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Ed
 Post subject: Assassin 236
PostPosted: Thu Apr 12, 2012 10:02 pm 
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Another tricky puzzle. I used a couple of advanced moves available fairly close to the start of my walkthrough. I usually like my puzzles to give more of a start before getting stuck. This cage structure plays havoc with the 45 rule but at least there are no disjoint cages. Hope you still enjoy the challenge.

Assassin 236

Image

Code: paste into solver:
3x3::k:3840:8961:1026:1026:10243:1540:5381:7686:7686:2567:3840:8961:8961:10243:1540:5381:5381:7686:2567:3840:8961:8961:10243:2312:2312:5381:7686:1289:1289:8961:8961:10243:6410:2571:2571:7686:7948:5133:10243:10243:10243:6410:6410:6410:2574:7948:5133:4879:4879:6160:9233:9233:2574:2574:7948:5133:5133:4879:6160:9233:9233:1810:1810:7948:7948:4883:2836:6160:9233:9233:4629:4629:4883:4883:4883:2836:6160:6160:6160:9233:4629:
solution: 
+-------+-------+-------+
| 5 4 3 | 1 8 2 | 7 9 6 |
| 1 2 7 | 9 6 4 | 8 5 3 |
| 9 8 6 | 3 5 7 | 2 1 4 |
+-------+-------+-------+
| 2 3 1 | 5 7 9 | 6 4 8 |
| 4 6 9 | 2 3 8 | 1 7 5 |
| 8 7 5 | 6 4 1 | 9 3 2 |
+-------+-------+-------+
| 7 5 2 | 8 9 3 | 4 6 1 |
| 3 9 8 | 4 1 6 | 5 2 7 |
| 6 1 4 | 7 2 5 | 3 8 9 |
+-------+-------+-------+
Cheerio
Ed
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Frank
 Post subject: Re: Assassin 236
PostPosted: Sat Apr 14, 2012 11:41 pm 
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I think you have a sadistic streak in you Ed :).
Here is how I did it:
It is fairly easy to show r5c345 = [{3,8},2] or [{2,9},3] The former causes a clash in N2.
That solves half the puzzle. The rest is still not a cakewalk, but drops out by combo analysis.
Altogether a thoroughly inelegant way of solving the puzzle. So hope the purists can come up with a cleaner solution :). As always many thanx Ed.
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Andrew
 Post subject: Re: Assassin 236
PostPosted: Mon Apr 16, 2012 7:55 pm 
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Thanks Ed for another challenging Assassin.

Frank wrote:
Altogether a thoroughly inelegant way of solving the puzzle. So hope the purists can come up with a cleaner solution :).
I don't think I'm a purist but my solving path may be a bit cleaner:
I used similar analysis to Frank to reduce R5C345 although at that stage I hadn't managed to eliminate {56}1 from R5C345. Then I used a short but very powerful forcing chain which cracked the puzzle.

At one time I could never find forcing chains. Now I seem to use them a lot, particularly when working on my backlog of harder puzzles.

Here is my walkthrough for A236:
Prelims

a) R1C34 = {13}
b) R12C6 = {15/24}
c) R23C1 = {19/28/37/46}, no 5
d) R3C67 = {18/27/36/45}, no 9
e) R4C12 = {14/23}
f) R4C78 = {19/28/37/46}, no 5
g) R7C89 = {16/25/34}, no 7,8,9
h) R89C4 = {29/38/47/56}, no 1
i) 10(3) cage at R5C9 = {127/136/145/235}, no 8,9
j) 19(3) cage at R6C3 = {289/379/469/478/568}, no 1

1. Naked pair {13} in R1C34, locked for R1, clean-up: no 5 in R2C6

2. 45 rule on C1234 2 innies R5C34 = 11 = {29/38/47/56}, no 1

3. 45 rule on C6789 2 innies R9C67 = 8 = {17/26/35}, no 4,8,9

4. 45 rule on N3 1 outie R4C9 = 1 innie R3C7 + 6, R3C7 = {123}, R4C9 = {789}, clean-up: R3C6 = {678}

