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 Post subject: Another Killer
PostPosted: Sat Jul 04, 2020 8:33 pm 
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I have completed another puzzle. Unlike my first puzzle, this one should be much harder.

3x3::k:2560:3329:3329:2562:0000:0000:0000:3331:3331:2560:0000:5124:2562:0000:3333:0000:0000:5894:0000:0000:5124:5124:5124:3333:1543:1543:5894:0000:2568:2568:0000:0000:0000:3081:5894:5894:0000:0000:1802:0000:0000:0000:3081:0000:0000:5387:5387:1802:0000:0000:0000:1292:1292:0000:5387:3597:3597:2318:4111:4111:4111:0000:0000:5387:0000:0000:2318:0000:2064:4111:0000:1041:3090:3090:0000:0000:0000:2064:2835:2835:1041:


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 Post subject: Re: Another Killer
PostPosted: Sun Jul 05, 2020 1:17 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 855
Location: Sydney, Australia
Hi again JBeck2862
Unfortunately, according to JSudoku, Another Killer is not a valid puzzle because it has at least 2 solutions. Jsudoku ("Solve" menu then "Check Grid Validity") from http://jcbonsai.free.fr/sudoku/JSudoku.exe or http://jcbonsai.free.fr/sudoku/JSudoku.jar

Cheers
Ed


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 Post subject: Re: Another Killer
PostPosted: Sun Jul 05, 2020 1:58 am 
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There is supposed to be a 5 in the central box. the code i pasted does not have one for some reason.


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 Post subject: Re: Another Killer
PostPosted: Sun Jul 05, 2020 6:56 pm 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 855
Location: Sydney, Australia
OK, good. Here is the corrected code
triple click code:
3x3::k:2560:3329:3329:2562:0000:0000:0000:3331:3331:2560:0000:5124:2562:0000:3333:0000:0000:5894:0000:0000:5124:5124:5124:3333:1543:1543:5894:0000:2568:2568:0000:0000:0000:3081:5894:5894:0000:0000:1802:0000:1291:0000:3081:0000:0000:5388:5388:1802:0000:0000:0000:1293:1293:0000:5388:3598:3598:2319:4112:4112:4112:0000:0000:5388:0000:0000:2319:0000:2065:4112:0000:1042:3091:3091:0000:0000:0000:2065:2836:2836:1042:
It gets a score of 8.25 and JSudoku has a terrible time so I won't be trying it. Sorry. 1.50 is more my territory.

Cheers
Ed


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 Post subject: Re: Another Killer
PostPosted: Mon Jul 06, 2020 4:06 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1724
Location: Lethbridge, Alberta, Canada
Just out of curiosity I imported Ed's code string into SudokuSolver.

This puzzle has far more open space than any I've ever attempted; I'm surprised that it has a unique solution. I won't be trying it. Most Assassins have SS scores in the 1.5 to 2.0 range.

However, if you can produce puzzles in that range, you're welcome as a new puzzle creator. I'm the opposite, I enjoying solving Killer Sudokus and some puzzles on the Other Variants forum, but I've never been tempted to try to create puzzles.


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 Post subject: Re: Another Killer
PostPosted: Sun Jul 12, 2020 9:45 am 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 635
I'm amazed that this is unique with so much open space. I've made puzzles with a lower number of cages but these were very large: sixes and sevens so little open space.

I've loaded the puzzle in JSudoku and added a few cages to bring it down to assassin level. SS gives it 1.55 but I think that that is an overstatement as JS solves it without fishes although very laboriously.

Image

JS Code:
3x3::k:2560:3329:3329:2562:29:30:2587:3331:3331:2560:1050:5124:2562:31:3333:2587:32:5894:33:1050:5124:5124:5124:3333:34:35:5894:36:2568:2568:2582:2582:3095:3081:5894:5894:37:38:1802:2584:39:3095:3081:40:3100:5388:5388:1802:2584:2069:2069:1293:1293:3100:5388:3598:3598:2319:4112:4112:4112:41:42:5388:43:44:2319:45:2065:4112:46:1042:3091:3091:47:48:49:2065:2836:2836:1042:

Solution:
267394185
814725936
539168247
728643519
341259768
956817324
695431872
172586493
483972651


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 Post subject: Re: Another Killer
PostPosted: Mon Jul 13, 2020 5:07 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 635
More White Space - 34

In order to minimize cages I started with an easy 17 givens vanilla. I then made each given into a doublet. not surprisingly a lot of solutions after playing around a bit I got to a unique solution with 34 spaces and it is assassin level, SS gives it 1.55 and JS uses 8 big fishes.

