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 Post subject: Ix Killer 6 - Return
PostPosted: Sun Oct 22, 2017 7:38 pm 
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Joined: Sat Mar 28, 2015 8:36 pm
Posts: 24
Recently I was having a conversation with someone and they happened to mention that they had been trying the sudoku puzzles in the newspaper, this eventually led to talk about x-wings and then Killer Sudoku, and that happened to rekindle some motivation to make Killer Sudoku. Luckily I still seem to remember the basic ideas of how to do it, so a new puzzle has been created.

ImageImage
SS Score: 1.30

Please note that there are disconnected cages at R1C13, R1C7R3C9, R7C1R9C3, and R79C9. A V2 or V3 of this puzzle may be coming if I can confirm a nice enough solve path for them.

Code: paste into solver:
3x3::k:2330:3842:2330:3861:3598:3598:2331:4371:4371:3842:3842:3352:3861:3861:3598:3843:3843:4371:2577:3352:4108:3588:3588:3080:3080:3843:2331:2577:2836:4108:4108:4101:4101:3080:3599:3599:2577:5121:2836:2822:2076:4101:2583:2583:3599:5121:5121:5121:2076:2822:4109:3862:3862:3862:2823:3344:3344:5120:2834:4109:4109:1802:2841:1821:3614:3344:5120:5120:2834:1802:3849:3849:3614:1821:2823:5120:4107:4107:4107:3849:2841:


Solution:
178549236
624731958
593682417
259418673
386257194
741396825
915863742
467925381
832174569


As always, any feedback or suggestions are appreciated.


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 Post subject: Re: Ix Killer 6 - Return
PostPosted: Sat Nov 25, 2017 7:09 pm 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1039
Location: Sydney, Australia
Thanks ixsetf!
You remember how to make them and I still remember how to solve them! Really enjoyed it. A couple of nicely hidden tricks.

Ix Killer 6 - Return
Start:
Prelims courtesy of SudokuSolver
Cage 14(2) n7 - cells only uses 5689
Cage 14(2) n2 - cells only uses 5689
Cage 7(2) n7 - cells do not use 789
Cage 7(2) n9 - cells do not use 789
Cage 8(2) n5 - cells do not use 489
Cage 13(2) n1 - cells do not use 123
Cage 9(2) n1 - cells do not use 9
Cage 9(2) n3 - cells do not use 9
Cage 10(2) n6 - cells do not use 5
Cage 11(2) n7 - cells do not use 1
Cage 11(2) n9 - cells do not use 1
Cage 11(2) n8 - cells do not use 1
Cage 11(2) n5 - cells do not use 1
Cage 11(2) n4 - cells do not use 1
Cage 10(3) n14 - cells do not use 89

Routine cage clean-up not done unless specified
1. "45" on n2: 1 innie r3c6 = 2

2."45" on n3: 1 innie r3c7 = 4
2. r4c7 = 6 (cage sum)
2. no 5 in 9(2)n3, no 3 in r3c9, no 7 in r1c7

3. "45" on n89: 1 outie r6c6 = 6
3a. r7c67 = 10, no 4,5

4. "45" on c123: 1 outie r4c4 = 4
4a. r34c3 = 12: no 1,2,6,8

5. "45" on n1: 2 innies r3c13 = 8 = [17]/{35}: no 6,9; no 7 in r3c1
5a. no 3 in r4c3 (split 12(2)r34c3)

6. r3c13 = 8 = [17]/{35}(step 5) and split 12(2)r34c3 = [39]/{57} -> 5 locked in one of those 3 cells
6a. ->no 5 in r12c3 since they see all of them (CPE)
6b. no 8 in r3c2

7. 14(2)r3c4 = {59/68} = one of 5/6
7a. combined cages 13(2)r2c3 + h8(2)r3c13 (step 6) can't be [76]+{35} since would leave no 5/6 for step 7.
7b. -> no 6 in r3c2
7b. no 7,9 in r2c3

8. "45" on r12: 3 outies r3c289 = 17 and must have {579} for r3c2 = {179/359}(no 6,8)
8a. must use 9: 9 locked for r3
8b. 14(2)r3c4 = {68} only: both locked for n2

9. r3c289 = 17 (step 8) and must have {17} for r3c9 = {179} only, 1 locked for n3, 7 locked for r3
9a. no 3 in r1c7
9b. no 8 in r2c3
9c. no 5 in r4c3 sp12(2)

10. naked pair {35} in r3c13: both locked for n1
10a. no 4,6 in 9(2)n1

11. 15(3)r2c7 must have 1,7,9 for r3c8 = {159/168/267/357}: if has 9 must also have 1
11a. -> [791] blocked from r3c289 (step 9)
11b. r3c2 = 9, r2c3 = 4

12. hidden killer triple 7,8,9 in n7 -> 11(2) must have one of 7,8,9 (no 5,6)
12a. and 13(3) must have one of 7,8,9 -> can't have a 6 or would exceed cage total