5. 45 rule on R1234 3 outies R5C345 = 1 innie R4C6 + 5, R5C34 = 11 (step 2) -> R4C6 = R5C5 + 6, R4C6 = {789}, R5C5 = {123}

6. 24(6) cage at R6C5 = {123459/123468/123567}
6a. R9C67 can only contain one of 1,2,3 (step 3) -> R6789C5 must contain two of 1,2,3
6b. Killer triple 1,2,3 in R5C5 and R6789C5, locked for C5
6c. 3 in N2 only in R123C4, locked for C4, clean-up: no 8 in R5C3 (step 2), no 8 in R89C4

7. 45 rule on N3 2(1+1) outies R3C6 + R4C9 = 15 = [69/78/87]
7a. R3C6 + R4C9 = [69]
or R3C6 + R4C9 = [78/87] => R4C6 = 9
-> 9 must be in R4C6 + R4C9, locked for R4, clean-up: no 1 in R4C78
7b. 9 in R4 only in R4C69, CPE no 9 in R5C78
7c. R4C69 = {789} both “see” R5C78 -> R5C78 cannot contain both of 7,8
7d. Max R4C6 + R5C78 = 9 + {68} = 23 -> no 1 in R5C6

8. 24(6) cage at R6C5 = {123459/123468/123567}, 4,8,9 can only be in C5
8a. 40(7) cage at R1C5 = {1456789/2356789} can only contain both of 8,9 in C5 if it also contains 4 in C5 -> R5C34 (step 2) cannot be {47} -> R5C34 = {29/56}/[38], no 4,7
8b. 7 in 40(7) cage only in R1234C5, locked for C5

9. 40(7) cage at R1C5 = {1456789/2356789}
9a. 2,3 of {2356789} must be in R5C45 (cannot be in R5C35 because R5C345 = [293/382] clashes with R4C6 + R5C5 = [93/82], step 5), no 2,3 in R5C3, clean-up: no 8,9 in R5C4 (step 8a)
[With hindsight I missed no 2 in R5C5 but this didn’t make much difference.]

10. 5 in R4 only in R4C345
10a. R4C69 contains 9 (step 7a) = {79/89} = 16,17
10b. 45 rule on R4 3 innies R4C345 = 13,14 = {157/256/158/257/356}, no 4
[Alternatively R4C12 = {14/23} + R4C78 = {28/37/46} must contain 4.]
10c. Locking hidden killer pair 1,6 in R4C12 + R4C78 and R4C345 for R4, 4 in R4 only in R4C12 + R4C78 -> R4C12 + R4C78 contains one of {14/46} -> R4C345 must contain one of 1,6 -> R4C345 = {157/256/158/356} (cannot be {257} which doesn’t contain either of 1,6)
[I could have written step 10b as 13(3) or 14(3) cage containing 5 cannot also contain 4, but then I wouldn’t have been able to follow up with step 10c.]

[At this stage I found a contradiction move to reduce 40(7) cage at R1C5 to one combination. Then I managed to find a more satisfying forcing chain; I hope that Ed found something better.]
11. 40(7) cage at R1C5 = {1456789/2356789}
11a. Consider combinations for R12C6 = {24}/[51]
R12C6 = {24}, locked for N2 => 40(7) cage = {2356789}
or R12C6 = [51] => R4C4 = 1 (hidden single in C4) => 40(7) cage = {2356789}
-> 40(7) cage = {2356789}, no 1,4, clean-up: no 7 in R4C6 (step 5)
11b. R5C45 = [23] (only places for 2,3 in 40(7) cage), R4C6 = 9 (step 5), R5C3 = 9 (step 2), clean-up: no 6 in R3C6 (step 7), no 3 in R3C7, no 9 in R89C4
11c. Naked quad {5678} in R1234C5, locked for C5
11d. Naked pair {78} in R3C6 + R4C9 (step 7), CPE no 7,8 in R3C9

12. R6C7 = 9 (hidden single in N6)

13. 24(6) cage at R6C5 = {123459} (only remaining combination) -> R9C67 = {35}, locked for R9, 2,9 locked for N8, clean-up: no 6 in R8C4

14. 19(3) cage at R6C3 = {478/568}, no 2,3

15. R4C6 = 9 -> 25(4) cage at R4C6 = {1789/4579}, no 6, 7 locked for R5

16. 45 rule on N6 1 remaining outie R5C6 = 1 remaining innie R4C9 -> R5C6 = {78}
[With hindsight there’s now naked pair {78} in R35C6, locked for C6.]