I'm sure it can be increased quite a bit but I have no idea of the maximum. I'll post this on the other site in case they have any views.

Note I believe the minimum number of cages is 14, see viewtopic.php?f=3&t=804


Image

JS Code:
3x3::k:13:2049:4098:14:2068:15:2308:2308:17:24:2049:4098:2068:25:3851:1541:26:1541:27:2579:2579:2068:3095:28:3851:1541:29:30:31:2579:3095:2310:1287:32:6166:33:3593:3593:34:35:2310:1287:36:6166:6166:3602:3602:3602:37:38:39:40:41:42:6154:6154:43:1544:1544:1544:44:45:2325:46:1548:6154:47:6147:48:49:2064:2325:50:1548:51:52:6147:6147:53:2064:2325:

Solution:
239716548
457298361
861534729
573942186
682153497
914867235
796321854
348675912
125489673


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 Post subject: Re: Another Killer
PostPosted: Sat Jul 18, 2020 1:49 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1724
Location: Lethbridge, Alberta, Canada
Interesting puzzles, about Assassin level but not suitable for regular Assassins. More White Space 34 was the easier of these two puzzles; it doesn't have any 45s but is solvable mainly because most of the cages are within a nonet.

I don't know JSudoku and very little about fishes. I used a number of forcing chains; I'd only call one of them moderate length, the rest were shorter.

Here is my walkthrough for More White Space 34:
Prelims

a) R12C2 = {17/26/35}, no 4,8,9
b) R12C3 = {79}
c) R1C78 = {18/27/36/45}, no 9
d) 15(2) cage at R2C6 = {69/78}
e) 12(2) cage at R3C5 = {39/48/57}, no 1,2,6
f) R45C5 = {18/27/36/45}, no 9
g) R45C6 = {14/23}
h) R5C12 = {59/68}
i) R89C2 = {15/24}
j) R89C8 = {17/26/35}, no 4,8,9
k) 8(3) cage at R1C5 = {125/134}
l) 6(3) cage at R2C7 = {123}
m) 10(3) cage at R3C2 = {127/136/145/235}, no 8,9
n) 24(3) cage at R4C8 = {789}
o) 24(3) cage at R7C1 = {789}
p) R7C456 = {123}
q) R789C9 = {126/135/234}
r) 24(3) cage at R8C5 = {789}

1a. Naked pair {79} in R12C3, locked for C3 and N1 -> R8C3 = 8, clean-up: no 1 in R12C2
1b. Naked pair {79} in R7C12, locked for R7 and N7
1c. Naked triple {123} in 6(3) cage at R2C7 = {123}, locked for N3, clean-up: no 6,7,8 in R1C78
1d. Naked pair {45} in R1C78, locked for R1 and N3, clean-up: no 3 in R2C2
1e. Naked triple {123} in R7C456, locked for R7 and N8
1f. 24(3) cage at R8C5 = {789}, locked for N8, 8 locked for R9
1g. 8(3) cage at R1C5 = {125/134}, 1 locked for N2
1h. 24(3) cage at R4C8 = {789}, locked for N6
1i. R5C89 = {78/79} (cannot be {89} which clashes with R5C12), 7 locked for R5 and N5, clean-up: no 2 in R4C5
1j. Killer pair 8,9 in R5C12 and R5C89, locked for R5, clean-up: no 1 in R4C5
1k. R789C9 = {126/135/234}
1l. R7C9 = {456} -> no 4,5,6 in R89C9
1m. Naked triple {123} in R289C9, locked for C9
1n. Naked triple {456} in R467C9, 6 locked for C9
1o. Killer triple 1,2,3 in R789C9 and R89C8, locked for N9
1p. 9 in N9 only in R89C7, locked for C7, clean-up: no 6 in R2C6
1q. 8 in N1 only in R123C1, locked for C1, clean-up: no 6 in R5C2
1r. Killer pair 2,5 in R12C2 and R89C2, locked for C2, clean-up: no 9 in R5C1
1s. Hidden killer triple 1,2,3 in R3C8, R6C8 and R89C8 for C8, R3C8 = {123}, R89C8 contains one of 1,2,3 -> R6C8 = {123}
1t. R146C4 = {789} (hidden triple in C4), clean-up: no 7,8,9 in R3C5
1u. Naked triple {789} in R1C349, locked for R1
1v. Killer pair 4,5 in R23C4 and R89C4, locked for C4
1w. Hidden killer pair 4,5 in R23C4 and R89C4 for C4, R23C4 contains one of 4,5 -> R89C4 must contain one of 4,5 = {46/56}, 6 locked for C4 and N8