13. hidden single 6 in c3 -> r5c3 = 6, r4c2 = 5

14. "45" on n4: 3 innies r4c13+r5c1 = 14 and must have 7/9 for r4c3 = {149/239/347}
14a. but r45c1 = [34] blocked by 10(3)r3c1 can't be [334]
14a. h14(3) = {149/239}(no 7) -> r4c3 = 9

15. 14(2)n7 = {68} only: both locked for n7

16.hidden single 9 in c1 -> r7c1 = 9, r9c3 = 2

17. 7(3)n7 = {34} only: both locked for n7

18. "45" on n9: 2 innies r79c7 = 12 = [39/75]

19. r7c67 = 10 = {37} only: both locked for r7

On from there. Much easier now but still quite a few steps to finally crack it.
Cheers
Ed


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 Post subject: Re: Ix Killer 6 - Return
PostPosted: Thu Dec 21, 2017 2:35 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Welcome back ixsetf and Ed! :) I suppose I could also welcome myself back ;) ; it's almost 6 months since my last post, on the Other Variants forum. So if my walkthrough looks like I'm out of practice, I was.

Some similarity between Ed's and my steps. Loved Ed's step 14 which is better than my step 8, but at that stage I hadn't place R5C3.

Here is my walkthrough:
There are disjoint cages R1C13, R1C7+R3C9, R7C1+R9C3 and R79C9

Prelims

a) R1C13 = {18/27/36/45}, no 9
b) R1C7+R3C9 = {18/27/36/45}, no 9
c) R2C3 + R3C2 = {49/58/67}, no 1,2,3
d) R3C45 = {59/68}
e) R4C2 + R5C3 = {29/38/47/56}, no 1
f) R5C4 + R6C5 = {29/38/47/56}, no 1
g) R5C5 + R6C4 = {17/26/35}, no 4,8,9
h) R5C78 = {19/28/37/46}, no 5
i) R7C1 + R9C3 = {29/38/47/56}, no 1
j) R7C5 + R8C6 = {29/38/47/56}, no 1
k) R7C8 + R8C7 = {16/25/34}, no 7,8,9
l) R79C9 = {29/38/47/56}, no 1
m) R8C1 + R9C2 = {17/26/35}, no 4,8,9
n) R8C2 + R9C1 = {59/68}
o) 10(3) cage at R3C1 = {127/136/145/235}, no 8,9

1a. 45 rule on N2 1 innie R3C6 = 2, clean-up: no 7 in R1C7, no 9 in R7C5
1b. 45 rule on N3 1 innie R3C7 = 4 -> R4C7 = 6 (cage sum), clean-up: no 5 in R1C7, no 9 in R2C3, no 3,5 in R3C9, no 5 in R5C3, no 4 in R5C8, no 1,3 in R7C8
1c. 45 rule on N14 1 outie R4C4 = 4, clean-up: no 7 in R5C34 + R6C5
1d. 45 rule on N5 1 remaining innie R6C6 = 6, clean-up: no 5 in R5C4 + R6C5, no 2 in R5C5 + R6C4, no 5 in R7C5
1e. 45 rule on N1 2 innies R3C13 = 8 = {17/35}
1f. 45 rule on N9 2 innies R7C79 = 12 = {39/57}
1g. R6C6 = 6 -> R7C67 = 10 = [19/37/73], clean-up: no 7 in R9C7
1h. R4C4 = 4 -> R34C3 = 12 = [39/57/75], clean-up: no 7 in R3C1
1i. R7C1 + R9C3 = {29/38/47} (cannot be {56} which clashes with R8C2 + R9C1)

2. Hidden killer triple 1,2,3 in R1C13, 15(3) cage at R1C2 and R3C13 for N1, R3C13 contains one of 1,3, 15(3) cage cannot contain more than one of 1,2,3 -> R1C13 and 15(3) cage must each contain one of 1,2,3 -> R1C13 = {18/27/36}, no 4,5
2a. Combined cages R1C13 + R3C13 = {18}{35}/{27}{35}/{36}{17}, 3 locked for N1

3. 45 rule on R6789 3 outies R5C245 = 15
3a. R5C45 cannot total 8 which clashes with R5C5 + R6C4, CCC -> no 7 in R5C2
3b. R5C45 cannot total 11 which clashes with R5C4 + R6C5, CCC -> no 4 in R5C2

4. 45 rule on R12 3 outies R3C289 = 17 = {179/368} (cannot be {359} because R3C9 only contains 1,6,7,8), no 5, clean-up: no 8 in R2C3
4a. R3C289 = {179/368}, 3 of {368} only in R3C8 -> no 6,8 in R3C8
4b. R3C89 cannot total 9 which clashes with R1C7 + R3C9, CCC -> no 8 in R3C2, clean-up: no 5 in R2C3
4c. 6 of {368} must be in R3C2 -> no 6 in R3C9, clean-up: no 3 in R1C7
4d. 9 of {179} must be in R3C2 (cannot be [791] because then no possible combination for 15(3) cage at R2C7), no 7 in R3C2, no 9 in R3C8, clean-up: no 6 in R2C3
[I can see a way to further reduce R3C289 but it’s above the SS score level, so I’ll leave it for now.]

