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 Post subject: Ix Killer 7
PostPosted: Tue Oct 31, 2017 4:10 am 
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Posts: 24
The reflection in a mirror isn't always perfect.

ImageImage
SS Score: 1.25

I have a V2 and V3 for this one that I will post later.

Code: paste into solver:
3x3::k:2049:2049:3861:3861:3861:3335:3335:4355:4355:2049:4882:4882:4882:3350:3350:3350:0000:4355:2063:6155:6155:788:3077:3077:0000:0000:0000:2063:4873:6155:788:6168:3077:6414:6414:6414:4873:4873:3853:6168:6168:6168:6414:2826:2826:3853:3853:3853:4614:6168:4371:1548:2826:3088:0000:0000:0000:4614:4614:4371:1548:1548:3088:3332:0000:4375:4375:4375:2833:2833:2833:5634:3332:3332:1800:1800:3840:3840:3840:5634:5634:


Solution:
435917682
192846357
678235491
289154763
741683925
563729148
917568234
356472819
824391576


As always, any feedback or suggestions are appreciated.


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 Post subject: Re: Ix Killer 7
PostPosted: Thu Dec 21, 2017 10:52 pm 
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Posts: 1893
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Thanks ixsetf for this puzzle. Much easier than Ix Killer 6.

Quote:
The reflection in a mirror isn't always perfect.
It would have been in the total for the 5-cell cage in N5 had been 25, but I expect you found out that 25 gave an unsolvable puzzle.

Here is my walkthrough:
Prelims

a) R1C67 = {49/58/67}, no 1,2,3
b) R34C1 = {17/26/35}, no 4,8,9
c) R34C4 = {12}
d) R67C6 = {89}
e) R67C9 = {39/48/57}, no 1,2,6
f) R9C34 = {16/25/34}, no 7,8,9
g) 8(3) cage at R1C1 = {125/134}
h) 19(3) cage at R2C2 = {289/379/469/478/568}, no 1
i) 24(3) cage at R3C2 = {789}
j) 19(3) cage at R4C2 = {289/379/469/478/568}, no 1
k) 11(3) cage at R5C8 = {128/137/146/236/245}, no 9
l) 6(3) cage at R6C7 = {123}
m) 11(3) cage at R8C6 = {128/137/146/236/245}, no 9
n) 22(3) cage at R8C9 = {589/679}

Steps resulting from Prelims
1a. 8(3) cage at R1C1 = {125/134}, 1 locked for N1, clean-up: no 7 in R4C1
1b. Naked triple {789} in 24(3) cage at R3C2, CPE no 7,8,9 in R12C3
1c. Naked pair {12} in R34C4, locked for C4, clean-up: no 5,6 in R9C3
1d. Naked pair {89} in R67C6, locked for C6, clean-up: no 4,5 in R1C7
1e. Naked triple {123} in 6(3) cage at R6C7, CPE no 1,2,3 in R89C7
1f. 22(3) cage at R8C9 = {589/679}, 9 locked for N9, clean-up: no 3 in R6C9

2a. 45 rule on R12 1 innie R2C8 = 5
2b. 45 rule on R89 1 innie R8C2 = 5
2c. 45 rule on R1 2 outies R2C19 = 8 = [17/26]
2d. 45 rule on R8 2 outies R8C19 = 12 = [39/48]
2e. 8(3) cage at R1C1 = {125/134}
2f. 5 of {125} must be in R1C1 -> no 2 in R1C1
2g. 22(3) cage at R8C9 = {589/679}
2h. 5 of {589} must be in R9C9 -> no 8 in R9C9
[Ed pointed out that I missed eliminating 9 from R9C9; similarly I missed eliminating 1 from R1C1. That would have simplified step 4 to a normal ALS block.]