2a. 6 in N3 only in R2C8 or in 15(2) cage at R2C6 = [96] -> no 9 in R2C8
2b. 9 in N3 only in R13C9, locked for C9

3a. R6C123 = {149/167/239/248/257/347} (cannot be {158} which clashes with R5C12, cannot be {356} which clashes with R5C1)
3b. Hidden killer triple 7,8,9 in R6C123 and R6C456 for R6, R6C123 contains one of 7,8,9 -> R6C456 must contain two of 7,8,9
3c. Killer triple 7,8,9 in R4C4 and R6C456, locked for N5, clean-up: no 1,2 in R5C5
3d. Killer pair 3,4 in R45C5 and R45C6, locked for N5
3e. Killer pair 1,2 in R45C6 and R5C4, locked for N5

4a. Consider combinations for R45C6 = {14/23}
R45C6 = {14}, locked for C6 => R8C6 = 5
or R45C6 = {23}, 3 locked for N5 => R45C5 = {45}, locked for C5 => R3C5 = 3 => 8(3) cage at R1C5 = {125}, 5 locked for C4 => R8C6 = 5 (hidden single in N8)
-> R8C6 = 5, R89C4 = {46}, 4 locked for C4, clean-up: no 1 in R9C2, no 3 in R9C8
4b. 8(3) cage at R1C5 = {125} (only remaining combination), 2,5 locked for N2, clean-up: no 7 in R4C4
4c. Killer pair 3,4 in R3C5 and R45C5, locked for C5
4d. R2C1 = 4 (hidden single in R2)
4e. R3C1 = 8 (hidden single in N1), clean-up: no 7 in R2C6
4f. Naked quad {6789} in R2C3568, locked for R2, clean-up: no 2 in R1C2
4g. Naked pair {36} in R1C26, locked for R1
4h. 3 in R2 only in R2C79, locked for N3
4i. R7C4 = 3 (hidden single in C4)
4j. 7 in N5 only in R6C456, locked for R6
4k. R6C123 (step 3a) = {149/239/248}, no 5,6
4l. Killer pair 8,9 in R5C2 and R6C123, locked for N4
4m. Consider permutations for 15(2) cage at R2C6 = [87/96]
15(2) cage = [87]
or 15(2) cage = [96] => R2C3 = 7, R2C8 = 8
-> no 8 in R2C5, no 7 in R2C8
4n. R7C7 = 8 (hidden single in C7)

5. 10(3) cage at R3C2 = {136/235} (cannot be {145} = {15}4 which clashes with R3C48, ALS block), no 4

6a. R89C8 = {17/26}/[35]
6b. Consider combinations for R789C9 = {126/135/234}
R789C9 = {126}, 6 locked for N9 => naked pair {45} in R17C8, 5 locked for C8
or R789C9 = {135/234}, 3 locked for N9
-> R89C8 = {17/26}, no 3,5
6c. Killer pair 1,2 in R3C8 and R89C8, locked for C8 -> R6C8 = 3
6d. 3 in N9 only in R789C9 = {135/234}, no 6, 3 locked for C9
6e. R17C8 = {45} (hidden pair for C8)
6f. Naked pair {45} in R7C89, locked for R7 and N9 -> R7C3 = 6
6g. 6 in C9 only in R46C9, locked for N6
6h. R2C7 = 3 (hidden single in N3)
6i. 10(3) cage at R3C2 (step 5) = {136/235} -> R3C2 = {36}, R34C3 = {13/25}
6j. Naked pair {36} in R13C2, locked for C2, 3 locked for N1
6k. 10(3) cage = [352/613] (cannot be [325] which clashes with R12C2) -> R3C3 = {15}, R4C3 = {23}

