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 Post subject: Ix Killer 2
PostPosted: Mon Apr 06, 2015 12:20 am 
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Addict
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Joined: Sat Mar 28, 2015 8:36 pm
Posts: 24
I named this puzzle for the cage pattern, as you can see a square clearly outlined. I think this is of a more moderate difficulty than the previous puzzle, again feedback is appreciated.

EDIT: As Andrew has noted below 11(2)n5 is a disconnected cage. I am not sure how to indicate this, so I will leave it as is for now and just let you all know that it is there.
ImageImage
SS Score: 1.45

Code: paste into solver:
3x3::k:3588:3588:3350:3350:0000:2839:2839:4360:4360:3588:3845:3845:4878:4878:4878:2057:2057:4360:1810:3845:2567:2567:4878:4874:4874:2057:2581:1810:5900:2567:3857:3857:2842:4874:4877:2581:0000:5900:5900:3857:0000:3600:4877:4877:0000:4115:5900:5643:2842:3600:3600:4611:4877:1812:4115:3590:5643:5643:5647:4611:4611:3841:1812:3842:3590:3590:5647:5647:5647:3841:3841:4096:3842:3842:792:792:0000:2329:2329:4096:4096:

Solution:
178542936
694731258
523689417
251498673
386257194
749316825
915863742
467925381
832174569


I will most likely start putting my puzzles in a series, something like "Ix Killer 1". Any naming suggestions?

(Moderator Note). This puzzle was originally posted as Square. It will be included in archive part L as Ix Killer 2 (Square).


Last edited by ixsetf on Mon Apr 06, 2015 4:21 am, edited 1 time in total.

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 Post subject: Re: Square
PostPosted: Mon Apr 06, 2015 3:02 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks ixsetf for posting your next killer.

Note that there is a 11(2) cage R4C6 + R6C4.

You wrote:
I will most likely start putting my puzzles in a series, something like "Ix Killer 1".
That's a good title for a series. We've had a series Pinata Killer n posted by Pinata, and HATMAN has his series Human Solvable n.

May I suggest that you change the title of A First Attempt to A First Attempt (aka Ix Killer 1) and the title of this puzzle to Square (aka Ix Killer 2).

Please feel free to post some of your puzzles as Assassins, when they are at the appropriate level which we've discussed by PM. I haven't yet started this puzzle but, from the SS score, it's in the right range.


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 Post subject:
PostPosted: Mon Apr 06, 2015 7:23 am 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Here is the PS-Code which even works for SumoCue.
SumoCue PS-Code:
3x3::k:3584:3584:3330:3330:4:2821:2821:4359:4359:3584:3850:3850:4876:4876:4876:2063:2063:4359:1810:3850:2580:2580:4876:4887:4887:2063:2586:1810:5916:2580:3870:3870:2848:4887:4898:2586:36:5916:5916:3870:40:3625:4898:4898:44:4141:5916:5679:2848:3625:3625:4659:4898:1845:4141:3639:5679:5679:5690:4659:4659:3901:1845:3903:3639:3639:5690:5690:5690:3901:3901:4167:3903:3903:842:842:76:2381:2381:4167:4167:


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 Post subject: Re: Ix Killer 2
PostPosted: Tue Apr 07, 2015 4:18 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks ixsetf for your next killer. I found it difficult to get started but once I'd found a way in it was an interesting puzzle.

Here is my walkthrough for Ix Killer 2 (Square):
Prelims

a) R1C34 = {49/58/67}, no 1,2,3
b) R1C67 = {29/38/47/56}, no 1
c) R34C1 = {16/25/34}, no 7,8,9
d) R34C9 = {19/28/37/46}, no 5
e) R4C6 + R6C4 = {29/38/47/56}, no 1
f) R67C1 = {79}
g) R67C9 = {16/25/34}, no 7,8,9
h) R9C34 = {12}
i) R9C67 = {18/27/36/45}, no 5
j) 8(3) cage at R2C7 = {125/134}
k) 10(3) cage at R3C3 = {127/136/145/235}, no 8,9
l) 19(3) cage at R3C7 = {289/379/469/478/568}, no 1
m) 22(3) cage at R6C3 = {589/679}

