The New Sudoku Players' Forum

by **urhegyi** » Thu Aug 19, 2021 7:49 pm

Code: Select all: 3.......6.7..4..8...9..3..15..7......4..2..59..8..51..1..6....2..3.......6......7 ED=8.3/8.3/8.3

one step solution possible!

by **Leren** » Thu Aug 19, 2021 8:29 pm

Code: Select all: *----------------------------------------------------------------* | 3 1258 245-1 | 12589 15789 12789 | 24579 2479 6 | | 26 7 256-1 | 1259 4 1269 | 2359 8 35 | | 2468 258 9 | 258 5678 3 | 2457 247 1 | |---------------------+----------------------+-------------------| | 5 39-12 P126 | 7 13689 14689 | 23468 2346 348 | |P67 4 P167 | 138 2 168 | 3678 5 9 | |B2679 B239 8 |p349 6-39 5 | 1 267-34 p34 | |---------------------+----------------------+-------------------| | 1 589 457 | 6 35789 4789 | 34589 349 2 | | 24789 2589 3 | 124589 15789 124789 | 45689 1469 458 | | 2489 6 245 | 1234589 13589 12489 | 34589 1349 7 | *----------------------------------------------------------------*

Sue de Coq: Base Cells r6c12 {23679} ; Row Pincer Cells r6c49 {349} ; Box Pincer Cells r4c3 {126} r5c13 {167} => - 1 r12c3, - 12 r4c2, - 39 r6c5; - 34 r6c8; stte

Leren

by **jco** » Thu Aug 19, 2021 8:38 pm

Code: Select all: .------------------------------------------------------------------. | 3 1258 245-1| 12589 15789 12789 | 24579 2479 6 | | 26 7 256-1| 1259 4 1269 | 2359 8 35 | | 2468 258 9 | 258 5678 3 | 2457 247 1 | |--------------------+------------------------+--------------------| | 5 39-12 d126 | 7 1389-6 1489-6 |c23468 c2346 b348 | |a67 4 a167 | 138 2 18-6 |b3678 5 9 | | 2679 239 8 | 349 369 5 | 1 267-34 b34 | |--------------------+------------------------+--------------------| | 1 589 457 | 6 35789 4789 | 34589 349 2 | | 24789 2589 3 | 124589 15789 124789 | 45689 1469 458 | | 2489 6 245 | 1234589 13589 12489 | 34589 1349 7 | '------------------------------------------------------------------'

(1=67)r5c13 - (6|7=348)b6p349 - (3|4|8=26)r4c78 - (2|6=1)r4c3 - loop => -(34)r6c8, -6 b5p236, -12 r4c2, -1 r12c3; ste

Edit 1: The intended meaning for the Sudoku move: if 1 is false at r5c13, then 67 is locked there, implying that it cannot be at r5c7, thus making 348 locked at b6p349, which in turn implies that 348 cannot be at r4c78, leaving
26 locked there, and this implies that 26 is false at r4c3, so 1 must be there; but this implies that 1 cannot be
at r5c13, leaving 67 locked there ... loop.
Edit 2: improved notation based on totuan observation (thanks!) and following eleven's way of writing the loop, and included missed eliminations: -1 r12c3, -1 r4c2 (my thanks to eleven!).

Website · by **denis_berthier** » Fri Aug 20, 2021 3:51 am

.

Code: Select all: Resolution state after Singles and whips[1]: +-------------------------+-------------------------+-------------------------+ ! 3 1258 1245 ! 12589 15789 12789 ! 24579 2479 6 ! ! 26 7 1256 ! 1259 4 1269 ! 2359 8 35 ! ! 2468 258 9 ! 258 5678 3 ! 2457 247 1 ! +-------------------------+-------------------------+-------------------------+ ! 5 1239 126 ! 7 13689 14689 ! 23468 2346 348 ! ! 67 4 167 ! 138 2 168 ! 3678 5 9 ! ! 2679 239 8 ! 349 369 5 ! 1 23467 34 ! +-------------------------+-------------------------+-------------------------+ ! 1 589 457 ! 6 35789 4789 ! 34589 349 2 ! ! 24789 2589 3 ! 124589 15789 124789 ! 45689 1469 458 ! ! 2489 6 245 ! 1234589 13589 12489 ! 34589 1349 7 ! +-------------------------+-------------------------+-------------------------+

