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 Post subject: Ix Killer 10
PostPosted: Tue Feb 26, 2019 9:09 pm 
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Addict
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Joined: Sat Mar 28, 2015 8:36 pm
Posts: 24
I decided to make a killer again, I hope you find it enjoyable.

ImageImage
SS Score: 1.40

Code: paste into solver:
3x3::k:3584:3584:3089:3089:5900:2574:2574:1549:1549:3584:6401:6401:6401:5900:6403:6403:6403:1549:3607:6401:2584:2565:5900:2075:3100:6403:2575:3607:6401:2565:2584:3848:3100:2075:6403:2575:2313:2313:2313:3848:3848:3848:6154:6154:6154:2836:6407:2586:2562:3848:2585:2564:6406:2832:2836:6407:2562:2586:3595:2564:2585:6406:2832:4114:6407:6407:6407:3595:6406:6406:6406:4886:4114:4114:2579:2579:3595:1813:1813:4886:4886:



Solution:
485761932
273594861
961382457
547918623
126453789
398627145
854279316
712836594
639145278


As an aside, I am currently trying to create a list of all Non-Con solution grids as a programming exercise. Hopefully, this list will be useful to someone. (if it does not already exist)


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 Post subject: Re: Ix Killer 10
PostPosted: Fri Mar 01, 2019 6:17 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Nice puzzle! Thanks heaps ixsetf! Very different feel to the ones I make. Complements mine really well.

This is how I got started. Steps 7 & 9 are the keys.

IxK10 start:
Preliminaries
Cage 14(2) n14 - cells only uses 5689
Cage 7(2) n89 - cells do not use 789
Cage 8(2) n26 - cells do not use 489
Cage 12(2) n12 - cells do not use 126
Cage 12(2) n35 - cells do not use 126
Cage 10(2) n57 - cells do not use 5
Cage 10(2) n48 - cells do not use 5
Cage 10(2) n36 - cells do not use 5
Cage 10(2) n59 - cells do not use 5
Cage 10(2) n68 - cells do not use 5
Cage 10(2) n15 - cells do not use 5
Cage 10(2) n78 - cells do not use 5
Cage 10(2) n23 - cells do not use 5
Cage 10(2) n24 - cells do not use 5
Cage 11(2) n69 - cells do not use 1
Cage 11(2) n47 - cells do not use 1
Cage 6(3) n3 - cells ={123}
Cage 23(3) n2 - cells ={689}
Cage 24(3) n6 - cells ={789}
Cage 9(3) n4 - cells do not use 789
Cage 19(3) n9 - cells do not use 1
Cage 15(5) n5 - cells ={12345}

NOTE: no clean-up done unless stated. Not much is needed for this optimised WT fortunately!
1. "45" on c1234: 1 innie r5c4 = 4
1a. on c6789: r5c6 = 3
1b. on r1234: r4c5 = 1
1c. on r6789: r6c5 = 2
1d. r5c5 = 5

2. 23(3)n2 = {689} locked for n2 and c5

3. 24(3)n6 = {789}: all locked for n6

4. 14(3)n8 = {347}: all locked for n8

5. 9(3)n4 = {126}: all locked for n4

6. 6(3)n3 = {123}: all locked for n3

7. 8(2)r3c6 = [26/53]
7a. 12(2)r3c7 = [48/57]
7b. r3c67 = {245} -> 2 in r3c34, which are both in 10(2) cages (= [28]) -> r3c67 = [54] -> r4c6 = 8; but this means 2 8's in r4
7c. no 2 in r3c34
[Andrew suggested this step as a forcing chain.
r3c67 = {245}, r3c6 = 2
or r3c67 = [54] -> r4c6 = 8, no 8 in r4c34 -> no 2 in r3c34 (10(2) cages
both ways, no 2 in r3c34]

8. 2 in r3 only in r3c26, r2c4 sees both those -> no 2 in r2c4 (Common Peer Elimination, CPE)

