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by **P.O.** » Sat Oct 23, 2021 10:27 am

Code: Select all: . 9 . . 6 4 1 . . . 6 4 . . 7 . . . 3 . 8 . . . . . 7 . . . . . 6 9 . 3 . . . 3 8 . . 4 . . . 5 7 . . . . . . . 3 . . . . . 1 . 5 . 9 . . . . . 4 . . . . . 3 7 . .9..641...64..7...3.8.....7.....69.3...38..4...57.......3.....1.5.9.....4.....37.

by **marek stefanik** » Sat Oct 23, 2021 11:51 am

Three steps (with LCs in between):

Code: Select all: .-----------------.----------------.-----------------. |a57–2 9 27 | 28 6 4 | 1 3 b258 | | 125 6 4 | 128 3 7 | 258 2589 289–5| | 3 12 8 | 125 9 125 | 4 6 7 | :-----------------+----------------+-----------------: |e78–12 4 127 | 125 125 6 | 9 d58–12 3 | | 1269 12 1269 | 3 8 1259 | 7 4 c256 | | 12689 3 5 | 7 4 129 | 28 128 268 | :-----------------+----------------+-----------------: | 269 7 3 | 4 25 8 | 256 259 1 | | 126 5 126 | 9 7 3 | 268 28 4 | | 4 8 29 | 6 125 125 | 3 7 29–5 | '-----------------'----------------'-----------------'

5r1c1 = r1c9 – r5c9 = (5–8)r4c8 = (8–7)r4c1 = 7r1c1 – Loop => –5r29c9, –12r4c18, –2r1c1

Code: Select all: .----------------.---------------.----------------. | 57 9 27 | 8–2 6 4 | 1 3 258 | | 125 6 4 | 18–2 3 7 | 258 2589 289 | | 3 12 8 |#15+2 9 #15+2 | 4 6 7 | :----------------+---------------+----------------: | 78 4 127 |#15+2#15 6 | 9 58 3 | | 1269 12 1269 | 3 8 1259 | 7 4 256 | | 2689 3 5 | 7 4 29 | 28 1 268 | :----------------+---------------+----------------: | 69 7 3 | 4 2 8 | 56 59 1 | | 126 5 126 | 9 7 3 | 268 28 4 | | 4 8 29 | 6 #15 #15 | 3 7 29 | '----------------'---------------'----------------'

UL 15r3c46, 15r4c45, 15r9c56; internals 2r3c46, 2r4c4 => –2r12c4

Code: Select all: .-------------.-----------.----------------. | 57 9 d27 | 8 6 4 | 1 3 e25 | |c25 6 4 | 1 3 7 | 258 2589 289 | | 3 1 8 | 5 9 2 | 4 6 7 | :-------------+-----------+----------------: | 78 4 17 | 2 15 6 | 9 58 3 | |a16–9 2 h69–1| 3 8 15 | 7 4 56 | | 68 3 5 | 7 4 9 | 28 1 268 | :-------------+-----------+----------------: | 69 7 3 | 4 2 8 | 56 59 1 | |b126 5 126 | 9 7 3 | 268 28 4 | | 4 8 g29 | 6 15 15 | 3 7 f29 | '-------------'-----------'----------------'

1r5c1 = (1–2)r8c1 = 2r2c1 – 2r1c3 = 2r1c9 – (2=9)r9c9 – 9r9c3 = 9r5c3 => –9r5c1, –1r5c3, stte

Marek

Edit: Marked the internals in the diagram

by **shye** » Sat Oct 23, 2021 12:14 pm

i had the same first two steps as marek, but took this path to finish

first an x-wing on 2s in r19 covered by c39
=> -2r8c3, -2r26c9

leaving this

Code: Select all: .-------------.-----------.--------------. | 57 9 27 | 8 6 4 | 1 3 25 | | 25 6 4 | 1 3 7 | 58 b2589 89 | | 3 1 8 | 5 9 2 | 4 6 7 | :-------------+-----------+--------------: | 78 4 17 | 2 15 6 | 9 #58 3 | |b169 2 b169 | 3 8 15 | 7 4 56 | | 68 3 5 | 7 4 9 | 2 1 68 | :-------------+-----------+--------------: |#69 7 3 | 4 2 8 | 56 #59 1 | |b126 5 #16 | 9 7 3 |#68 2-8 4 | | 4 8 29 | 6 15 15 | 3 7 29 | '-------------'-----------'--------------'