3a. 45 rule on N4 2 innies R4C13 = 11 = [29/38] -> R34C1 = [53/62]
3b. 24(3) cage at R3C2 = {789}, 7 locked for R3 and N1
3c. 45 rule on N6 2 innies R6C79 = 9 = [18/27] -> R67C9 = [75/84]
3d. 6(3) cage at R6C7 = {123}, 3 locked for R7 and N9
3e. Hidden pair 8,9 in R2C2 + R3C23 for N1 -> R2C2 = {89}
3f. Hidden pair 1,2 in R7C78 + R8C8 for N9 -> R8C8 = {12}
3g. 19(3) cage at R2C2 = {289/379/469/478}
3h. 3 of {379} must be in R2C3 -> no 3 in R2C4
3i. 11(3) cage at R8C6 = {128/137/146/236}
3j. 7 of {137} must be in R8C7 -> no 7 in R8C6

4. R34C1 = [62] (cannot be [53] because R348C1 = [534] clashes with 8(3) cage at R1C1)
4a. R2C1 = 1 -> R2C9 = 7 (step 2c), R34C4 = [21], clean-up: no 6 in R1C6, no 5 in R7C9
4b. R2C1 = 1 -> R1C12 = 7 = [34/43/52]
4c. 5 in N1 only in R1C13, locked for R1, clean-up: no 8 in R1C7
4d. R2C9 = 7 -> R1C89 = 10 = {19/28} (cannot be {46} which clashes with R1C67), no 3,4,6
4e. R67C9 = [84], R67C6 = [98], clean-up: no 2 in R1C8 (step 4d)
4f. R8C9 = 9 -> R8C1 = 3 (step 2d), R9C89 = 13 = [76/85], clean-up: no 4 in R1C2 (step 4b), no 1 in R1C8 (step 4d), no 4 in R9C4
4g. 5 in N9 only in R9C79, locked for R9, clean-up: no 2 in R9C3
4h. R8C1 = 3 -> R9C12 = 10 = [82/91] (cannot be [46] which clashes with R9C34)
4i. 6 in N3 only in R12C7, locked for C7
4j. 4 in N7 only in R89C3, locked for C3
4k. Naked pair {23} in R1C2 + R2C3, locked for N1 -> R1C3 = 5, R1C1 = 4 -> R1C2 = 3 (cage sum), R2C3 = 2, R1C6 = 7 -> R1C7 = 6
4l. R1C3 = 5 -> R1C45 = 10 = [91], R1C89 = [82]
4m. R9C8 = 7 -> R9C9 = 6 (cage sum), R9C4 = 3 -> R9C3 = 4, R8C7 = 8
4n. R9C7 = 5 -> R9C56 = 10 = [91], R9C12 = [82]
4o. R2C3 = 2 -> R2C24 = 17 = [98], naked pair {78} in R3C23 -> R4C3 = 9 (cage sum)
4p. Naked pair {57} in R56C1, locked for C1 and N6
4q. R8C7 = 8 -> R8C68 = 3 = [21], naked pair {23} in R7C78 -> R6C7 = 1 (cage sum)
4r. Naked pair {35} in R45C9, locked for C9 and N6
4s. Naked triple {468} in R456C2, locked for C2 and N4 -> R56C3 = [13]
4t. Naked triple {246} in R456C8, locked for C8 and N6 -> R45C7 = [79]

5a. 12(3) cage at R3C5 = {345} (only remaining combination), CPE no 3,4 in R2C6
5b. 18(3) cage at R6C4 = {567} (only remaining combination), CPE no 6,7 in R8C4
5c. 45 rule on N5 2 remaining innies R4C6 + R6C4 = 11 = [47/56]
5d. 12(3) cage at R3C5 = {345}, 3 locked for R3 and N2 -> R3C78 = [49], R2C7 = 3, R3C56 = {35} -> R4C6 = 4 (cage sum), R6C4 = 7 (step 5c)
5e. Naked pair {56} in R7C45, locked for R7 and N8

6a. R4C78 + R5C7 = [769] = 22 -> R4C9 = 3 (cage sum)
6b. R5C3 + R6C13 = [153] = 9 -> R6C2 = 6 (cage sum)

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at Easy 1.25. There was only one key step in my walkthrough and that was an easy one to spot, so I won't use Ruud's term One Trick Pony for this puzzle; I think that implies one fairly well hidden key step.
Thanks Ed for pointing out my careless omission. I've added a note after step 2 of my walkthrough.

