! 9 18 24 ! 12567 1237 1356 ! ! 5 2 1 ! 67 3 67 ! 4 9 8 ! ! 3467 678 9 ! 24 18 5 ! 1267 1237 136 ! +-------------------+-------------------+-------------------+ ! 8 3 5 ! 14 6 9 ! 12 124 7 ! ! 1 9 7 ! 348 2 348 ! 68 5 46 ! ! 2 4 6 ! 5 7 18 ! 3 18 9 ! +-------------------+-------------------+-------------------+

z-chain[4]: b9n4{r7c8 r8c9} - c6n4{r8 r4} - c3n4{r4 r3} - c8n4{r3 .} ==> r7c8≠2, r8c9≠4, r7c8≠1, r7c4≠4, r3c8≠4
with z-candidates = n4r7c8
singles ==> r7c4=1, r7c7=2, r9c6=8, r9c8=1, r7c8=4, r8c9=6, r8c7=8, r3c8=8, r2c4=8, r2c9=4, r3c3=4, r4c3=3, r2c7=5, r4c9=5
whip[1]: r3n3{c6 .} ==> r1c4≠3, r1c6≠3, r2c6≠3
singles ==> r2c6=7, r2c1=3, r5c6=6, r5c4=7

Code: Select all: +-------------+-------------+-------------+ ! 67 5 8 ! 26 4 12 ! 9 37 13 ! ! 3 1 2 ! 8 9 7 ! 5 6 4 ! ! 9 67 4 ! 36 5 13 ! 17 8 2 ! +-------------+-------------+-------------+ ! 467 678 3 ! 9 18 24 ! 167 27 5 ! ! 5 2 1 ! 7 3 6 ! 4 9 8 ! ! 467 678 9 ! 24 18 5 ! 167 237 13 ! +-------------+-------------+-------------+ ! 8 3 5 ! 1 6 9 ! 2 4 7 ! ! 1 9 7 ! 34 2 34 ! 8 5 6 ! ! 2 4 6 ! 5 7 8 ! 3 1 9 ! +-------------+-------------+-------------+

biv-chain[4]: r1c4{n6 n2} - b5n2{r6c4 r4c6} - r4c8{n2 n7} - r1n7{c8 c1} ==> r1c1≠6
stte

Very close to Defise's or Cenoman's solution.

by **jco** » Tue Jan 04, 2022 2:31 pm

After basics

Code: Select all: .------------------------------------------------------------. | 2367 3567 8 | 12367 4 12367 | 9 137 135 | | 2347 1 c25 | 2378 9 2378 | b578 6 345 | | 9 3467 347 | 13678 5 13678 |bw(1)78 13478 2 | |------------------+------------------+----------------------| | 3467 34678 347 | 9 18 24 | 12567 1237 1356 | | 5 2 1 | 67 3 67 | 4 9 8 | | 3467 34678 9 | 24 18 5 | 1267 1237 136 | |------------------+------------------+----------------------| | 8 345 5-2 | 1345 6 9 |BWv12 B124 7 | | 1347 9 347 | 1348 2 1348 |bw(1)68 5 aAV146 | | 124 45 6 | 1458 7 148 | 3 1248 9 | '------------------------------------------------------------'

1. Almost Kraken (2=1)r7c7 - (1)r38c7* = Kraken Cell (146)r8c9 => -2 r7c3 [9 placements]
Kraken Cell (146)r8c7
(1)r8c9 - (1=2)r7c7
(4)r8c9 - (4=12)r7c78
(6)r8c9 - (6*=785)r238c7 - (5=2)r2c3
--

Code: Select all: .-------------------------------------------------------. | 367 5 8 | 12367 4 12367 | 9 137 13 | | 347 1 2 | 378 9 378 | 578 6 345 | | 9 67 c34 | 13678 5 13678 | 178 b13478 2 | |---------------+------------------+--------------------| | 3467 678 d34 | 9 18 e24 | 12567 1237 1356 | | 5 2 1 | 67 3 67 | 4 9 8 | | 3467 678 9 | 24 18 5 | 1267 1237 136 | |---------------+------------------+--------------------| | 8 3 5 | 1-4 6 9 | 12 a124 7 | | 1 9 7 | 348 2 f348 | 68 5 6-4 | | 2 4 6 | 5 7 18 | 3 18 9 | '-------------------------------------------------------'

2. (4)r7c8 = r3c8 - r3c3 = r4c3 - r4c6 = (4)r8c4 => -4r7c4, -4 r8c9 [18 placements, 1 LC]
--

Code: Select all: .-----------------------------------------. | 67 5 8 | 26 4 a12 | 9 a37 a13 | | 3 1 2 | 8 9 7 | 5 6 4 | | 9 67 4 | 36 5 13 | 17 8 2 | |-------------+------------+--------------| | 467 678 3 | 9 18 4-2| 167 b27 5 | | 5 2 1 | 7 3 6 | 4 9 8 | | 467 678 9 | 24 18 5 | 167 237 13 | |-------------+------------+--------------| | 8 3 5 | 1 6 9 | 2 4 7 | | 1 9 7 | 34 2 34 | 8 5 6 | | 2 4 6 | 5 7 8 | 3 1 9 | '-----------------------------------------'

3. (2=137)r1c698 - (7=2)r4c8 => -2 r4c6;ste

Website · by **denis_berthier** » Tue Jan 04, 2022 3:46 pm

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Thanks for all the solutions.

Considering the 1st eliminations in the answers (except eleven's, which follows a different path), it may be interesting to note that there are only 2 (n2r9c8 and n5r2c3) erasable by a whip[6]. They lead to the same state after Singles and whips[1]. In the fewer steps approach, both candidates have the same score (54).

After that, the second elimination can be the z-chain[4] I've given or a finned swordfish (both with the same score (73). Again, both lead to the same resolution state after Singles and whips[1].
(There are many possibilities for the third and last step).

The New Sudoku Players' Forum

Almost symmetric 7.8

Almost symmetric 7.8

Re: Almost symmetric 7.8

Re: Almost symmetric 7.8

Re: Almost symmetric 7.8

Re: Almost symmetric 7.8

Re: Almost symmetric 7.8

Re: Almost symmetric 7.8