7a. R6C123 (step 4k) = {149/248}, 4 locked for R6 and N4
7b. {248} = [284], no 2 in R6C3
[Now a slightly longer forcing chain to crack the puzzle.]
7c. Consider combinations for R6C123
R6C123 = {149} => R5C12 = [68] => R4C8 = 8 (hidden single in N6), R4C4 = 9 => R3C5 = 3
or R6C123 = {248} = [284] => 4 in N7 only in R89C2 = {24}, 2 locked for C2 => R12C2 = [35]
-> R3C2 = 6, R34C3 = 4 = [13], R1C1 = 2, R12C2 = [35]
7d. R6C3 = 4 -> R6C12 = 10 = {19}, locked for R6 and N4, R5C2 = 8 -> R5C1 = 6, R5C89 = [97], R4C8 = 8
7e. R3C7 = 7 -> R2C6 = 8
7f. R4C4 = 9 -> R3C5 = 3, clean-up: no 6 in R4C5

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at 1.5 for my last forcing chain.


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 Post subject: Re: Another Killer
PostPosted: Sat Jul 18, 2020 1:57 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1724
Location: Lethbridge, Alberta, Canada
Then, having solved More White Space 34 I went back to HATMAN modification of J Beck's non-human-solvable killer. The harder of these two, even though it did have a few 45s. I was surprised at HATMAN's comment that JSudoku didn't use any fishes; I used some forcing chains, finding the right ones was the hardest part of this puzzle.

Step 9b corrected; also a few minor changes.
Here is my walkthrough:
Prelims

a) R12C1 = {19/28/37/46}, no 5
b) R1C23 = {49/58/67}, no 1,2,3
c) R12C4 = {19/28/37/46}, no 5
d) R12C7 = {19/28/37/46}, no 5
e) R1C89 = {49/58/67}, no 1,2,3
f) R23C2 = {13}
g) R23C6 = {49/58/67}, no 1,2,3
h) R4C23 = {19/28/37/46}, no 5
i) R4C45 = {19/28/37/46}, no 5
j) R45C6 = {39/48/57}, no 1,2,6
k) R45C7 = {39/48/57}, no 1,2,6
l) R56C3 = {16/25/34}, no 7,8,9
m) R56C4 = {19/28/37/46}, no 5
n) R56C9 = {39/48/57}, no 1,2,6
o) R6C56 = {17/26/35}, no 4,8,9
p) R6C78 = {14/23}
q) R7C23 = {59/68}
r) R78C4 = {18/27/36/45}, no 9
s) R89C6 = {17/26/35}, no 4,8,9
t) R89C9 = {13}
u) R9C12 = {39/48/57}, no 1,2,6
v) R9C78 = {29/38/47/56}, no 1

1a. 45 rule on N5 1 innie R5C5 = 5, clean-up: no 7 in R45C6, no 7 in R4C7, no 2 in R6C3, no 3 in R6C56, no 7 in R6C9
1b. Killer pair 1,2 in R6C56 and R6C78, locked for R6, clean-up: no 6 in R5C3, no 8,9 in R5C4
1c. R23C6 = {58/67} (cannot be {49} which clashes with R45C6), no 4,9

2a. Naked pair {13} in R23C2, locked for C2 and N1, clean-up: no 7,9 in R12C1, no 7,9 in R4C3, no 9 in R9C1
2b. Naked pair {13} in R89C9, locked for C9 and N9, clean-up: no 9 in R56C9, no 8 in R9C78

3a. Killer triple 3,4,5 in R45C7, R56C9 and R6C78, locked for N6
3b. 5 in N6 only in R45C7 = [57] or R56C9 = [75] (locking cages), 7 locked for R5 and N6, clean-up: no 3 in R6C4
[Alternatively I could have used the 45 in step 8a with 6 in N6 only in R4C89 + R5C8 so no 7 in them.]