BUG+5
||8r2c8
||5r2c8 - (5=8)r4c8
||1r5c3 - (1=68)r8c37
||6r5c1 - (6=9)r7c1 - (9=58)r47c8
||6r8c1 - (6=9)r7c1 - (9=58)r47c8
=> -8r8c8 stte

thought of the (5|8)r2c8 guardians as a naked pair with r4c8 but didnt know how to notate that nicely

by **eleven** » Sat Oct 23, 2021 3:09 pm

Code: Select all: *-------------------------------------------------------------------* | 257 9 7-2 | *28' 6 4 | 1 3 *25'8 | | 125 6 4 | 128 3 7 | 258 2589 2589 | | 3 12 8 | 125 9 125 | 4 6 7 | |----------------------+---------------------+----------------------| | 1278 4 127 | 125 125 6 | 9 1258 3 | | 1269 12 ^1269 | 3 8 1259 | 7 4 a256* | | 12689 3 5 | 7 4 129 | 28 128 268 | |----------------------+---------------------+----------------------| | 269 7 3 | 4 25 8 | 256 259 1 | | 126 5 ^126 | 9 7 3 | 26*8 28' 4 | | 4 8 *29' | 6 125 125 | 3 7 a2'59 | *-------------------------------------------------------------------*

2 in r1c3 implies 9r9c3 and 85*r1c49 -> 2r9c9 -> *6r5c9 and 86r8c87 -> no 6 in c3 => -2r1c3, stte
(too hard for me to write as AIC)

by **Cenoman** » Sat Oct 23, 2021 9:43 pm

In one step:

Code: Select all: +----------------------+---------------------+----------------------+ | 257 9 27 | 28 6 4 | 1 3 258 | | 125 6 4 | 128 3 7 | 258 2589 2589 | | 3 12 8 | 125 9 125 | 4 6 7 | +----------------------+---------------------+----------------------+ | 1278 4 127 | 125 125 6 | 9 1258 3 | | 1269 12 1269 | 3 8 1259 | 7 4 256 | | 12689 3 5 | 7 4 129 | 28 128 268 | +----------------------+---------------------+----------------------+ | 269 7 3 | 4 25 8 | 256 259 1 | | 126 5 126 | 9 7 3 | 268 28 4 | | 4 8 29 | 6 125 125 | 3 7 259 | +----------------------+---------------------+----------------------+

Kraken cell (256)r5c9
(2)r5c9-r5c2=r3c2- (2=7)r1c3
(5)r5c9-r1c9=(5)r1c1
(6)r5c9-r6c9=r6c1-r7c1=(6-5)r7c7=r2c7-r1c9=(5)r1c1
=> -7 r1c1; ste

eleven wrote:2 in r1c3 implies 9r9c3 and 85*r1c49 -> 2r9c9 -> *6r5c9 and 86r8c87 -> no 6 in c3 => -2r1c3, stte
(too hard for me to write as AIC)

Your logic can be written into a TM 6x6

Code: Select all: 2r9c3 9r9c3 28r1c49 5r1c9 9r9c9 5r9c9 2r9c9 5r5c9 2r5c9 6r5c9 6r5c3 6r8c3 28r8c78 6r8c7 ---------------------------------------- -2r1c3

This could be written as a net (hard to write as AIC, because of the two trivalue cells).

With a change in the last row:

Code: Select all: 2r9c3 9r9c3 28r1c49 5r1c9 9r9c9 5r9c9 2r9c9 5r5c9 2r5c9 6r5c9 6r5c3 6r8c3 5r2c7 628r268c7 ---------------------------------------- -2r1c3

you get the matrix of the following kraken-AALS
(9)r9c9 - (9=2)r9c3
(25)r59c9 - (5=82)r1c49
(6)r5c9 - r5c3 = r8c3 - (6=285)r268c7 - (5=82)r1c49
----------------------------------------
=> -2 r1c3
...that can be written as an AIC:
(2=9)r9c3 = [(25)r59c9 = (6)r5c9 - r5c3 = r8c3 - (6=285)r268c7] - (5=82)r1c49 => -2 r1c3; ste

by **P.O.** » Tue Oct 26, 2021 1:39 pm

Code: Select all: after singles and intersections: 257 9 27 28 6 4 1 3 258 125 6 4 128 3 7 258 2589 2589 3 12 8 125 9 125 4 6 7 1278 4 127 125 125 6 9 1258 3 1269 12 1269 3 8 1259 7 4 256 12689 3 5 7 4 129 28 128 268 269 7 3 4 25 8 256 259 1 126 5 126 9 7 3 268 28 4 4 8 29 6 125 125 3 7 259

one step solution with two simultaneous chains:

c3n6{r5 r8} - c7n6{r8 r7} - c7n5{r7 r2} - c1n5{r2 r1} - c1n7{r1 r4} - c1n8{r4 r6} - r6n6{c1 c9} => r5c9 r6c1 <> 6
r5n5{c9 c6} - r4c3{n1n2 n7} - r3c2{n2 n1} - r5c9{n2n5 n6} => r5c9 <> 2
ste.

Cenoman wrote:In one step:
Kraken cell (256)r5c9
(2)r5c9-r5c2=r3c2- (2=7)r1c3
(5)r5c9-r1c9=(5)r1c1
(6)r5c9-r6c9=r6c1-r7c1=(6-5)r7c7=r2c7-r1c9=(5)r1c1
=> -7 r1c1; ste

krakens are powerful and interesting solving technique, i will certainly write some code to find them.

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