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Ed
 Post subject: Assassin 304
PostPosted: Thu Nov 20, 2014 9:33 pm 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
First time I solved this my comment saved in the ss file was "woah! Hard as. Was completely stumped for a long time - several times in fact. Must have missed something big". Then, after the second solve, "Much easier 2nd time around. Not my favourite puzzle due to .........(deleted to avoid any chance of spoiler). Very hidden key steps but not complicated." It gets a score of 'just' 1.30. Hope you guys enjoy the challenge more than I did.

Assassin 304
Image

Code: paste into solver:
3x3::k:7680:7680:3841:3841:3842:1795:1796:6149:6149:7680:7680:5638:2311:3842:1795:1796:6149:6149:7680:5638:5638:2311:5384:5384:5384:2569:2569:7680:3850:3083:5638:2316:2316:5384:2569:6669:3850:3850:3083:2062:9743:3344:6669:6669:6669:4369:3850:4370:2062:9743:9743:3344:3344:6669:4369:2323:2323:4370:4370:9743:3344:2836:2836:4369:2325:2325:4370:9743:9743:9743:9238:4119:2328:2328:9238:9238:9238:9238:9238:4119:4119:
Solution: 
+-------+-------+-------+
| 7 4 6 | 9 8 1 | 3 2 5 |
| 3 1 2 | 5 7 6 | 4 9 8 |
| 9 5 8 | 4 2 3 | 7 6 1 |
+-------+-------+-------+
| 6 2 5 | 7 1 8 | 9 3 4 |
| 1 9 7 | 6 3 4 | 5 8 2 |
| 8 3 4 | 2 5 9 | 6 1 7 |
+-------+-------+-------+
| 4 8 1 | 3 9 7 | 2 5 6 |
| 5 6 3 | 1 4 2 | 8 7 9 |
| 2 7 9 | 8 6 5 | 1 4 3 |
+-------+-------+-------+
Cheers
Ed
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Afmob
 Post subject:
PostPosted: Fri Nov 21, 2014 10:03 pm 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Killer, Ed! As you said it wasn't particular hard but there were a lot of moves available right from the start. The main question was: Which ones are useful?

Edit: Ed found a mistake in my former step 3c. I've fixed it.

A304 Walkthrough:
1. R789
a) Outies R9 = 16(2) = {79} locked for R8+N9
b) 11(2) @ N9 <> 2,4
c) 36(6) = 789{156/246/345} -> 8 locked for R9
d) 9(2) @ R9 = {27} locked for R9+N7 since (36,45) are Killer pairs of 36(6)
e) 36(6) = 5789{16/34} -> R8C8 = 7; 5 locked for R9
f) 9(2) @ R7 <> {36} since it's a Killer pair of 11(2)

2. C1234 !
a) ! Innies+Outies C1234: -8 = R7C5 - R9C34 -> R9C3 <> 8 (IOU @ N8)
b) Innies+Outies N7: -1 = R6C1 - R9C3: R9C3 <> 1, R6C1 = (23458)
c) 17(3) <> 1
d) 9 locked in Innies N7 = 18(3) = 9{36/45}
e) Innies C12 = 19(3) <> 1,2,3 and R3C2 <> 4 since R78C2 <> 7,9
f) Both 9(2) @ R78: R78C3 <> 6,8
g) 8 locked in Innies C12 = 19(3) @ N8 = 8{47/56} for C2
h) R4C1 <> 9 since it sees all 9 of C2
i) Outies N1 = 22(2+1) <> 1,2,3,4 since R4C1 <= 8

3. R123 !
a) Innies+Outies N3: -4 = R4C8 - R3C7 -> R4C8 <> 6; R3C7 <> 1,2,3,4
b) ! Innies N2 = 14(3): R3C56 <> 6,7,8,9 since R1C4 >= 6 and {167} blocked by Killer pair (67) of 15(2)
c) ! Innies N2 = 14(3) <> 6 since (356) is a Killer triple of 7(2)
d) 15(2) @ N1: R1C3 <> 9
e) Outies N23 = 18(2+1): R4C7 = (6789) since R1C3 <= 8 and R4C8 <= 5
f) Outies R123 = 25(4) must have one of (1234) -> R4C8 <> 5
g) Innies+Outies N3: -4 = R4C8 - R3C7: R3C7 <> 9
h) 9 locked in R3C13 @ R3 for N3