Now it's time for me to catch up on the Other Variants forum. I've still got some SSS ORC puzzles to work on and haven't yet tried Meandokus, which seem popular with azpaull and wellbeback. There's also a Human Solvable on this forum which I haven't yet tried.


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 Post subject: Re: Ix Killer 7
PostPosted: Fri Dec 22, 2017 2:12 am 
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Andrew wrote:
It would have been in the total for the 5-cell cage in N5 had been 25, but I expect you found out that 25 gave an unsolvable puzzle.


Indeed, the main idea that I had making this puzzle was that I wanted something with the mirror property (not sure if there is an official name for this) everywhere except for the central cell. I often try to give myself some constraint like this to make the puzzles more interesting.

Anyways, I was waiting for a solution to be posted before I revealed the V2 of this puzzle. I expect that you will not find this one quite so easy, although perhaps not quite as hard as some V2 assassins.

ImageImage
SS Score: 2.15

Code: paste into solver:
3x3::k:0000:0000:3844:3844:3844:0000:0000:0000:0000:0000:4872:4872:4872:3344:3344:3344:0000:0000:2060:6161:6161:774:3074:3074:0000:2570:2570:2060:4877:6161:774:6151:3074:6419:6419:6419:4877:4877:3860:6151:6151:6151:6419:2830:2830:3860:3860:3860:4609:6151:4357:1554:2830:3083:2569:2569:0000:4609:4609:4357:1554:1554:3083:0000:0000:4367:4367:4367:2819:2819:2819:0000:0000:0000:0000:0000:3840:3840:3840:0000:0000:


Solution:
435917682
192846357
678235491
289154763
741683925
563729148
917568234
356472819
824391576


As always, any feedback or suggestions are appreciated.


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 Post subject: Re: Ix Killer 7
PostPosted: Sat Dec 23, 2017 6:04 am 
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The original is another nice puzzle. As Andrew said, a lot easier than #6. I used a mirror solution. An even simpler way than Andrew's very nice solution. But it took me a long time to spot the key so didn't feel an easy puzzle. Very unusual for Andrew's step 2h to miss part of my step 5a so he wasn't able to use my breakthrough (step 7).

Not fond of monster V2's anymore so will leave that one....unless you found a nice elegant solution which I can try to find.

More V1s please!

Ix Killer 7
start:
Preliminaries courtesy of SudokuSolver
Cage 3(2) n25 - cells ={12}
Cage 17(2) n58 - cells ={89}
Cage 7(2) n78 - cells do not use 789
Cage 8(2) n14 - cells do not use 489
Cage 12(2) n69 - cells do not use 126
Cage 13(2) n23 - cells do not use 123
Cage 6(3) n69 - cells ={123}
Cage 24(3) n14 - cells ={789}
Cage 8(3) n1 - cells do not use 6789
Cage 22(3) n9 - cells do not use 1234
Cage 11(3) n89 - cells do not use 9
Cage 11(3) n6 - cells do not use 9
Cage 19(3) n4 - cells do not use 1
Cage 19(3) n12 - cells do not use 1

1. "45" on r12: 1 innie r2c8 = 5

2. "45" on r89: 1 innie r8c2 = 5

3. "45" on r1: 2 outies r2c19 = 8 = [17/26]

4. "45" on r9: 2 outies r8c19 = 12 = [39/48]

5. 22(3)r8c9 = {589/679}
5a. 5 in {589} must be in r9c9 and 9 in {679} must be in r8c9 -> no 8,9 in r9c9

6. "45" on n6: 2 innies r6c79 = 9 = [18/27]

7. 12(2)r6c9: [75] blocked by r29c9 = two of {567} (ALS block) -> r67c9 = [84] only permutation
7a. r6c7 = 1 (h9(2)r6c79)

8. r8c19 = [39](h12(2))

9. "45" on n4: 2 innies r4c13 = 11 = [29] only permutation

10. hidden single 1 in n9 -> r8c8 = 1
10a. hidden single 9 in n6 -> r5c7 = 9
10b. hidden single 1 in n4 -> r5c3 = 1
10c. r2c19 = [17](h8(2))

on from there.
Thanks Ixsetf!
Ed


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 Post subject: Re: Ix Killer 7
PostPosted: Tue Dec 26, 2017 3:49 am 
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ixsetf wrote:
The reflection in a mirror isn't always perfect.