9. "45" on n3, 4 outies r12c7 + r4c89 - 6 = 1 innie r3c7
9a. r3c7 = (45) -> 4 outies = 10 or 11
9b. r12c6 must have 4 for n2 and r89c4 must have 2 for n6
9c. but 4 outies = {24}+{23}=11 blocked by 8(2)r3c6 = 2 in r3c6 or 3 in r4c7
9d. no other way to have 2 in r12c6 since min. r4c89 = 5 -> no 2 in r12c6

10. r3c6 = 2 (hsingle n2), r4c7 = 6
10a. no 4 in r3c9

11. r1c67 = [19], r2c6 = 4 (hsingle n2)

12. r3c7 = 4 (hsingle n3)
12a. -> outies n3 = 10; r12c6 = 5 -> r4c89 = 5 = {23} only: 3 locked for r4 and n6
12b. r1c34 = {57}: both locked for r1

13. r1c89 = {23}: both locked for r1 and r2c9 = 1

14. 12(2)r1c3 = {57}: 7 locked for r1

15. 4 in r1 only in 14(3)n1 -> no 6 in r1c12 since 14(3) can't be {446}
15a. -> r1c12 = {48}: 8 locked for r1 and n1
15b. and r2c1 = 2

cracked. One big long clean-up from there.
Cheers
Ed


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 Post subject: Re: Ix Killer 10
PostPosted: Mon Mar 04, 2019 10:12 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Welcome back ixsetf! Thanks for a nice puzzle. My walkthrough complements Ed's since our key steps were in the same area but very different.

Ed's walkthrough is, as usual, an optimised one; mine, also as usual, is how I solved it with a couple of comments of things which proved unnecessary after I spotted my step 6c.

Here is my walkthrough for Ix Killer 10:
Prelims

a) R1C34 = {39/48/57}, no 1,2,6
b) R1C67 = {19/28/37/46}, no 5
c) R34C1 = {59/68}
d) 10(2) cage at R3C3 = {19/28/37/46}, no 5
e) 10(2) cage at R3C4 = {19/28/37/46}, no 5
f) 8(2) cage at R3C6 = {17/26/35}, no 4,8,9
g) 12(2) cage at R3C7 = {39/48/57}, no 1,2,6
h) R34C9 = {19/28/37/46}, no 5
i) R67C1 = {29/38/47/56}, no 1
j) 10(2) cage at R6C3 = {19/28/37/46}, no 5
k) 10(2) cage at R6C4 = {19/28/37/46}, no 5
l) 10(2) cage at R6C6 = {19/28/37/46}, no 5
m) 10(2) cage at R6C7 = {19/28/37/46}, no 5
n) R67C9 = {29/38/47/56}, no 1
o) R9C34 = {19/28/37/46}, no 5
p) R9C67 = {16/25/34}, no 7,8,9
q) 23(3) cage at R1C5 = {689}
r) 6(3) cage at R1C8 = {123}
s) 9(3) cage at R5C1 = {126/135/234}, no 7,8,9
t) 24(3) cage at R5C7 = {789}
u) 19(3) cage at R8C9 = {289/379/469/478/568}, no 1
v) 15(5) cage at R4C5 = {12345}

Steps resulting from Prelims and Initial Placements
1a. Naked triple {689} in 23(3) cage at R1C5, locked for C5 and N2, clean-up: no 3,4 in R1C3, no 1,2,4 in R1C7, no 1,2,4 in R4C3, no 2 in R4C7
1b. Naked triple {123} in 6(3) cage at R1C8, locked for N3, clean-up: no 7 in R1C6, no 9 in R4C6, no 7,8,9 in R4C9
1c. Naked triple {789} in 24(3) cage at R5C7, locked for R5 and N6, clean-up: no 1 in R3C6, no 1,2,3 in R7C6, no 2,3,4 in R7C9
1d. 45 rule on R1234 1 innie R4C5 = 1
1e. 45 rule on R6789 1 innie R6C5 = 2
1f. 45 rule on C1234 1 innie R5C4 = 4
1g. 45 rule on C6789 1 innies R5C6 = 3 -> R5C5 = 5
1h. Naked triple {126} in 9(3) cage at R5C1, locked for N4
1i. Naked triple {347} in 14(3) cage at R7C5, locked for N8
Clean-ups: no 8 in R1C3, no 7 in R1C7, no 8 in R3C1, no 6,7,8,9 in R3C3, no 7 in R3C6, no 7,8,9 in R3C7, no 9 in R3C9, no 5 in R4C7, no 3,7 in R6C3, no 3,6 in R6C7, no 5,9 in R7C1, no 6,7,8,9 in R7C3, no 8,9 in R7C4, no 8 in R7C6, no 6,7,8,9 in R7C7, no 9 in R7C9, no 3,6,7 in R9C3, no 3,4 in R9C7