1) Simplest-first solution, in W4:
z-chain[4]: c2n3{r4 r6} - b4n9{r6c2 r6c1} - r6n7{c1 c8} - r6n2{c8 .} ==> r4c2≠2
z-chain[4]: r6n7{c1 c8} - r6n6{c8 c5} - b2n6{r3c5 r2c6} - r2c1{n6 .} ==> r6c1≠2
biv-chain[4]: r5n3{c4 c7} - b6n7{r5c7 r6c8} - r6n2{c8 c2} - b4n3{r6c2 r4c2} ==> r4c5≠3
biv-chain[4]: r6n2{c2 c8} - b6n7{r6c8 r5c7} - r5c1{n7 n6} - r2c1{n6 n2} ==> r1c2≠2, r3c2≠2
z-chain[4]: r6n7{c8 c1} - r5c1{n7 n6} - r3n6{c1 c5} - r3n7{c5 .} ==> r1c8≠7
z-chain[4]: r5c1{n6 n7} - r6n7{c1 c8} - r6n6{c8 c5} - r3n6{c5 .} ==> r2c1≠6
naked-single ==> r2c1=2
t-whip[4]: r6n7{c8 c1} - r5c1{n7 n6} - r3n6{c1 c5} - r6n6{c5 .} ==> r6c8≠2, r6c8≠3, r6c8≠4
stte

2) 1-step solutions?
Considering there exists such an elementary solution with chains of length ≤ 4, all the 1-step solutions based on chains are absurdly long.
Here is an as much, but not more absurd one based on forcing chains, applied to the trivalue candidates in r6c4

FORCING[3]-T&E(W1) applied to trivalue candidates n3r6c4, n4r6c4 and n9r6c4 :
===> 8 values decided in the three cases: n8r4c9 n1r1c2 n6r6c5 n6r2c6 n8r3c2 n7r7c3 n5r9c4 n5r3c5
===> 106 candidates eliminated in the three cases: n2r1c2 n5r1c2 n8r1c2 n1r1c3 n2r1c3 n1r1c4 n2r1c4 n5r1c4 n1r1c5 n5r1c5 n1r1c6 n2r1c6 n8r1c6 n9r1c6 n2r1c7 n7r1c7 n9r1c7 n7r1c8 n6r2c1 n1r2c3 n6r2c3 n2r2c4 n5r2c4 n1r2c6 n2r2c6 n9r2c6 n2r2c7 n5r2c7 n2r3c1 n8r3c1 n2r3c2 n5r3c2 n5r3c4 n8r3c4 n6r3c5 n7r3c5 n8r3c5 n4r3c7 n5r3c7 n1r4c2 n2r4c2 n3r4c5 n6r4c5 n8r4c5 n1r4c6 n6r4c6 n8r4c6 n4r4c7 n6r4c7 n8r4c7 n2r4c8 n3r4c8 n3r4c9 n4r4c9 n7r5c3 n1r5c4 n6r5c6 n8r5c7 n6r6c1 n3r6c5 n9r6c5 n3r6c8 n4r6c8 n6r6c8 n8r7c2 n4r7c3 n5r7c3 n5r7c5 n7r7c5 n7r7c6 n3r7c7 n4r7c8 n4r8c1 n7r8c1 n8r8c2 n2r8c4 n5r8c4 n8r8c4 n9r8c4 n1r8c5 n5r8c5 n4r8c6 n8r8c6 n9r8c6 n4r8c7 n4r8c8 n8r8c9 n2r9c1 n5r9c3 n1r9c4 n2r9c4 n3r9c4 n4r9c4 n8r9c4 n9r9c4 n5r9c5 n8r9c5 n9r9c5 n1r9c6 n4r9c6 n8r9c6 n3r9c7 n4r9c7 n5r9c7 n4r9c8 n9r9c8

