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HATMAN
 Post subject: Paper Killer
PostPosted: Sat Mar 20, 2010 11:00 am 
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Paper Killer

While working on my next Human Solvable I came up with this nice one. Although SS gives it a 1.1 I feel it is much lower and expect it can be easily done on paper by most of you.

However that is not the point - the purpose is to find the starting move sequence that then makes it very easy, perhaps no candidates for some of you.

I was unsure about posting this here, however given the death of DJApe's site there does not seem to be a place to post interesting sub-assassin killers. Then SS gave it a 1.1 score so I though "Hey it's marginal".

Image

Sumocue Code:
3x3:d:k:2048:2048:2:3:4356:4356:4356:2055:2055:2048:10:11:12:13:1294:15:16:2055:18:19:20:21:22:1294:2072:25:26:27:28:2333:2078:2078:32:2337:34:35:4644:37:2333:39:2072:41:2337:43:3884:4644:46:2333:48:49:50:2337:52:3884:4644:55:2072:57:58:59:60:61:3884:2111:64:3905:66:67:68:69:70:2119:2111:2111:3905:4171:4171:4171:78:2119:2119:

Solution:

+-------+-------+-------+
| 2 5 9 | 8 6 4 | 7 1 3 |
| 1 7 3 | 5 9 2 | 6 8 4 |
| 8 6 4 | 1 7 3 | 2 5 9 |
+-------+-------+-------+
| 9 4 2 | 3 5 6 | 1 7 8 |
| 7 3 6 | 4 1 8 | 5 9 2 |
| 5 8 1 | 7 2 9 | 3 4 6 |
+-------+-------+-------+
| 6 2 5 | 9 4 1 | 8 3 7 |
| 3 9 7 | 2 8 5 | 4 6 1 |
| 4 1 8 | 6 3 7 | 9 2 5 |
+-------+-------+-------+
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Børge
PostPosted: Sat Mar 20, 2010 7:05 pm 
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Paper Killer images with udosuk Style Killer Cages: 
Image     Image

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Andrew
 Post subject: Re: Paper Killer
PostPosted: Sat Mar 20, 2010 11:48 pm 
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Thanks HATMAN for a fun killer. My approach was a mix of elimination solving with a couple of paper killer steps thrown in; one can certainly get the early steps without needing elimination solving.

Rating Comment:
I'll rate my walkthrough for Paper Killer at Easy 1.25 because I used a couple of ALS blocks; maybe SS and some human solvers consider those steps to be blocking killer pairs and rate them lower. Similarly step 3 might be considered so obvious that people wouldn't call it a Grouped X-Wing; my rating is based on the ALS blocks rather than that step

Here is my walkthrough for Paper Killer. Step 3 may be unnecessary but it's interesting so I kept it in.

Prelims

a) R23C6 = {14/23}
b) R4C45 = {17/26/35}, no 4,8,9
c) R89C3 = {69/78}
d) 8(3) cage in N1 = {125/134}
e) 8(3) cage at R1C8 = {125/134}
f) 8(3) disjoint cage at R3C3 = {125/134}
g) 9(3) cage at R4C3 = {126/135/234}, no 7,8,9
h) 9(3) cage at R4C7 = {126/135/234}, no 7,8,9
i) 8(3) cage in N7 = {125/134}
j) 8(3) cage in N9 = {125/134}

Steps resulting from Prelims
1a. 8(3) cage in N1 = {125/134}, 1 locked for N1
1b. 8(3) cage at R1C8 = {125/134}, 1 locked for N3
1c. 8(3) cage in N7 = {125/134}, 1 locked for N7
1d. 8(3) cage in N9 = {125/134}, 1 locked for N9

2. 8(3) disjoint cage at R3C3 = {125/134} -> R5C5 = 1, placed for both diagonals, clean-up: no 7 in R4C45

3. The four 8(3) corner cages must have 1 in one of R1289 and one of C1289 (because no 1s in R19C19), grouped X-Wings for 1, no other 1 in R1289 and C1289, clean-up: no 4 in R3C6

4. 1 in C3 only in 9(3) cage at R4C3 = {126/135}, no 4

5. 1 in C7 only in 9(3) cage at R4C7 = {126/135}, no 4

6. Naked quad {2345} in R1C9 + R3C7 + R7C3 + R9C1, locked for D/

7. 45 rule on C9 2 innies R34C9 = 2 outies R19C8 + 14 -> R34C9 = 17 = {89}, locked for C9, R19C8 = 3 = {12}, locked for C8

8. 8(3) cages in N3 and N9 must have different combinations (ALS block in C9) -> one must be {125} and the other {134}
8a. 2 of the {125} cage must be in R19C8 -> no 2 in R1289C9
8b. Naked quad {1345} in R1289C9, locked for C9

9. 9(3) cage at R4C7 (step 5) = {135} (cannot be {126} which clashes with 15(3) cage at R5C9, ALS block), locked for C7 and N6, clean-up: no 2,4 in R7C3 (step 2)
9a. 4 in N6 only in R456C8, locked for C8
9b. Killer pair 3,5 in R7C3 and 8(3) cage, locked for N7

