The New Sudoku Players' Forum

by **yzfwsf** » Mon Nov 14, 2022 2:42 am

..9.6.4...7.....6.5....1..77..3.8...9...4...6......2.....8...2.....9.1...2...3..8

Code: Select all: *-----------* |..9|.6.|4..| |.7.|...|.6.| |5..|..1|..7| |---+---+---| |7..|3.8|...| |9..|.4.|..6| |...|...|2..| |---+---+---| |...|8..|.2.| |...|.9.|1..| |.2.|..3|..8| *-----------*

by **Leren** » Mon Nov 14, 2022 5:01 am

Not too hard :

Code: Select all: *---------------------------------------------* | 38 38 9 | 57 6 57 | 4 1 2 | | 2 7 1 | 49 *38 49 |*38 6 5 | | 5 6 4 | 2 *38 1 |*9-38 389 7 | |----------------+--------------+-------------| | 7 1 6 | 3 2 8 | 5 4 9 | | 9 358 2 | 1 4 57 | 378 378 6 | | 348 3458 358 | 69 57 69 | 2 378 1 | |----------------+--------------+-------------| | 1346 9 357 | 8 157 46 | 67 2 34 | | 3468 3458 3578 | 4567 9 2 | 1 57 34 | | 146 2 57 | 4567 157 3 | 679 579 8 | *---------------------------------------------*

UR Type 1 : (38) r23c57 => - 38 r5c7; some basics

Code: Select all: *-------------------------------------------* | 38 38 9 |a57 6 57 | 4 1 2 | | 2 7 1 | 49 38 49 | 38 6 5 | | 5 6 4 | 2 38 1 | 9 38 7 | |----------------+--------------+-----------| | 7 1 6 | 3 2 8 | 5 4 9 | | 9 358 2 | 1 4 57 | 38 378 6 | | 348 3458 38 | 69 57 69 | 2 378 1 | |----------------+--------------+-----------| | 1346 9 357 | 8 157 46 | 67 2 34 | | 3468 348 c378 |b467 9 2 | 1 5 34 | | 146 2 d57 | 467-5 157 3 | 67 9 8 | *-------------------------------------------*

W Wing : (5=7) r1c4 - r8c4 = r8c3 - (7=5) r9c3 => - 5 r9c4; stte

Leren

by **Cenoman** » Mon Nov 14, 2022 5:44 pm

Same start as Leren's, different finish.

Code: Select all: +-----------------------+--------------------+-------------------+ | 38 38 9 | 57 6 57 | 4 1 2 | | 2 7 1 | 49 38* 49 | 38* 6 5 | | 5 6 4 | 2 38* 1 | 38+9* 389 7 | +-----------------------+--------------------+-------------------+ | 7 1 6 | 3 2 8 | 5 4 9 | | 9 358 2 | 1 4 57 | 378 378 6 | | 348 3458 358 | 69 57 69 | 2 378 1 | +-----------------------+--------------------+-------------------+ | 1346 9 357 | 8 157 46 | 67 2 34 | | 3468 3458 3578 | 4567 9 2 | 1 57 34 | | 146 2 57 | 4567 157 3 | 679 579 8 | +-----------------------+--------------------+-------------------+

1. UR(38)r23c57 using single internal => +9 r3c8; lcls, 3 placements

Code: Select all: +----------------------+--------------------+------------------+ | 38 38 9 | 57 6 57 | 4 1 2 | | 2 7 1 | 49 38* 49 | 38* 6 5 | | 5 6 4 | 2 38* 1 | 9 38* 7 | +----------------------+--------------------+------------------+ | 7 1 6 | 3 2 8 | 5 4 9 | | 9 358 2 | 1 4 57 | 38* 38+7* 6 | | 348 3458 38 | 69 57 69 | 2 378 1 | +----------------------+--------------------+------------------+ | 1346 9 357 | 8 157 46 | 67 2 34 | | 3468 348 378 | 467 9 2 | 1 5 34 | | 146 2 57 | 4567 157 3 | 67 9 8 | +----------------------+--------------------+------------------+

2. DP(38)r23c5, b3p48, r5c78 using single internal => +7 r5c8; ste

by **shye** » Tue Nov 15, 2022 10:44 am

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

same as Cenoman, but wanted to also point out the nice 38 reverse BUG available here from the start (unfortunately, doesnt resolve the puzzle on its own)

by **jovi_al01** » Wed Nov 16, 2022 2:01 am

i know the above solutions were likely what was intended, but i could not help but look for a way to crack the puzzle in one step (at least, i would consider this "one step"). here's what i've found!
after basics:

Code: Select all: .------------------.---------------.--------------. | 38 38 9 |A57 6 B57 | 4 1 2 | | 2 7 1 | 49 38 49 | 38 6 5 | | 5 6 4 | 2 38 1 | 389 389 7 | :------------------+---------------+--------------: | 7 1 6 | 3 2 8 | 5 4 9 | | 9 358 2 | 1 4 A57 | 378 378 6 | | 348 3458 358 | 69 B57 69 | 2 378 1 | :------------------+---------------+--------------: | 1346 9 357 | 8 157 46 | 67 2 34 | | 3468 3458 3578 |*4567 9 2 | 1 *57 34 | | 146 2 #57 | 4567 157 3 | 679 579 8 | '------------------'---------------'--------------'

some digit relabeling with [57] is possible (cells in the middle stack marked with A and B).
cells of interest are marked in the bottom band.

(A)r9c3 => Ar8c8 (relabeling hidden single in r8).
||
(B)r9c3 => Br8c4 (relabeling hidden single in b8), Ar8c8 (relabeling naked single)

regardless, Ar8c8, which is then a relabeling hidden single in b4.
+5r1c4, +5r5c6, +5r8c8
stte

[minor edits made for clarity]

Website · by **denis_berthier** » Wed Nov 16, 2022 4:36 am

.

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 1238 138 9 ! 57 6 57 ! 4 1358 1235 ! ! 12348 7 1348 ! 459 358 459 ! 3589 6 12359 ! ! 5 3468 3468 ! 249 238 1 ! 389 389 7 ! +----------------------+----------------------+----------------------+ ! 7 1456 12456 ! 3 125 8 ! 59 1459 1459 ! ! 9 1358 12358 ! 1257 4 257 ! 3578 13578 6 ! ! 1348 13458 13458 ! 15679 157 5679 ! 2 134578 1345 ! +----------------------+----------------------+----------------------+ ! 1346 9 13457 ! 8 157 4567 ! 3567 2 345 ! ! 3468 3458 34578 ! 24567 9 24567 ! 1 3457 345 ! ! 146 2 1457 ! 14567 157 3 ! 5679 4579 8 ! +----------------------+----------------------+----------------------+ 225 candidates.

After more Singles, whips[1] and Pairs - eliminating more than half of the candidates (117):

Code: Select all: +----------------+----------------+----------------+ ! 38 38 9 ! 57 6 57 ! 4 1 2 ! ! 2 7 1 ! 49 38 49 ! 38 6 5 ! ! 5 6 4 ! 2 38 1 ! 389 389 7 ! +----------------+----------------+----------------+ ! 7 1 6 ! 3 2 8 ! 5 4 9 ! ! 9 358 2 ! 1 4 57 ! 378 378 6 ! ! 348 3458 358 ! 69 57 69 ! 2 378 1 ! +----------------+----------------+----------------+ ! 1346 9 357 ! 8 157 46 ! 67 2 34 ! ! 3468 3458 3578 ! 4567 9 2 ! 1 57 34 ! ! 146 2 57 ! 4567 157 3 ! 679 579 8 ! +----------------+----------------+----------------+ 108 candidates.

there are two 2-step solutions in Z4:
z-chain[4]: c8n5{r8 r9} - r9c3{n5 n7} - r7n7{c3 c5} - r6n7{c5 .} ==> r8c8≠7 with z-candidates = n7r7c7 n7r6c8
naked-single ==> r8c8=5
whip[1]: b7n5{r9c3 .} ==> r6c3≠5
biv-chain[3]: c4n5{r1 r9} - r9c3{n5 n7} - r8n7{c3 c4} ==> r1c4≠7
(OR biv-chain[3]: r9c3{n5 n7} - r8n7{c3 c4} - r1c4{n7 n5} ==> r9c4≠5)
stte

Note that using UR1 (two of them) doesn't make the solution much simper (in BC3).

Website · by **denis_berthier** » Wed Nov 16, 2022 5:39 am

jovi_al01 wrote:some digit relabeling with [57] is possible (cells in the middle stack marked with A and B)...