Code: Select all: +----------------+----------------+----------------+ ! 3 1 45 ! 89 789 7 ! 45 249 6 ! ! 2 7 25 ! 19 4 6 ! 39 8 35 ! ! 46 8 9 ! 2 5 3 ! 27 247 1 ! +----------------+----------------+----------------+ ! 5 39 126 ! 7 19 49 ! 23 46 8 ! ! 67 4 16 ! 38 2 18 ! 367 5 9 ! ! 279 239 8 ! 349 6 5 ! 1 27 34 ! +----------------+----------------+----------------+ ! 1 59 7 ! 6 389 489 ! 4589 39 2 ! ! 289 259 3 ! 14 789 127 ! 5689 169 45 ! ! 489 6 24 ! 5 13 29 ! 89 13 7 ! +----------------+----------------+----------------+

stte

3) a 2-step solution in W4:
Without increasing the length of the necessary chains, here is a much more interesting 2-step solution in W4 (obtained with the fewer-steps algorithm, after a single try). (Indeed, this is the only 2-step solution possible in W4 with the heuristic of the algorithm.)
You can notice that these steps were already present in the simplest-first solution (which implies that the other steps were not necessary).

=====> STEP #1
z-chain[4]: r5c1{n6 n7} - r6n7{c1 c8} - r6n6{c8 c5} - r3n6{c5 .} ==> r2c1≠6
naked-single ==> r2c1=2
=====> STEP #2
whip[4]: r6n7{c8 c1} - r5c1{n7 n6} - r6n6{c1 c5} - r3n6{c5 .} ==> r6c8≠2
stte

by **totuan** » Fri Aug 20, 2021 4:18 am

jco wrote:
Code: Select all
.------------------------------------------------------------------. | 3 1258 1245 | 12589 15789 12789 | 24579 2479 6 | | 26 7 1256 | 1259 4 1269 | 2359 8 35 | | 2468 258 9 | 258 5678 3 | 2457 247 1 | |--------------------+------------------------+--------------------| | 5 139-2 d126 | 7 1389-6 1489-6 |c23468 c2346 b348 | |a67 4 a167 | 138 2 18-6 |b3678 5 9 | | 2679 239 8 | 349 369 5 | 1 267-34 b34 | |--------------------+------------------------+--------------------| | 1 589 457 | 6 35789 4789 | 34589 349 2 | | 24789 2589 3 | 124589 15789 124789 | 45689 1469 458 | | 2489 6 245 | 1234589 13589 12489 | 34589 1349 7 | '------------------------------------------------------------------'

(1=67)r5c13 - (67=348)b6p349 - (348=26)r4c78 - (2|6=1)r4c3 - loop => -(34)r6c8, -6 b5p236, -2 r4c2; ste

Maybe I'm wrong, but I don't see the loop here - can't read from right to left. If I were you I would present as below:

(6)r6c5=(67)r6c18/r5c1-(267)r5c3/r6c18=(12)r5c3/r6c2-(12=6)r4c3*-r4c78=(67)r5c7/r6c8-(38=8)r5c467 => r4c56, r5c6<>6
or
(X-wing 6’s:r25c36)=(6)r4c36-r4c78=(67)r5c17/r6c8-(267)r5c3/r6c8=(12)r5c3/r6c12-(12=6)r4c3 => r5c1<>6