Steps resulting directly and indirectly from Prelims
1a. Naked pair {79} in R67C1, locked for C1
1b. Naked pair {12} in R9C34, locked for R9, clean-up: no 7,8 in R9C67
1c. 8(3) cage at R2C7 = {125/134}, 1 locked for N3, clean-up: no 9 in R4C9

2. 45 rule on N5 1 innie R5C5 = 5, clean-up: no 6 in R4C6 + R6C4

3. Caged X-Wing for 9 in R67C1 and 22(3) cage at R6C3, no other 9 in R67, clean-up: no 2 in R4C6
3a. 18(3) cage at R6C7 = {378/468/567}, no 1,2
3b. 10(3) cage at R3C3 = {127/136/145/235}
3c. 7 of {127} must be in R34C3 (R34C3 cannot be {12} which clashes with R9C3), no 7 in R3C4

4. 45 rule on N3 3 innies R1C7 + R3C79 = 20 = {389/479/569/578}, no 2, clean-up: no 9 in R1C6, no 8 in R4C9

5. 45 rule on N7 3 innies R7C13 + R9C3 = 16 = {169/178/259} (cannot be {268} because R7C1 only contains 7,9)
5a. R7C1 = 7,9 -> no 7,9 in R7C3
5b. 22(3) cage at R6C3 = {589/679}
5c. 6 of {679} must be in R7C3 -> no 6 in R6C3 + R7C4

6. 45 rule on R1 2 outies R2C19 = 1 innie R1C5 + 10
6a. Min R2C19 = 11, no 1 in R2C1, no 2 in R2C9
6b. Max R2C19 = 17 -> max R1C5 = 7

7. 45 rule on R9 1 innie R9C5 = 2 outies R8C19 + 2
7a. Max R8C19 = 7, no 7,8,9 in R8C19
7b. Min R8C19 = 3 -> no 3,4 in R9C5

8. 45 rule on C89 3 outies R258C7 = 1 innie R5C9 + 2
8a. Max R258C7 = 11, no 9 in R58C7
8b. Min R258C7 = 6 -> min R5C9 = 4

9. 45 rule on N7 4(2+2) outies R6C13 + R79C4 = 25, max R6C13 = 17 -> min R79C4 = 8, no 5 in R7C4
9a. R67C1 and 22(3) cage both contain 9 -> R6C13 + R79C4 = [7972/7981/9592] (R6C13 cannot be [97/98] which together with R7C4 = 9 make R6C13 + R79C4 more than 25) -> no 7,8 in R6C3

10. 45 rule on N4 5 innies R456C1 + R46C3 = 22, R6C13 = [79/95/97] = 14,16 -> R4C13 + R5C1 = 6,8 = {123/125/134}, no 6,7,8, 1 locked for N4, clean-up: no 1 in R3C1

11. 45 rule on N8 5 innies R7C46 + R9C456 = 23 = {13469/13478/13568/14567/23468/23567} (cannot be {12389/12479/12569/12578} because 1,2 only in R9C4, cannot be {23459} because R7C4 + R9C5 are both at least 6)
11a. R7C46 + R9C456 only contain two of 6,7,8,9 -> no 6,7,8 in R7C4 + R9C6, clean-up: no 3 in R9C7
11b. 18(3) cage at R6C7 (step 3) = {378/468/567}
11c. R7C6 = {345} -> no 3,4,5 in R67C7

12. 45 rule on N9 3 innies R7C79 + R9C7 = 14
12a. 14(3) cage must contain at least one of 1,2,3 -> R7C9 = {123}, clean-up: no 1,2,3 in R6C9