I hadn't coded eleven replacement for 2 digits in 2 cells but I added this to CSP-Rules [minor update on GitHub]. Here is what it gives, starting from the same resolution state as you, i.e.:

Code: Select all: +----------------+----------------+----------------+ ! 38 38 9 ! 57 6 57 ! 4 1 2 ! ! 2 7 1 ! 49 38 49 ! 38 6 5 ! ! 5 6 4 ! 2 38 1 ! 389 389 7 ! +----------------+----------------+----------------+ ! 7 1 6 ! 3 2 8 ! 5 4 9 ! ! 9 358 2 ! 1 4 57 ! 378 378 6 ! ! 348 3458 358 ! 69 57 69 ! 2 378 1 ! +----------------+----------------+----------------+ ! 1346 9 357 ! 8 157 46 ! 67 2 34 ! ! 3468 3458 3578 ! 4567 9 2 ! 1 57 34 ! ! 146 2 57 ! 4567 157 3 ! 679 579 8 ! +----------------+----------------+----------------+

Code: Select all: (solve-sukaku-grid-by-eleven-replacement2 5 7 5 6 6 5 +----------------+----------------+----------------+ ! 38 38 9 ! 57 6 57 ! 4 1 2 ! ! 2 7 1 ! 49 38 49 ! 38 6 5 ! ! 5 6 4 ! 2 38 1 ! 389 389 7 ! +----------------+----------------+----------------+ ! 7 1 6 ! 3 2 8 ! 5 4 9 ! ! 9 358 2 ! 1 4 57 ! 378 378 6 ! ! 348 3458 358 ! 69 57 69 ! 2 378 1 ! +----------------+----------------+----------------+ ! 1346 9 357 ! 8 157 46 ! 67 2 34 ! ! 3468 3458 3578 ! 4567 9 2 ! 1 57 34 ! ! 146 2 57 ! 4567 157 3 ! 679 579 8 ! +----------------+----------------+----------------+) AFTER APPLYING ELEVEN''S REPLACEMENT METHOD to 2 digits 5 and 7 in 2 cells r5c6 and r6c5, the resolution state is: +-------------------+-------------------+-------------------+ ! 38 38 9 ! 57 6 57 ! 4 1 2 ! ! 2 57 1 ! 49 38 49 ! 38 6 57 ! ! 57 6 4 ! 2 38 1 ! 389 389 57 ! +-------------------+-------------------+-------------------+ ! 57 1 6 ! 3 2 8 ! 57 4 9 ! ! 9 3578 2 ! 1 4 5 ! 3578 3578 6 ! ! 348 34578 3578 ! 69 7 69 ! 2 3578 1 ! +-------------------+-------------------+-------------------+ ! 1346 9 357 ! 8 157 46 ! 657 2 34 ! ! 3468 34578 3578 ! 4576 9 2 ! 1 57 34 ! ! 146 2 57 ! 4576 157 3 ! 6579 579 8 ! +-------------------+-------------------+-------------------+ THIS IS THE PUZZLE THAT WILL NOW BE SOLVED. RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens.

After Singles and whips[1], we have a few easy chains (possibly reducible to only one):

Code: Select all: biv-chain[3]: r4c7{n5 n7} - r7n7{c7 c3} - r9c3{n7 n5} ==> r9c7≠5 biv-chain[3]: r7c6{n6 n4} - r9n4{c4 c1} - b7n1{r9c1 r7c1} ==> r7c1≠6 biv-chain[3]: c1n6{r8 r9} - r9n4{c1 c4} - b8n7{r9c4 r8c4} ==> r8c4≠6 hidden-single-in-a-row ==> r8c1=6 biv-chain[3]: r1c2{n3 n8} - c1n8{r1 r6} - b4n4{r6c1 r6c2} ==> r6c2≠3 biv-chain[3]: r8c8{n5 n7} - b8n7{r8c4 r9c4} - r9c3{n7 n5} ==> r9c8≠5, r8c2≠5, r8c3≠5 stte

Without using the assumption of uniqueness and without replacement, the solution was in Z4, so there is some gain. Of course, replacement has own complexity cost.

P.S. I understand that what you're doing after replacement is different. For me, it was more a question of trying eleven replacement in 2 cells.

The New Sudoku Players' Forum

Hard No.2

Hard No.2

Re: Hard No.2

Re: Hard No.2

Re: Hard No.2

Re: Hard No.2

Re: Hard No.2

Re: Hard No.2