totuan

by **P.O.** » Fri Aug 20, 2021 4:59 am

Code: Select all: two steps: 3 1258 1245 12589 15789 12789 24579 2479 6 26 7 1256 1259 4 1269 2359 8 35 2468 258 9 258 5678 3 2457 247 1 5 1239 e(1-26) 7 13689 14689 23468 2346 348 a-6+7 4 e(16-7) 138 2 168 b36-78 5 9 d*2×679 d*239 8 349 369 5 1 c-2346+7 34 1 589 457 6 35789 4789 34589 349 2 24789 2589 3 124589 15789 124789 45689 1469 458 2489 6 245 1234589 13589 12489 34589 1349 7 depth: 3 candidate: 6 from cell (((6 1 4) (2 6 7 9))) ((6 0) (5 1 4) (6 7)) if R5C1 is not 6 ((7 0) (5 1 4) (6 7)) it is 7 ((7 1 1) (6 8 6) (2 3 4 6 7)) R6C8 is 7 ((2 2 1 11) ((6 1 4) (2 6 7 9)) ((6 2 4) (2 3 9))) one of R6C1 or R6C2 is 2 ((6 3 2 32) ((4 3 4) (1 2 6)) ((5 3 4) (1 6 7))) a pair: one is 6 3 1258 1245 12589 15789 12789 24579 2479 6 26 7 1256 1259 4 1269 2359 8 35 b24-68 258 9 258 c5+678 3 2457 247 1 5 1239 g+1-2-6 7 13689 14689 23468 2346 348 a+6-7 4 g-1-6+7 138 2 168 36×78 5 9 f*2×79 f*239 8 349 d3-69 5 1 e-234+67 34 1 589 457 6 35789 4789 34589 349 2 24789 2589 3 124589 15789 124789 45689 1469 458 2489 6 245 1234589 13589 12489 34589 1349 7 depth: 4 candidate: 7 from cells (((5 7 6) (3 6 7 8)) ((6 1 4) (2 7 9))) ((7 0) (5 1 4) (6 7)) if R5C1 is not 7 ((6 0) (5 1 4) (6 7)) it is 6 ((6 1 1) (3 5 2) (5 6 7 8)) R3C5 is 6 ((6 2 1) (6 8 6) (2 3 4 6 7)) R6C8 is 6 ((2 3 1 11) ((6 1 4) (2 7 9)) ((6 2 4) (2 3 9))) one of R6C1 or R6C2 is 2 ((7 4 22) (5 3 4) (1 6 7)) R5C3 is 7 from a pair ste.

by **urhegyi** » Fri Aug 20, 2021 8:10 am

I found another interesting diamond:

Code: Select all: ..8..2....3..6..7.6..9....4.6.1....5..9...8..3....4.6.2....3..9.7..8..5....5..1.. ED=6.7/6.7/6.7

Website · by **denis_berthier** » Fri Aug 20, 2021 9:19 am

.
The second puzzle has a solution in 4 non-W1 steps using only Subsets and Finned-Fish:

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 14579 1459 8 ! 347 13457 2 ! 3569 139 136 ! ! 1459 3 1245 ! 48 6 158 ! 259 7 128 ! ! 6 125 1257 ! 9 1357 1578 ! 235 1238 4 ! +-------------------+-------------------+-------------------+ ! 478 6 247 ! 1 2379 789 ! 23479 2349 5 ! ! 1457 1245 9 ! 2367 2357 567 ! 8 1234 1237 ! ! 3 1258 1257 ! 278 2579 4 ! 279 6 127 ! +-------------------+-------------------+-------------------+ ! 2 1458 1456 ! 467 147 3 ! 467 48 9 ! ! 149 7 1346 ! 246 8 169 ! 2346 5 236 ! ! 489 489 346 ! 5 2479 679 ! 1 2348 23678 ! +-------------------+-------------------+-------------------+

finned-swordfish-in-columns: n8{c9 c4 c1}{r9 r2 r6} ==> r6c2≠8
singles ==> r4c1=8, r6c4=8, r2c4=4
finned-swordfish-in-columns: n7{c4 c1 c7}{r7 r1 r5} ==> r5c9≠7
finned-swordfish-in-columns: n9{c2 c8 c5}{r9 r1 r4} ==> r4c6≠9
singles ==> r4c6=7, r5c1=7, r3c3=7
whip[1]: c1n5{r2 .} ==> r1c2≠5, r2c3≠5, r3c2≠5
whip[1]: c6n9{r9 .} ==> r9c5≠9
naked-pairs-in-a-block: b1{r2c3 r3c2}{n1 n2} ==> r2c1≠1, r1c2≠1, r1c1≠1
stte