4. C123
a) 9 locked in 15(4) @ C2 = {1239} locked for N4; R5C1 <> 9
b) 2 locked in 22(4) @ C3 = 2{389/479/569/578} <> 1 for N1
c) 30(6) = 13{4589/4679/5678} -> 3 locked for N1
d) 3 locked in R89C3 @ C3 for N7
e) 17(3) = {458} -> R6C1 = 8; 4,5 locked for C1+N7
f) 12(2) = {57} locked for C3+N4
g) Outies N1 = 22(2+1) = 6+{79} -> R4C1 = 6; 7,9 locked for C4

5. N89
a) R6C3 = 4, R7C2 = 8, R7C3 = 1
b) 11(2) = {56} locked for R7+N9
c) R7C1 = 4, R8C1 = 5
d) Innies N9 = 11(3) = {128} locked for C7+N9; R7C7 = 2
e) 17(4) = {1349} since R7C45 <> 2,8 -> R7C4 = 3, R7C5 = 9, R8C4 = 1

6. N236
a) 9(2) = {45} locked for C4+N2
b) 21(4) = {2379} since R3C45 = (123) -> R3C7 = 7, R4C7 = 9; 2,3 locked for R3+N2
c) Outies N236 = 10(2) = [64] -> R1C3 = 6, R5C6 = 4
d) 13(4) = {1246} -> R6C7 = 6, R6C8 = 1
e) 26(5) = {24578}

7. Rest is singles.

Rating:
Easy 1.25. I used IOU and a Killer triple combo block.
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Andrew
 Post subject: Re: Assassin 304
PostPosted: Thu Nov 27, 2014 8:24 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1894
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin.

I was without my computer for 8 days; since then I've been catching up with things.

My solving path is somewhat longer, maybe because I'd got a bit out of practice at solving Assassins.

Here is my walkthrough for Assassin 304:
Thanks Ed for your comments and simplifications.

Prelims

a) R1C34 = {69/78}
b) R12C5 = {69/78}
c) R12C6 = {16/25/34}, no 7,8,9
d) R12C7 = {16/25/34}, no 7,8,9
e) R23C4 = {18/27/36/45}, no 9
f) R45C3 = {39/48/57}, no 1,2,6
g) R4C56 = {18/27/36/45}, no 9
h) R56C4 = {17/26/35}, no 4,8,9
i) R7C23 = {18/27/36/45}, no 9
j) R7C89 = {29/38/47/56}, no 1
k) R8C23 = {18/27/36/45}, no 9
l) R9C12 = {18/27/36/45}, no 9
m) 10(3) cage at R3C8 = {127/136/145/235}, no 8,9
n) 13(4) cage at R5C6 = {1237/1246/1345}, no 8,9

1. 45 rule on N1 2 outies R4C14 = 1 innie R1C3 + 7, min R1C3 = 6 -> min R4C14 = 13, no 1,2,3 in R4C14

2. 45 rule on N3 1 innie R3C7 = 1 outie R4C8 + 4, R3C7 = {56789}, R4C8 = {12345}

3. 45 rule on R9 2 outies R8C89 = 16 = {79}, locked for R8 and N9, clean-up: no 2,4 in R7C89, no 2 in R8C23
3a. 9 in R9 only in R9C3456, locked for 36(6) cage at R8C8 -> R8C8 = 7
3b. 7 in R9 only in R9C12 = {27}, locked for R9 and N7
3c. R8C9 = 9 -> R9C89 = 7 = {16/34}, no 5,8
3d. Killer pair 3,6 in R7C89 and R9C89, locked for N9
3e. 2 in N9 only in R78C7, locked for C7, clean-up: no 5 in R12C7
3f. 2 in N9 only in R78C7, CPE no 2 in R7C6
3g. R7C23 = {18/45} (cannot be {36} which clashes with R7C89), no 3,6
3h. Killer pair 5,8 in R7C23 and R7C89, locked for R7

4. 45 rule on N7 1 innie R9C3 = 1 outie R6C1 + 1, no 1,6,9 in R6C1, no 1 in R9C3

5. 45 rule on C12 3 innies R378C2 = 19 = {469/478/568} (cannot be {289/379} because 2,7,9 only in R3C2), no 1,2,3, clean-up: no 8 in R7C3, no 6,8 in R8C3
5a. 7,9 of {469/478} only in R3C2 -> no 4 in R3C2

6. 45 rule on C89 1 outie R5C7 = 1 remaining innie R6C8 + 4, R5C7 = {56789}, no 6 in R6C8