4. 45 rule on C6 3 innies R167C6 = 12 = {129/147/246} (cannot be {138/345} which clash with R45C6, cannot be {156/237} which clash with R89C6), no 3,5,8

5. R7C23 = {59/68}, R9C12 = [39]/{48/57} -> combined cage R7C23 + R9C12 = {59}{48}/{68}[39]/{68}{57}, 8 locked for N7

6. 45 rule on N1 3 innies R2C3 + R3C13 = 18 = {279/459/567} (cannot be {468} which clashes with R1C23), no 8

7. 45 rule on N1 2 outies R3C45 = 1 innie R3C1 + 2, IOU no 2 in R3C45

[Now it gets harder.]
8a. 45 rule on N6 3 innies R4C89 + R5C8 = 16 = {169/268}
8b. Consider combinations for R4C89 + R5C8
R4C89 + R5C8 = {169} => R4C23 and R4C45 both cannot be {19} which clashes with R4C89 (ALS block)
or R4C89 + R5C8 = {268}, locked for N6, R6C78 = {14}, locked for R6, 4 locked for N6 => R56C9 = [75], R6C56 = {26}, 6 locked for R6, R56C3 = [43] => R4C23 = [91] (cannot be {28} which clashes with R4C89 + R5C8, ALS block), locked for R4
-> R4C45 = {28/37/46}, no 1,9
[Note. I could have taken the R4C89 + R5C8 = {268} path through to a contradiction but that’s not my solving style, I’ll look for an alternative method to make that elimination.]
8c. 1 in N5 only in R56C4 = [19] or R6C56 = {17} -> R56C4 = [19/28]/{46} (cannot be {37}, locking-out cages), no 3,7

9a. Consider combinations for R23C6 = {58/67}
R23C6 = {58}
or R23C6 = {67}, locked for C6 and N2 => R89C6 = {35}, 3 locked for C6 => R45C6 = {48}, R6C4 = 9 (hidden single in N5), R5C4 = 1 => R12C4 = {28}
-> 8 in R12C4 + R23C6, locked for N2
9b. Consider combinations for R78C4 = {18/27/36/45}
R78C4 = {18/27}, locked for C4 => 8 in N2 only in R23C6 = {58}
or R78C4 = {36/45} => R89C6 = {17/26} (cannot be {35} which clashes with R78C4) => 5 in C6 only in R23C6 = {58}
-> R23C6 = {58}, locked for C6 and N2, clean-up: no 2 in R12C4, no 4 in R45C6, no 3 in R89C6
[I hadn’t expected R78C4 to crack this puzzle, mostly easier from here.]
9c. Naked pair {39} in R45C6, locked for N5, 9 locked for C6, clean-up: no 7 in R4C45, no 1 in R5C4
9d. R6C56 = {17} (hidden pair in N5), locked for R6, clean-up: no 4 in R6C78
9e. Naked pair {23} in R6C78, locked for N6, 3 locked for R6, clean-up: no 9 in R45C7, no 4 in R5C3
9f. R4C89 + R5C8 = {169} (hidden triple in N6), 1 locked for C8
9g. 9 in R6 only in R6C12, locked for N4 and 21(4) cage at R6C1, clean-up: no 1 in R4C3
9h. R167C6 (step 4) = {147} (cannot be {246} because R6C6 only contains 1,7), locked for C6
9i. Naked pair {26} in R89C6, locked N8, clean-up: no 3 in R78C4
9j. Killer pair 4,8 in R56C4 and R78C4, locked for C4, clean-up: no 6 in R12C4, no 2,6 in R4C5

10a. R2C3 + R3C13 (step 6) = {279/459/567}
10b. 20(4) cage at R2C3 = {1469/2369/3467} (cannot be {1379} = {79}{13} which clashes with R3C2, cannot be {2459/2567} = {25}[94]/{25}{67} because R2C3 + R3C13 only contains one of 2,5), no 5
10c. Killer pair 1,3 in R3C2 and 20(4) cage, locked for R3
10d. Killer pair 1,3 in R12C4 and 20(4) cage, locked for N2
10e. 20(4) cage = {1469/2369/3467}, CPE no 6 in R3C1
10f. 1 in N3 only in R12C7 = {19}, 9 locked for C7 and N3, clean-up: no 4 in R1C89, no 2 in R9C8
10g. R2C8 = 3 (hidden single in N3) -> R23C2 = [13], R6C78 = [32], R12C7 = [19], R2C4 = 7 -> R1C4 = 3, R1C6 = 4, clean-up: no 9 in R1C23
10h. R1C15 = [29] (hidden pair in R1) -> R2C1 = 8, R2C5 = 2 (hidden single in N2), R23C6 = [58], clean-up: no 5 in R1C23, no 4 in R9C2
10i. Naked pair {67} in R1C23, locked for R1 and N1 -> R23C3 = [49], R3C1 = 5, R2C9 = 6, R4C89 = [19], R3C9 = 7 (cage sum), R3C78 = [24], R5C8 = 6, R45C6 = [39], R5C7 = 7 (hidden single in N6) -> R4C7 = 5, clean-up: no 6,7 in R4C2, no 3 in R5C3, no 5 in R7C2, no 7 in R9C2, no 9 in R9C8
10j. Naked pair {48} in R56C9, locked for C9 -> R1C89 = [85]