There are also solutions in 2 non-W1 steps, using only a Finned-Fish and a bivalue-chain[3], e.g.:
finned-swordfish-in-rows: n8{r7 r6 r3}{c8 c2 c4} ==> r2c4≠8
singles ==> r2c4=4, r6c4=8, r4c1=8
biv-chain[3]: r9c1{n9 n4} - b1n4{r1c1 r1c2} - c2n9{r1 r9} ==> r9c6≠9, r9c5≠9, r8c1≠9
stte

by **jco** » Fri Aug 20, 2021 12:08 pm

Hi totuan!

totuan wrote:
jco wrote:
Code: Select all
.------------------------------------------------------------------. | 3 1258 1245 | 12589 15789 12789 | 24579 2479 6 | | 26 7 1256 | 1259 4 1269 | 2359 8 35 | | 2468 258 9 | 258 5678 3 | 2457 247 1 | |--------------------+------------------------+--------------------| | 5 139-2 d126 | 7 1389-6 1489-6 |c23468 c2346 b348 | |a67 4 a167 | 138 2 18-6 |b3678 5 9 | | 2679 239 8 | 349 369 5 | 1 267-34 b34 | |--------------------+------------------------+--------------------| | 1 589 457 | 6 35789 4789 | 34589 349 2 | | 24789 2589 3 | 124589 15789 124789 | 45689 1469 458 | | 2489 6 245 | 1234589 13589 12489 | 34589 1349 7 | '------------------------------------------------------------------'

(1=67)r5c13 - (67=348)b6p349 - (348=26)r4c78 - (2|6=1)r4c3 - loop => -(34)r6c8, -6 b5p236, -2 r4c2; ste

Maybe I'm wrong, but I don't see the loop here - can't read from right to left. If I were you I would present as below:

(6)r6c5=(67)r6c18/r5c1-(267)r5c3/r6c18=(12)r5c3/r6c2-(12=6)r4c3*-r4c78=(67)r5c7/r6c8-(38=8)r5c467 => r4c56, r5c6<>6
or
(X-wing 6’s:r25c36)=(6)r4c36-r4c78=(67)r5c17/r6c8-(267)r5c3/r6c8=(12)r5c3/r6c12-(12=6)r4c3 => r5c1<>6

totuan

Thank you for this observation and for the suggested moves!
My attempt at reading the chain from right to left:

if 1 is false at r4c4, then 2 or 6 must be true there, so 2|6 is false at r4c78, i.e, 2 false and 6 false at that cell.
This implies that 348 is locked there, so 3|4|8 is false at b6p349, i.e., 3 false, 4 false and 8 false there, so
67 is locked there, so 6|7 is false at r5c13, i.e., 6 false and 7 false there so 1 must be there. This in turn implies that 1 is false at r4c4 ... loop

Let me explain the Sudoku move (loop) in words (in the way I found it):
if 1 is false at r5c13, then 67 is locked there, implying that it cannot be
at r5c7, thus making 348 locked at b6p349, which in turn implies that 348 cannot be at r4c78, leaving
26 locked there, and this implies that 26 is false at r4c3, so 1 must be there; but this implies that 1 cannot be
at r5c13, leaving 67 locked there ... loop.
@Cenoman: please help me to write this loop in a proper way if something is missing!

Edit: improved the text.
Edit 2: thank you eleven for sharing that way of writing the loop!
(also the description of it and additional eliminations that I missed).
I made corrections accordingly in my first post.

by **eleven** » Fri Aug 20, 2021 1:33 pm

My way:
(1=67)r5c13 - (6|7=348)b6p349 - (3|4|8=126)r4c378, loop

btw you missed -1r12c3, r4c2.