7. 38(7) cage at R8C5 must contain 7 in R5C5 + R6C56 + R7C6, CPE no 7 in R45C6, clean-up: no 2 in R4C5

8. Hidden killer pair 1,4 in R789C7 and R9C89 for N9, R9C89 contains one of 1,4 -> R789C7 must contain one of 1,4
8a. Killer pair 1,4 in R12C7 and R789C7, locked for C7

9. 45 rule on N3 3 innies R3C789 = 14 = {158/167/239/257} (cannot be {149/356} which clash with R12C7, cannot be {248/347} because 10(3) cage at R3C8 cannot be {24}4/{34}3), no 4 in R3C789

10. 45 rule on N2 3 innies R1C4 + R3C56 = 14 = {149/158/239/248/257/347} (cannot be {167} which clashes with R12C5, cannot be {356} which clashes with R12C6), no 6, clean-up: no 9 in R1C3
10a. R1C4 = {789} -> no 7,8,9 in R3C56
10b. 7 in C6 only R67C6, locked for 38(7) cage at R8C5, no 7 in R56C5

11. 45 rule on N23 2 outies R4C78 = 1 innie R1C4 + 3
11a. Min R1C4 = 7 -> min R4C78 = 10, R4C78 must contain one of 6,7,8,9 -> R4C7 = {6789}

12. 45 rule on N236 1 innie R1C4 = 2 outies R5C6 + R7C7 + 3
12a. Max R5C6 + R7C7 = 6, no 6 in R5C6

13. 45 rule on C1234 2 innies R9C34 = 1 outie R7C5, IOU no 8 in R9C3, clean-up: no 7 in R6C1 (step 4)

14. 17(3) cage at R6C1 = {269/359/368/458}, no 1
14a. 1 in N7 only in R78C3, locked for C3
14b. 1 in N7 only in R7C23 = [81] or R8C23 = [81] (locking cages) -> 8 in R78C2, locked for C2 and N7
14c. 8 in R78C2 -> R378C2 (step 5) = {478/568}, no 9
14d. 17(3) cage = {458} can only be [845] -> no 4 in R68C1, clean-up: no 5 in R9C3 (step 4)

15. 45 rule on N4 3 innies R4C1 + R6C13 = 18 = {279/369/468/567} (cannot be {378/459} which clash with R45C3
15a. 2,3 of {279/369} must be in R6C1 -> no 2,3 in R6C3

16. 2 in C3 only in R23C3, locked for N1
16a. 22(4) cage at R2C3 contains 2 = {2479/2569/2578} (cannot be {2389} because R3C2 only contains 5,6,7), no 3

17. 17(3) cage at R6C1 (step 14) = {269/359/368/458}
17a. R4C1 + R6C13 (step 15) = {369/468/567} (cannot be {279} which clashes with 17(3) cage + R9C1, killer ALS block), no 2, 6 locked for N4, clean-up: no 3 in R9C3 (step 4)
17b. R6C1 = {358} -> no 5,8 in R4C1 + R6C3
17c. R4C1 + R6C13 = {369} must be [639] (cannot be [936] which clashes with 17(3) cage = {359}) -> no 9 in R4C1
[Ed suggested that the eliminated of [927] in step 17a and [936] in step 17c are blocking cages.]

18. 1,3 in N1 only in 30(6) cage at R1C1 = {134589/134679} (cannot be {135678} which clashes with R1C3 and/or R3C2), 9 locked for N1

19. R4C14 = R1C3 + 7 (step 1), min R1C3 = 6 -> min R4C14 = 13, max R4C1 = 7 -> min R4C4 = 6

20. 22(4) cage at R2C3 (step 16a) = {2479/2569/2578}
20a. 9 of {2569} must be in R4C4 -> no 6 in R4C4

21. 45 rule on N1 3(2+1) outies R1C4 + R4C14 = 22
[I could have used this 45 a lot earlier, but it wasn’t useful then.]
21a. Max R14C4 = 17 -> no 4 in R4C1
21b. 30(6) cage at R1C1 (step 18) = {134679} (only remaining combination, cannot be {134589 because R4C1 only contains 6,7), no 5,8, 4 locked for N1
21c. Caged X-Wing for 7 in 30(6) cage and R9C12, no other 7 in C12
21d. 15(4) cage at R4C2 = {1239/1248}, no 5
21e. 8 in C1 only in R56C1, locked for N4, clean-up: no 4 in R45C3
[Step 21 simplified.]