10. 9(3) cage at R4C3 (step 4) = {126} (cannot be {135} which clashes with R7C3), locked for C3 and N4, clean-up: no 9 in R89C3
10a. Naked pair {78} in R89C3, locked for C3 and N7
10b. 4,9 in C3 only in R123C3, locked for N1, clean-up: no 3 in 8(3) cage in N1

11. Naked triple {125} in 8(3) cage in N1, locked for N1
11a. Naked triple {349} in R123C3, locked for C3 and N1 -> R7C3 = 5, placed for D/, R3C7 = 2 (step 2), placed for D/, R1C8 = 1, R9C8 = 2, clean-up: no 3 in R2C6
11b. R2C1 = 1 (hidden single in R2), R8C9 = 1 (hidden single in R8), R9C2 = 1 (hidden single in R9)

12. R8C9 = 1, R9C8 = 2 -> R9C9 = 5 (cage sum), placed for D\, R1C1 = 2, placed for D\, R1C2 = 5, clean-up: no 3,6 in R4C5

13. 16(3) cage at R9C4 = {367} (only remaining combination, cannot be {349} which clashes with R9C1), locked for R9 and N8 -> R9C1 = 4, placed for D/, R8C1 = 3, R89C3 = [78], R9C7 = 9, R12C9 = [34], R2C6 = 2, R3C6 = 3

14. R4C4 = 3 (hidden single on D\), R4C5 = 5, R4C7 = 1
14a. R3C4 = 1 (hidden single in N2), R6C3 = 1 (hidden single in C3), R7C6 = 1 (hidden single in N8)

15. 18(3) cage at R5C1 = {567} (only remaining combination) -> R7C1 = 6, R56C1 = {57}, locked for C1 and N4, R8C2 = 9, placed for D/, R3C1 = 8, R3C9 = 9, R4C19 = [98], R3C3 = 4, placed for D\, R12C3 = [93], R4C2 = 4, R7C2 = 2, R7C9 = 7, R7C7 = 8, placed for D\, R8C8 = 6, placed for D\, R2C2 = 7, placed for D\, R2C8 = 8, placed for D/

16. 45 rule on R1 1 remaining innie R1C4 = 8

and the rest is naked singles without using diagonals.
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HATMAN
 Post subject: Re: Paper Killer
PostPosted: Sun Mar 21, 2010 1:50 pm 
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Andrew

Neat solution but not the prize.

Maurice
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Andrew
 Post subject: Re: Paper Killer
PostPosted: Sun Mar 21, 2010 7:49 pm 
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Thanks! Maybe I'm too methodical a solver. I'll be interested to see what anyone better at lateral thinking comes up with.
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Frank
 Post subject: Re: Paper Killer
PostPosted: Sun Mar 21, 2010 11:53 pm 
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Thanks HATMAN - great fun. Haven't finished it yet but here are some thoughts:


1. The 1 in the split 8(3) cage must go in r5c5.
2. The four corners belong to 8(3) cages and are common peers so must be {2345} - sum to 14.
3. 45 rule on r19 and c19 gives 8 cells totalling 180 - 15 - 16 - 17 - 18 - 4*8 - 14. <- the 14 is because the 4 corners are counted twice.
Total = 68 = 4 * 17. So there are 4 {89} pairs in r19 and c19.
4. I have eliminated {134} from the split 8(3) cage but it is inelegant - it needs more work :).
5. That leaves the split 8(3) cage as {125} and everything seems to roll from there.
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HATMAN
 Post subject: Re: Paper Killer
PostPosted: Mon Mar 22, 2010 9:53 am 
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Frank

Your 2,3 are what I intended - but it rolls on from there.

Andrew

The 1.1 did not use the overlap move. Your solution is probably the lowest count as overlaps come quite late in most people's solving hierarchies (but not mine).

Maurice
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Frank
 Post subject: Re: Paper Killer
PostPosted: Mon Mar 22, 2010 8:18 pm 
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Hi again:

I redid the puzzle and you are right Maurice - after my steps 1, 2 and 3 the puzzle just rolls along.
My step 4 comes out in the wash - more like a tsunami actually after the start! :)

Thanx again for a fun puzzle.

Cheers - Frank
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HATMAN
 Post subject: Re: Paper Killer
PostPosted: Mon Mar 22, 2010 10:46 pm 
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Frank

What I meant was keep to the pattern:

4. cages in C9,R9,R1,C1 must contain 67 hence are: 672, 673, 674, 675 - hence:
5. Outies C9,R9,R1,C1 are r19c8={12}, r8c19={13}, r2c19={14},r19c2={15}

then the flood.
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Frank
 Post subject: Re: Paper Killer
PostPosted: Mon Mar 22, 2010 11:51 pm 
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Maurice - yes - that is exactly what I did.
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