For those not familiar with the mirror concept in sudokus, all the cages if corresponding positions about the centre have to be pairs of cages of the same size; if they are 2-cell cages their totals must add up to 20, for example the 8(2) cage at R3C1 and the 12(2) cage at R6C9, if they are 3-cell cages then they must add up to 30 as for the 8(3) cage at R1C1 and the 22(3) cage at R8C9. In this puzzle there are also 4-cell cages 25(4) at R4C7 and 15(4) at R5C3. But the 24(5) cage at R4C5 stops it being a perfect mirror puzzle; it would be one if it was a 25(5) cage but unfortunately that would have made this puzzle unsolvable.

For a detailed explanation see this post by udosuk in the Assassin 123 "Roulette" thread.

If a killer meets the perfect mirror requirements, then it provides a shortcut which gives R5C5 = 5. Also corresponding cells mirrored about the centre cell, for example R1C1 and R9C9, must total 10.


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 Post subject: Re: Ix Killer 7
PostPosted: Tue Feb 20, 2018 4:37 am 
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Thanks ixsetf for the V2. Not as hard as the SS score would suggest, but still quite a lot of work.

Here is my walkthrough for IX Killer 7 V2:
Prelims

a) R34C1 = {17/26/35}, no 4,8,9
b) R34C4 = {12}
c) R3C89 = {19/28/37/46}, no 5
d) R67C6 = {89}
e) R67C9 = {39/48/57}, no 1,2,6
f) R7C12 = {19/28/37/46}, no 5
g) 19(3) cage at R2C2 = {289/379/469/478/568}, no 1
h) 24(3) cage at R3C2 = {789}
i) 19(3) cage at R4C2 = {289/379/469/478/568}, no 1
j) 11(3) cage at R5C8 = {128/137/146/236/245}, no 9
k) 6(3) cage at R6C7 = {123}
l) 11(3) cage at R8C6 = {128/137/146/236/245}, no 9

Steps resulting from Prelims
1a. Naked triple {789} in 24(3) cage at R3C2, CPE no 7,8,9 in R12C3
1b. Naked pair {12} in R34C4, locked for C4
1c. Naked pair {89} in R67C6, locked for C6
1d. Naked triple {123} in 6(3) cage at R6C7, CPE no 1,2,3 in R89C7

2a. 45 rule on N4 2 innies R4C13 = 11 = [29/38] -> R34C1 = [53/62]
2b. 24(3) cage at R3C2 = {789}, 7 locked for R3 and N1, clean-up: no 3 in R3C89
2c. 19(3) cage at R4C2 = {469/478/568} (cannot be {289} which clashes with R4C3, cannot be {379} which clashes with R4C13), no 2,3
2d. Killer pair 8,9 in 19(3) cage and R4C3, locked for N4
2e. 45 rule on N6 2 innies R6C79 = 9 = [18/27] -> R67C9 = [75/84]
2f. 6(3) cage at R6C7 = {123}, 3 locked for R7 and N9, clean-up: no 7 in R7C12
2g. 9 in R6 only in R6C456, locked for N5
2h. 11(3) cage at R5C8 = {146/236/245} (cannot be {128} which clashes with R6C7, cannot be {137} which clashes with R6C79), no 7,8
2i. Killer pair 1,2 in 11(3) cage and R6C7, locked for N6
2j. 1 in R4 only in R4C456, locked for N5

3. 45 rule on R34567 2 innies R3C7 + R7C3 = 11 = [29/38/47/56/65/92], no 1,8 in R3C7, no 1,4 in R7C3
3a. 45 rule on N5 4 innies R46C46 = 21 cannot contain both of 1,2, R4C4 = {12} -> no 1,2 in R4C6