22. R9C3 = 1 outie R6C1 + 1 (step 4)
22a. R4C1 + R6C13 (step 15) = {369/468/567}
22b. 7 of {567} must be in R6C3 (R6C13 cannot be [56] which clashes with R6C1 + R9C3 = [56], IOD clash) -> no 6 in R6C3
22c. R4C1 = 6 (hidden single in N4), clean-up: no 3 in R4C56
22d. 30(6) cage at R1C1 = {134679}, 7 locked for N1, clean-up: no 8 in R1C4
[Cracked. The rest is fairly straightforward.]

23. R1C4 + R4C14 = 22 (step 21), R4C1 = 6 -> R14C4 = 16 = {79}, locked for C4, clean-up: no 2 in R23C4, no 1 in R56C4
23a. R23C4 = {18/45} (cannot be {36} which clashes with R56C4), no 3,6
23b. R1C4 + R3C56 (step 10) = {239/257/347} (cannot be {149} which clashes with R23C4), no 1

24. 17(3) cage at R6C1 (step 14) = {359/458}
24a. 4,9 only in R7C1 -> R7C1 = {49}
24b. 3 in N7 only in R8C13, locked for R8

25. R378C2 = {568} (hidden triple in C2), no 4, clean-up: no 5 in R78C3

26. 45 rule on N2 2 outies R34C7 = 1 innie R1C4 + 7
26a. R1C4 = {79} -> R34C7 = 14,16 = [59/68/79] (cannot be [97] which clashes with R14C4 = [97]) -> R3C7 = {567}, R4C7 = {89}, clean-up: no 4,5 in R4C8 (step 2)
26b. 8,9 in N3 only in 24(4) cage at R1C8 = 89{16/25/34}, no 7
[Ed has suggested to me that it's not really cracked until after step 26a.]

27. 7 in N3 only in R3C79, locked for R3
27a. R3C789 (step 9) = {167/257}, no 3
27b. Killer pair 5,6 in R3C2 and R3C789, locked for R3, clean-up: no 4 in R2C4
27c. R1C4 + R3C56 (step 23b) = {239/347}, 3 locked for R3 and N2, clean-up: no 4 in R12C6
27d. 4 in N2 only in R3C456, locked for R3

28. R3C1 = 9 (hidden single in R3), R7C1 = 4, R7C3 = 1 -> R7C2 = 8, R8C123 = [563], R6C1 = 8 (cage sum), R9C3 = 9, clean-up: no 3 in R7C89
28a. Naked pair {56} in R7C89, locked for R7 and N9 -> R7C47 = [32], clean-up: no 5 in R56C4, no 1 in R9C89 (step 3c)
28b. Naked pair {34} in R9C89, locked for R9 and N9
28c. Naked pair {18} in R89C7, locked for C7, clean-up: no 6 in R12C7
28d. Naked pair {34} in R12C7, locked for C7 and N3

29. R4C7 = 9 -> R14C4 = [97] -> R1C3 = 6, R45C3 = [57], clean-up: no 6 in R2C5, no 1 in R2C6, no 4 in R4C5, no 2,4 in R4C6
[I had, of course, noticed from the start that 15(2) cage at R1C3 and 15(2) cage at R1C5 must have different combinations -> CPE no 6 in R1C6 but that didn’t lead to anything then.
Just realised that I forgot about some clean-ups in R5C7 and R6C8 using step 6, which would have made things slightly shorter.]
29a. Naked pair {78} in R12C5, locked for C5 and N2, clean-up: no 1 in R23C4
29b. R23C4 = [54]
29c. Naked pair {23} in R3C56, locked for R3 and N2, R4C7 = 9 -> R3C7 = 7 (cage sum)
29d. R23C3 = [28], R3C2 = 5
29e. Naked pair {16} in R3C89, locked for N3, R4C8 = 3 (cage sum), R9C8 = 4

30. R7C7 = 2 -> 13(4) cage at R5C6 = {1246} (only remaining combination) -> R6C7 = 6, R5C6 = 4, R6C8 = 1

31. R6C3 = 4, R7C45 = [39] -> R8C4 = 1 (cage sum)

and the rest is naked singles.

Rating Comment:
Maybe a little high but I'll rate my walkthrough for A304 at Hard(?) 1.25.
I think that step 14b is technically locking cages but it's so obvious that my rating doesn't take account of this step.
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