5. 15(3) cage at R2C7 = {159/168/267/357} (cannot be {258} which clashes with R1C7 + R3C9)
5a. 6 of {168/267} must be in R2C8 -> no 2,8 in R2C8
5b. Killer pair 1,7 in R1C7 + R3C9 and 15(3) cage, locked for N3

6. 16(3) cage at R4C5 = {178/259/358}
6a. 2 of {259} must be in R4C5 -> no 9 in R4C5

[Just spotted another way to do it, which only works after I retrospectively added step 4d.]
7. R2C3 + R3C2 = [49/76], R3C13 = [17]/{35} -> combined cage R2C3 + R3C2 + R3C13 = [49]{35}/[76]{35} (cannot be [4917] which clashes with R3C289 = 9{17}, overlapping cages) -> R3C13 = {35}, locked for R3 and N1, clean-up: no 6 in R1C13, no 9 in R3C45, no 5 in R4C3 (step 1h)
7a. Naked pair {68} in R3C45, locked for R3 and N2 -> R3C2 = 9, R2C3 = 4, clean-up: no 1 in R1C7, no 7 in R4C2, no 2 in R5C3, no 7 in R7C1, no 5 in R9C1
7b. Naked pair {17} in R3C89, locked for N3
7c. 4 in N2 only in 14(3) cage at R1C5 = {149/347}, no 5
7d. 10(3) cage at R3C1 = {136/145/235} (cannot be {127} because R3C1 only contains 3,5), no 7
7e. 4,6 of {136/145} only in R5C1 -> no 1 in R5C1
7f. Killer pair 2,8 in R1C13 and R1C7, locked for R1
7g. 17(3) cage at R1C8 = {269/359/368}
7h. 2,8 of {269/368} must be in R2C9 -> no 6 in R2C9

8. R34C3 (step 1h) = [39] (cannot be [57] because cannot then place 7 in N7), clean-up: no 2,8 in R4C2 + R7C1
8a. R3C1 = 5 -> R45C1 = 5 = [14/23/32], no 6, clean-up: no 2 in R9C2
8b. 7 in N4 only in R6C123, locked for R6, clean-up: no 1 in R5C5

9. 6 in R5 only in R5C2 or R5C3 + R4C2 = [65] -> no 5 in R5C2
9a. 45 rule on R6 2 innies R6C45 = 1 outie R5C2 + 4
9b. R6C45 cannot total 6 -> no 2 in R5C2
9c. R6C45 cannot total 7 (because R5C25 cannot both be 3) -> no 3 in R5C2
9d. R5C2 = {168} -> R6C45 = 5, 10, 12 = [32/19/39], clean-up: no 3,8 in R5C4, no 3 in R5C5
9e. Naked pair {29} in R5C4 + R6C5, locked for N5
[Cracked. The rest is fairly straightforward; some clean-ups omitted in step 10.]

10. 13(3) cage at R7C2 = {148/157/238/247} (cannot be {256} which clashes with R8C2 + R9C1, cannot be {346} because 3,4 only in R7C2), no 6
10a. 3,4 on {238/247} must be in R7C2 -> no 2 in R7C2
10b. R5C3 = 6 (hidden single in C3) -> R4C2 = 5, clean-up: no 9 in R9C1
10c. R7C1 = 9 (hidden single in N7) -> R9C3 = 2, clean-up: no 7 in R1C1, no 1 in R7C6, no 3 in R9C7 (step 1f)
10d. Naked pair {68} in R8C2 + R9C1, locked for N7, clean-up: no 1 in R8C1 + R9C2
10e. Naked pair {34} in R8C1 + R9C2, locked for N7
10f. Naked pair {37} in R7C67, locked for R7 -> R7C23 = [15], R8C3 = 7, R5C2 = 8, R8C2 = 6, R9C1 = 8, R12C2 = [72] -> R2C1 = 6 (cage sum)
10g. R5C2 = 8, R6C3 = 1 -> R6C12 = 11 = [74]
10h. R6C4 = 3 -> R5C5 = 5
10i. 16(3) cage at R4C5 = {178}, 8 locked for R4
10j. R5C9 = 4 (hidden single in N6) -> R4C89 = 10 = {37}, locked for R4 and N6
10k. R5C78 = {19}, locked for R5 and N6, R5C6 = 7, R7C67 = [37] -> R9C7 = 5 (step 1f) -> R9C56 = 11 = [74], R9C2 = 3
10l. R1C1 = 1, R12C6 = [91], R4C6 = 8, R8C5 = 5 -> R7C5 = 6
10m. And after clean-ups: R79C9 = [29]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at Heavy 1.25, based on step 7 and 8; maybe it was being out of practice, but it felt harder than that to spot some steps.

No point in renaming this puzzle now, but it's at a level where it could have been posted as an Assassin. I checked my file and found that ixsetf created Assassins 318 and 321X.


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