4. 45 rule on N4 3 outies R3C123 = 21 = {579/678}
4a. Combined cages R3C123 + R3C89 = 5{79}{28}/5{79}{46}/6{78}{19}, 9 locked for R3, clean-up: no 2 in R7C3 (step 3)
4b. 45 rule on N6 3 outies R7C789 = 9 = {135/234}
4c. Combined cages R7C12 + R7C789 = {19}{23}4/{28}{13}5/{46}{13}5, 1 locked for R7
[Taking steps 4a and 4c a bit further …]
4d. R3C123 + R3C89 (step 4a) = 5{79}{28}/5{79}{46}/6{78}{19}
R3C123 + R3C89 = 5{79}{28} => R3C4 = 1, R3C56 = {34} (cannot be {36} because 12(3) cage cannot be {36}3, cannot be {46} because no 2 in R4C6), R3C7 = 6
or R3C123 + R3C89 = 5{79}{46} => R3C5 = 8 (hidden single in R3), R34C6 = [13], R3C4 = 2, R3C7 = 3
or R3C123 + R3C89 = 6{78}{19} => R3C4 = 2, R3C567 = {345}
-> 12(3) cage at R3C5 = {345}/[813], R3C7 = {3456}, clean-up: no 9 in R7C3 (step 3)
4e. R46C46 = 21 (step 3a) = {1389/1479/1569/1578/2379/2469/2478/2568} can only contain one of 3,4,5, R4C6 = {345} -> no 3,4,5 in R6C4
4f. R7C12 + R7C789 (step 4c) = {19}{23}4/{28}{13}5/{46}{13}5
R7C12 + R7C789 = {19}{23}4 => R7C6 = 8, R7C45 = {567} (5 must be in R7C45 because no 5 in R6C4), R7C3 = {67}
or R7C12 + R7C789 = {28}{13}5 => R7C6 = 9, R7C45 = {46} (cannot be {47} because 18(3) cage cannot be 7{47}, R7C3 = 7
or R7C12 + R7C789 = {46}{13}5 => R7C5 = 2 (hidden single in R7), R67C4 = {79}, R7C3 = {78}
-> R7C3 = {678}, 18(3) cage at R6C4 = {279/468/567}, clean-up: no 6 in R3C7 (step 3)
4g. Hidden killer pair 6,9 in R3C123 and R3C89 for R3, R3C123 contains one of 6,9 -> R3C89 must contain one of 6,9 -> R3C89 = {19/46}, no 2,8
4h. R3C4 = 2 (hidden single in R3) -> R4C4 = 1
4i. R46C46 = {1389/1479/1569} (cannot be {1578} which clashes with R6C9), 9 locked for N5
4j. Consider placement for 9 in N5
R6C4 = 9 => R7C45 = 9 = [72] (cannot be {45} which clashes with R7C9)
or R6C6 = 9 => R7C6 = 8
-> R7C12 = {19/46}, no 2,8
4k. Killer pair 1,4 in R7C12 and R7C789, locked for R7
4l. 18(3) cage at R6C4 = {279/567}, no 8
4m. 2 of {279} must be in R7C5 -> no 9 in R7C5

5. R3C123 (step 4) = {579/678}, R3C89 = {19/46}
5a. Consider placements for R3C7 = {345}
R3C7 = 3 => R7C3 = 8 (step 3) => R4C3 = 9 => R3C23 = {78}
or R3C7 = 4 => R3C89 = {19} (locked for R3) => R3C23 = {78}
or R3C7 = 5, R3C1 = 6 => R3C23 = {78}
-> R3C1 = 6, R3C23 = {78}, locked for R3, N1 and 24(3) cage at R3C2, R4C1 = 2, R4C3 = 9, clean-up: no 4 in R3C89, no 4 in R7C2
5b. Naked pair {19} in R3C89, locked for R3 and N3
5c. 12(3) cage at R3C5 = {345}, CPE no 3,4,5 in R12C6
5d. R5C7 = 9 (hidden single in N6)
5e. 19(3) cage at R2C2 = {289/379/469} (cannot be {478/568} because 6,7,8 only in R4C4), no 5
5f. 6,7,8 only in R2C4 -> R2C4 = {678} -> R2C2 = 9, clean-up: no 1 in R7C1
5g. 19(3) cage at R4C2 = {478/568}
5h. 4 of {478} must be in R45C2 (R45C2 cannot be {78} which clashes with R3C2), no 4 in R5C1