13. R7C46 + R9C456 (step 11) = {13469/13478/13568/14567/23468/23567}
13a. R6C13 + R79C4 (step 9a) = [7972/7981] (cannot be [9592] because R7C46 + R9C456 cannot contain both of 2,9) -> R6C13 = [79], R7C1 = 9, clean-up: no 4 in R1C4, no 4 in R4C6
13b. 22(3) cage at R6C3 = {589/679}, 5,6 only in R7C3 -> R7C3 = {56}
13c. R456C1 + R46C3 = 22 (step 10), R6C13 = [79] = 16 -> R4C13 + R5C1 = 6 = {123}, locked for N4, clean-up: no 2,3 in R3C1
13d. 23(4) cage at R4C2 = {4568}, 5 locked for C2
13e. R79C4 = [72/81] -> R7C46 + R9C456 = {13478/13568/23567}, no 9, 3 locked for C6 and N8, clean-up: no 8 in R1C7, no 8 in R6C4

14. 9 in R9 only in R9C89, locked for N9
14a. 16(3) cage at R8C9 contains 9 = {169/259/349}, no 7,8

15. Hidden killer pair 7,8 in 15(3) cage at R8C1 and R9C5 for R9, 15(3) cage cannot contain both of 7,8 -> 15(3) cage must contain one of 7,8 and R9C5 = {78}
15a. Naked pair {78} in R7C4 + R9C5, locked for N8
15b. R7C46 + R9C456 (step 13e) = {13478} (only remaining combination) -> R9C4 = 1, R79C6 = {34}, locked for C6 and N8, clean-up: no 7 in R1C7, no 4 in R9C7
15c. R7C13 + R9C3 = 16 (step 5), R7C1 = 9, R9C3 = 2 -> R7C3 = 5, R7C4 = 8 (cage sum for 22(3) cage), R9C5 = 7

16. 18(3) cage at R6C7 (step 3) = {378/468} -> R6C7 = 8
16a. R8C8 = 8 (hidden single in N9)
16b. 15(3) cage at R7C8 = {168/258/348}, no 7
16c. R7C7 = 7 (hidden single in N9) -> R7C6 = 3, R9C6 = 4 -> R9C7 = 5
16d. R7C79 + R9C7 = 14 (step 12), R79C7 = [75] -> R7C9 = 2, R6C9 = 5, R7C5 = 6, clean-up: no 6 in R1C6, no 8 in R3C9
16e. 23(4) cage at R4C2 = {4568} -> R4C2 = 5, 8 locked for R5

17. R1C7 + R3C79 (step 4) = {479} (only remaining combination) R3C9 = 7, R13C7 = {49}, locked for C7 and N3 -> 8(3) cage at R2C7 = {125}, locked for N3, R4C9 = 3, R4C13 = [21], R5C1 = 3, R3C1 = 5, R4C7 = 6, clean-up: no 5,8 in R1C6
17a. Naked pair {68} in R12C9, locked for C9 and N3 -> R1C8 = 3, R9C89 = [69] , R5C9 = 4, R8C9 = 1
17b. R9C12 = [83], R8C1 = 4 (cage sum), R12C1 = [16], R1C2 = 7 (cage sum)

18. R6C2 = 4 (hidden single in N4)
18a. 1 in N5 only in 14(3) cage at R5C6 = {167} (only possible combination) -> R5C6 = 7, R6C56 = [16], R6C8 = 2, R6C4 = 3 -> R4C6 = 8

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for Ix 2 at Easy 1.5. I used a Caged X-Wing and combination analysis of overlapping hidden cages.


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 Post subject: Re: Ix Killer 2
PostPosted: Mon Apr 13, 2015 10:49 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Really nice puzzles you're putting up ixsetf! Thanks! I found this one quite hard - had to go large: some big combos and a ruudiculous "45" but hopefully easy enough to follow. Please let me know if anything is not really easy to understand. [Many thanks Andrew for some corrections including noticing some very poor punctuation from an English teacher: smiley to self :naughty: :) ]