Reading from right to left:
if r4c378 is not 126, one of 348 must be there (in r4c78),
then there cant be a triple 348 in b6p349 and one of 67 must be there (in r4c7),
then there can't be a pair 67 in r5c13, and 1 must be there,
( then 126 can't be in r4c378 ..., loop )

by **P.O.** » Fri Aug 20, 2021 3:14 pm

Code: Select all: two steps also for the second one: 14579 1459 8 347 13457 2 3569 139 136 1459 3 1245 48 6 158 259 7 128 6 125 1257 9 1357 f157+8 235 e123-8 4 a47-8 6 247 1 2379 7×89 23479 2349 5 1457 1245 9 2367 2357 567 8 1234 1237 3 1258 1257 278 2579 4 279 6 127 2 c145-8 1456 467 147 3 467 d4+8 9 149 7 1346 246 8 169 2346 5 236 b4+89 489 346 5 2479 679 1 2348 23678 depth: 2 candidate: 8 from cell (((4 6 5) (7 8 9))) ((8 0) (4 1 4) (4 7 8)) ((8 0) (9 1 7) (4 8 9)) ((8 1 1) (7 8 9) (4 8)) ((8 2 1) (3 6 2) (1 5 7 8)) singles: ( r2c4b2 n4 r4c1b4 n8 r6c4b5 n8 ) c1+4579 b1-45+9 8 37 1357 2 3569 139 136 159 3 125 4 6 158 259 7 128 6 125 1257 9 1357 1578 235 1238 4 8 6 247 1 2379 79 23479 2349 5 1457 1245 9 2367 2357 567 8 1234 1237 3 125 1257 8 2579 4 279 6 127 2 1458 1456 67 147 3 467 48 9 14×9 7 1346 26 8 169 2346 5 236 d-4+9 a48-9 346 5 247×9 67×9 1 2348 23678 depth: 2 candidate: 9 from cells (((8 1 7) (1 4 9)) ((9 5 8) (2 4 7 9)) ((9 6 8) (6 7 9))) ((9 0) (9 2 7) (4 8 9)) ((9 0) (1 2 1) (1 4 5 9)) ((4 1 10) (1 1 1) (1 4 5 7 9)) ((9 2 9) (9 1 7) (4 9)) ste.

by **totuan** » Fri Aug 20, 2021 5:00 pm

Hi eleven & jco,
Thanks for reply, now I see the loop but a bit defferent

Code: Select all: *--------------------------------------------------------------------------------------* | 3 1258 245-1 | 12589 15789 12789 | 24579 2479 6 | | 26 7 256-1 | 1259 4 1269 | 2359 8 35 | | 2468 258 9 | 258 5678 3 | 2457 247 1 | |----------------------------+----------------------------+----------------------------| | 5 39-12 126 | 7 13689 14689 | 23468 2346 348 | | 67 4 167 | 138 2 168 | 3678 5 9 | | 279-6 239 8 | 349 369 5 | 1 27-346 34 | |----------------------------+----------------------------+----------------------------| | 1 589 457 | 6 35789 4789 | 34589 349 2 | | 24789 2589 3 | 124589 15789 124789 | 45689 1469 458 | | 2489 6 245 | 1234589 13589 12489 | 34589 1349 7 | *--------------------------------------------------------------------------------------*

(2)r4c78=(2-7)r6c8=(7)r5c7-(7=16)r5c13-(16=2)r4c3 => loop => r4c2<>2
And all weaklinks => stronglinks: (2-7)r6c8 => r6c8<>346; (7=16)r5c13-(16=2)r4c3 => r4c2,r12c3<>1, r6c1<>6

totuan

by **eleven** » Fri Aug 20, 2021 8:17 pm

Ah nice, this one needs only the 167-ALS.

@urhegyi
Please don't post two puzzles in the same thread here, that can become confusing.

In the second one i like the link 8r9c12 = 4r78c4:
49 in r9c12 both kills the 9 in the ALS 24679 b8b1489, so the other digits must be there, and the 4r9c5, so the 4 only can be in r78c4.
(The other way: if 4 is not in r78c4, either 4r9c5 or 9r9c56 -> one of r9c12 must be 8)

Maybe someone has a good idea how to notate that.