11a. 8 in N9 only in 16(4) cage at R7C5 = [31]{48}, clean-up: no 8 in R78C4
11b. R9C7 = 6 (hidden single in N9) -> R9C8 = 5, R9C4 = 9, R9C2 = 8 -> R9C1 = 4
11c. R6C4 = 8 (hidden single in C4)

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at Hard 1.5 because of the difficulty finding the right forcing chains.


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 Post subject: Re: Another Killer
PostPosted: Fri Jul 24, 2020 1:28 am 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 210
Location: California, out of London
Yes - agree with the previous comments. I tried the original puzzle and got nowhere. For the first time in years I ran JSudoku and tried to follow what it did. No joy :)

Anyway - thanks to jbeck for the original puzzle, and to HATMAN for the simpler version. After one tricky step at the beginning it all fell out quite easily for me, so I agree with HATMAN's comment in that 1.55 seems too high. Here's how I did it.
Corrections thanks to Andrew.
Another Killer WT:
1. Innies n5 -> r5c5 = 5
4(2)n1 = {13}
4(2)n9 = {13}

2. Innies n6 = r4c89 + r5c8 = +16(3) and must contain a 6 and one of (12)
-> Be from {169} or {268}
-> One of the 12(2)s in n6 must be {57}
-> Either r45c7 = [57] or r56c9 = [75]
-> 7 in n6 in r5c79

3! 5 in r4 only in r4c1 or r4c7
Given Innies n6 = +16(3) -> IOD r4 -> r4c1 + 15 = r5c678
-> Trying 12(2)r5c9 = [75] puts r4c1 = 5 puts r5c678 = +20(3) = {389}
But it also puts 23(4)r2c9 = {2489} which leaves no place for 6 in n6
-> 12(2)r4c7 = [57]

Straightforward from here

4. -> 12(2)r5c9 = {48}
-> 5(2)n6 = {23}
-> 8(2)n5 = {17}
-> (HS 3 in n5) 12(2)n5 = {39}
-> 8(2)n8 = {26}
-> 13(2)n2 - {58}

5. Also 23(4)r2c9 can only be {1679} with 1 in r4c8 and 7 in r23c9
-> r17c9 = [52]
-> r1c8 = 8

6. 11(2)n9 only from [47] or [65]
-> 10(2)n3 = {19}
-> 23(4)r2c9 = [{67}19] and r5c8 = 6
-> 12(2)n5 = [39]
Also Innies n3 = {234} with 4 in c8.

7. r36c7 = {23}
-> r789c7 = {468}
-> 16(4)r7c5 can only be [31{48}]
-> 11(2)n9 = [65]
Also -> 9(2)n8 = {45}
-> 10(2)r4c4 = [64]
-> 10(2)r5c4 = [28]

8. HS 3 in n2/c4/r1 -> 10(2)n2 = [37]
-> r39c4 = [19]
Also r23c9 = [67]
-> 13(2)n1 = {67}
-> 10(2)n1 = [28]

9. Also 4(2)n1 = [13]
-> 10(2)n3 = [19]
Also -> Uncaged cells n3 = [324]
-> 5(2)n6 = [32]

10. Also -> r2c3 = 4
-> 20(4)r2c3 = [4916]
-> r3c1 = 5
Also uncaged cells n2 = [942]

11. 4 in r9 only in r9c12
-> 12(2)n7 = [48]
-> 14(2)n7 = [95]
etc.


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