2a. R67C1 = {38/47}/[92] (cannot be [56] which clashes with R34C1), no 5,6
2b. 2 in C7 only in R789C7, locked for N9
2c. 1 in C9 only in R12C9, locked for N3
2d. 1 in C8 only in R678C8, locked for 25(5) cage at R6C8, no 1 in R8C67

3. 45 rule on R1 1 innie R1C5 = 2 outies R2C19 + 3
3a. Max R2C19 = 6 -> max R2C1 = 5

4. 45 rule on C1 2 outies R19C2 = 1 innie R5C1 + 10, min R19C2 = 11, no 1 in R19C2

5. 45 rule on C9 2 outies R19C8 = 1 innie R5C9 + 1
5a. Min R5C9 = 7 -> min R19C8 = 8 -> min R9C8 = 5

6. 45 rule on N3 5(2+3) outies R12C6 + R4C689 = 18
[The first key step.]
6a. Min R4C689 = 12 -> max R12C6 = 6, no 7 in R2C6
[I continued working on these outies until I spotted step 6c which made that work unnecessary.]
6b. 7 in N2 only in R123C4, locked for C4, clean-up: no 3 in R3C3, no 3 in R7C3
6c. Consider permutations for 12(2) cage at R3C7 = [48/57]
12(2) cage = [48] => R6C6 = 7 (hidden single in N5) => R7C7 = 3 => R4C7 = 6, R3C6 = 2
or 12(2) cage = [57] => R3C6 = 2 => R4C7 = 6
-> 8(2) cage at R3C6 = [26], clean-up: no 4 in R1C6, no 8 in R1C7, no 4 in R3C3, no 4 in R3C9, no 8 in R4C3, no 8 in R4C4, no 5 in R7C9, no 1 in R9C6, no 5 in R9C7
[Cracked. The rest is straightforward.]
[At this stage I spotted R9C67 = [52] (cannot be [61] which clashes with 10(2) cage at R6C7, but it wasn’t necessary after working through the many placements in the rest of step 6.]
6d. R1C67 = [19], clean-up: no 3 in R1C4
6e. Naked pair {57} in R1C34, locked for R1
6f. 10(2) cage at R3C3 = [19], clean-up: no 5 in R3C1, no 1 in R7C7
6g. 6 in N5 only in R6C46 –> 4 in R7C37, locked for R7, clean-up: no 7 in R6C1
6h. R2C6 = 4 (hidden single in C6)
6i. R3C7 = 4 (hidden single in N3) -> R4C6 = 8, R6C4 = 6 -> R7C3 = 4, R6C6 = 7 -> R7C7 = 3, R6C7 = 1 -> R7C6 = 9, R9C7 = 2 -> R9C6 = 5, R4C1 = 5 -> R3C1 = 9, R7C5 = 7, R8C6 = 6, clean-up: no 4,8 in R6C1, no 4 in R6C9, no 2 in R7C1, no 8 in R9C34
6j. R9C34 = [91], 10(2) cage at R6C3 = [82], R67C1 = [38], 10(2) cage at R3C4 = [37], R1C34 = [57], R46C2 = [49], R67C9 = [56], R6C8 = 4, R8C4 = 8

7. R2C1 = 2 -> R1C12 = 12 = [48], 23(3) cage at R1C5 = [698]
7a. R3C9 = 7 -> R4C9 = 3
7b. 4 in N9 only in 19(3) cage at R8C9 = {478} (only remaining combination) -> R8C9 = 4

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at Easy 1.5; I used a short forcing chain.


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