Code: Select all: *---------------------------------------------------------------------------* | 14579 1459 8 | 347 13457 2 | 3569 139 136 | | 1459 3 1245 | b48 6 158 | 259 7 128 | | 6 125 1257 | 9 1357 1578 | 235 1238 4 | |------------------------+------------------------+-------------------------| | 478 6 247 | 1 2379 789 | 23479 2349 5 | | 1457 1245 9 | 2367 2357 567 | 8 1234 1237 | | 3 d1258 1257 | c278 2579 4 | 279 6 127 | |------------------------+------------------------+-------------------------| | 2 145-8 1456 | #467 147 3 | 467 48 9 | | 149 7 1346 | #246 8 169 | 2346 5 236 | | a49+8 a49+8 346 | 5 #2479 #679 | 1 2348 23678 | *---------------------------------------------------------------------------*

8r9c12 == 4r78c4 - (4=8)r2c4 - r6c4 = 8r6c2, -8r7c2, stte

[Edit:]typo correted, tkx jco

by **jco** » Fri Aug 20, 2021 9:48 pm

Hi eleven
Nice solution!

eleven wrote:(...)
In the second one i like the link 8r9c12 = 4r78c4:
49 in r9c12 both kills the 9 in the ALS 24679 b8b3689, so the other digits must be there, and the 4r9c5, so the 4 only can be in r78c4.
(The other way: if 4 is not in r78c4, either 4r9c5 or 9r9c56 -> one of r9c12 must be 8)
Maybe someone has a good idea how to notate that.
(..)

Here is my attempt:
(8=49)r9c12-(4|9)r9c56=(91b8p26 & 4r78c4)
(for the last part, 9 has to be at r8c6,1 at r7c5, and (4)r78c4).
=> (8)r9c12=(4)r78c4
(Btw small typo in the location of your ALS: b8p1489.)

[(8=49)r9c12-(4|9)r9c56=(91b8p26 & 4r78c4)-(4=8)r2c4 etc; but the link is not made explicit when written this way]

Edit: improved my attempt (thanks to Cenoman!).

by **Cenoman** » Fri Aug 20, 2021 10:58 pm

First puzzle. (Inspired by JCO's set of cells)

Code: Select all: +------------------------+-----------------------------+------------------------+ | 3 1258 1245 | 12589 15789 12789 | 24579 2479 6 | | 26 7 1256 | 1259 4 1269 | 2359 8 35 | | 2468 258 9 | 258 5678 3 | 2457 247 1 | +------------------------+-----------------------------+------------------------+ | 5 b39-12 a126 | 7 13689 14689 | d23468 d2346 348 | | 67 4 167 | 138 2 168 | 3678 5 9 | | b279-6 b239 8 | 349 369 5 | 1 c27-346 34 | +------------------------+-----------------------------+------------------------+ | 1 589 457 | 6 35789 4789 | 34589 349 2 | | 24789 2589 3 | 124589 15789 124789 | 45689 1469 458 | | 2489 6 245 | 1234589 13589 12489 | 34589 1349 7 | +------------------------+-----------------------------+------------------------+

AHS loop: (2)r4c3 = (239-7)b4p278 = (7-2)r6c8 = (2)r4c78 loop => -12 r4c2, -346 r6c8, -6r6c1; ste

The ugly form:

Hidden Text: Show

Second puzzle:

Code: Select all: +------------------------+------------------------+-------------------------+ | 14579 1459 8 | 347 13457 2 | 3569 139 136 | | 1459 3 1245 | c48 6 158 | 259 7 128 | | 6 125 1257 | 9 1357 1578 | 235 1238 4 | +------------------------+------------------------+-------------------------+ | 478 6 247 | 1 2379 789 | 23479 2349 5 | | 1457 1245 9 | 2367 2357 567 | 8 1234 1237 | | 3 e1258 1257 | d278 2579 4 | 279 6 127 | +------------------------+------------------------+-------------------------+ | 2 145-8 1456 | b467 a147* 3 | 467 a48* 9 | | 149 7 1346 | b246 8 169 | 2346 5 236 | | a489* a489* 346 | 5 a2479* 679 | 1 2348 23678 | +------------------------+------------------------+-------------------------+

Almost ALS W-Wing:
[(8=4)r7c8 - r7c5*=*r9c5 - (4=98)r9c12] = (4)r78c4 - (4=8)r2c4 - r6c4 = (8)r6c2 => -8r7c2; ste

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