Start to IxK2(square)
20 steps:
Preliminaries
Cage 3(2) n78 - cells ={12}
Cage 16(2) n47 - cells ={79}
Cage 7(2) n69 - cells do not use 789
Cage 7(2) n14 - cells do not use 789
Cage 13(2) n12 - cells do not use 123
Cage 9(2) n89 - cells do not use 9
Cage 10(2) n36 - cells do not use 5
Cage 11(2) n5 - cells do not use 1
Cage 11(2) n23 - cells do not use 1
Cage 8(3) n3 - cells do not use 6789
Cage 22(3) n478 - cells do not use 1234
Cage 10(3) n124 - cells do not use 89
Cage 19(3) n236 - cells do not use 1

Clean-up not done unless stated.
1. 3(2)r9c3 = {12} only: both locked for r9
1a. no 7,8 in 9(2)r9c6

2. 16(2)r6c1 = {79} only: both locked for c1

3. "45" on n5: 1 innie r5c5 = 5

4. 16(2)r6c1 and 22(3)r6c3 must both have 9 -> 9 locked for r67 (Caged X-wing)
4a. 9 in r6 only in n4: 9 locked for n4

5. 23(4)n4 = {2678/3578/4568}(no 1)
5a. must have 8: 8 locked for n4

6. "45" on n7: 4 outies r6c13+r79c4 = 25. Max. r6c13 = 16 -> min. r79c4 = 9 -> min. r7c4 = 7

7. 18(3)r6c7 = {378/468/567}(no 1,2)

8. "45" on r9: 1 innie r9c5 - 2 = 2 outies r8c19
8a. min. 2 outies = 3 -> min. r9c5 = 6
8b. max. 2 outies = 7: no 7,8,9 in r8c19

9. Hidden killer pair 1,2 in n8 -> 22(4)n8 must have 1 or 2 for n8
9a. = {1489/1579/1678/2389/2479/2569/2578} (no eliminations yet)

10. Hidden killer triple 3,4,5 in n8 since 22(3) can only have one of them
10a. 22(3) = {1489/1579/2389/2479/2569/2578}(no eliminations)
10b. r79c6 = {345}
10c. no 3 in r9c7

11. 18(3)r6c7 = {378/468/567}: can't have more than one of 3,4,5 which must go in r7c6 -> no 3,4,5 in r67c7
11a. must have 3 in r7c6 or 6 in r67c7 -> [36] blocked from 9(2)r9c6
11b. 9(2) = {45} only: both locked for r9

12. max. r67c37 = 30 since min. r7c46 = 10 and cages sum to 40
12a. max. r9c37 = 7 -> max. r679c37 = 37
12b. "45" on n8: 1 innie r9c5 + 29 = 6 outies r679c37
12c. -> max. r9c5 = 8

13. 15(3)n7 must have 3,6,8 for r9c1 = {168/258/267/348/357/456}(no 9)

14. 9 in r9 only in 16(3)n9 = {169/259/349}(no 7,8)
14a. must have one of 3,6 for r9c89 = {169/349}(no 2,5)
14b. 1 and 4 only in r9c8 -> r9c8 = (14)
14c. 9 locked for n9

15. 15(3)n7 must have two of {3678} for r9c12 = {168/267/348/357}
15a. must have 1,2,4,5 which are only in r8c1 -> no 3,6 in r8c1

16. Hidden killer pair 7,8 in r9 since r9c12 can't have both -> r9c5 = (78)

17. from step 9a, 22(4)n8 = {1489/1579/1678/2389/2479/2569/2578}
17a. but r7c4 + r9c5 = two of {789} -> {1489/1579/2389/2479/2578} all blocked
17b. = {2569} only: all locked for n8
17c. r9c3467 = [2145], r7c6 = 3 -> r67c7 = 15 = {78} only: both locked for c7
17d. deleted

18. "45" on n7: 2 remaining innies r7c13 = 14 = [95] only permutation
18a. -> r6c3 + r7c4 = 17 = [98] only
18b. r67c7 = [87]

19. 8 in r9 only in n7: 8 locked for n7

20. "45" on n9: 1 innie r7c9 = 2
Cheers
Ed


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