6. 9 in N2 only in R1C45 -> 15(3) cage at R1C3 = {159/249}
6a. 2 of {249} must be in R1C3 -> no 4 in R1C3
6b. 8 in N2 only in R2C45, locked for R2
6c. 8 in N2 only in 19(3) cage R2C2 = [928] or 13(3) cage at R2C5 = [814] => 19(3) cage cannot be [946] (locking-out cages), no 4 in R2C3, no 6 in R2C4, also no 2 in R2C7
6d. Consider combinations for 19(3) cage at R2C2 = {289/379}
19(3) cage = [928] => 15(3) cage at R1C2 = {159}
or 19(3) cage = [937] => R2C5 = 8 (hidden single in N2) => 13(3) cage at R2C5 = [814] => R3C7 = {35}, 4 in R3 only in R3C56, locked for N2 => 15(3) cage at R1C3 = {159}
-> 15(3) cage at R1C3 = {159}, locked for R1
6e. R1C3 + R2C1 = {15} (hidden pair in N1)
6f. 4 in N1 only in R1C12, locked for R1
6g. Hidden killer triple 6,7,8 in R1C6, R2C4 and 13(3) cage at R2C5, R1C6 = {67}, R2C4 = {78} for N2 -> 13(3) cage must contains one of 6,7,8 in N2
6h. 13(3) cage can only contain one of 6,7,8 -> no 6,7 in R2C7
6i. 13(3) cage = {148/346} (cannot be {157} which clashes with R2C1), no 5,7
6j. 8 of {148} must be in R2C5, 6 of {346} must be in R2C6 -> no 1,6 in R2C5
6k. Killer pair 3,8 in 19(3) cage and 13(3) cage, locked for R2
6l. 6 in N2 only in R12C6, locked for C6

7. 18(3) cage at R6C4 (step 4l) = {279/567}, R46C46 (step 4i) = {1389/1479/1569}
7a. Consider placements for R1C4 = {59}
R1C4 = 5 => R3C56 = {34}, locked for 12(3) cage at R3C5 => R4C6 = 5, R6C4 = 6 => 18(3) cage = {567}
or R1C4 = 9 => 18(3) cage = {567}
-> 18(3) cage at R6C4 = {567}
7b. 18(3) cage = {567}, 5 locked for R7 and N8 -> R7C9 = 4, R6C9 = 8, R67C6 = [98], R7C1 = 9 -> R7C2 = 1
7c. Naked pair {23} in R7C78, locked for N9 and 6(3) cage at R6C7 -> R6C7 = 1
7d. R5C3 = 1 (hidden single in N4), 15(3) cage at R1C3 = [591], R12C6 = [76], R2C4 = 8 -> R2C3 = 2 (cage sum)
7e. 5 in N2 only in R3C56, locked for R3 and 12(3) cage at R3C5, no 5 in R4C6
7f. R3C7 + R7C3 = 11 (step 3) = [47] (only remaining combination), R2C57 = [43], R3C23 = [78], R7C78 = [23]
7g. R3C56 = {35} -> R4C6 = 4 (cage sum)
7h. Naked pair {56} in R7C45, locked for N8 and 18(4) cage at R6C4 -> R6C4 = 7
7i. Naked pair {34} in R89C4, locked for C4 and N8
7j. Naked pair {12} in R89C6, locked for C6 and N8
7k. R5C1 = 7 (hidden single in C1) -> R45C2 = 12 = [84]
7l. R6C8 = 4 (hidden single in N6) -> R5C89 = 7 = {25}, locked for R5 and N6
[When I analysed cages in R12, I hadn’t expected that they’d provide the key to unlocking R7, but I couldn’t see any direct way to solve R7.]

8. 17(3) cage at R8C3 = {467} (only remaining combination) = [647]
8a. R9C5 = 9 -> R9C67 = 6 = [15]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at Hard 1.5 for the analysis in step 4; I also used some other shorter forcing chains.

If you post your V3 I'll have a try at it, but first I've got other puzzles which I haven't yet tried including Ix Killer 8 V2 and several puzzles in the Other Variants forum.


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