17. 45 rule on N6 3 remaining innies R4C9 + R5C78 = 16 = {178/457}, 7 locked for N6, clean-up: no 3 in R4C78
17a. Killer pair 2,4 in R4C12 and R4C78, locked for R4

18. 3 in N6 only in R6C89, locked for R6
18a. 10(3) cage at R5C9 contains 3 = {136/235}, no 4

19. 45 rule on N47 2 remaining innies R46C3 = 6 = [15], R1C34 = [31], clean-up: no 5 in R1C6, no 7 in R23C1, no 4 in R4C12

20. Naked pair {24} in R12C6, locked for C6 and N2

21. Naked pair {23} in R4C12, locked for R4 and N4, clean-up: no 8 in R4C78
21a. Naked pair {46} in R4C78, locked for R4 and N6

22. 10(3) cage at R5C9 (step 18a) = {235} (only remaining combination) -> R5C9 = 5, R6C89 = {23}, clean-up: no 2 in R7C8

23. R5C12 = {46} (hidden pair in R5), locked for N4, CPE no 4,6 in R8C2
23a. Naked pair {78} in R6C12, locked for R6, CPE no 7,8 in R8C2

24. 19(3) cage at R6C3 (step 14) = {568} (only remaining combination) -> R67C4 = [68], R6C6 = 1, R6C5 = 4, clean-up: no 5 in R8C4
24a. Naked pair {47} in R89C4, locked for C4 and N8 -> R4C4 = 5

25. Naked pair {39} in R23C4, locked for 35(7) cage at R1C2, no 9 in R1C2
25a. 35(7) cage contains 1,3,5,9 = {1235789/1345679}, 7 locked for N1

26. 6 in C6 only in R78C6, locked for 36(7) cage at R6C6, no 6 in R78C7 + R9C8
26a. 36(7) cage contains 1,6,9 and at least one of 3,5 = {1236789/1345689}, 8 locked for N9

27. 9 in N9 only in 18(3) cage at R8C8 = {279/369/459}, no 1

28. 1 in N9 only in R7C89 = {16}, locked for R7 and N9
28a. 18(3) cage at R8C8 (step 27) = {279/459}, no 3
28b. 3 in N9 only in R789C7, locked for C7
28c. R8C6 = 6 (hidden single in N8)

29. 20(4) cage at R5C2 = {2468/2567/3467} (cannot be {2369/2459} because R6C2 only contains 7,8, cannot be {2378} because R5C2 only contains 4,6, cannot be {3458} because 3,5 only in R7C2) -> R5C2 = 6, R5C1 = 4, clean-up: no 6 in R23C1
29a. R6C2 = {78} -> R7C23 = [25/34/42/52], no 7,9

30. R5C1 = 4 -> 31(5) cage at R5C1 = {34789} (only remaining combination), 7,8 locked for C1, clean-up: no 2 in R23C1

31. Naked pair {19} in R23C1, locked for C1 and N1

32. Naked triple {378} in R678C1, locked for C1 and 31(5) cage at R5C1 -> R8C2 = 9, R4C12 = [23], R9C1 = 6, R1C1 = 5
32a. R9C2 = 1 (hidden single in N7), R9C9 = 9 (hidden single in N9), R9C5 = 2, R78C5 = [91]

33. R1C1 = 5 -> R23C2 = 10 = {28}, locked for C2 and N1 -> R6C2 = 7, R6C1 = 8, R1C2 = 4, R12C6 = [24], R7C2 = 5, R7C3 = 2 (step 29a), R7C6 = 3, R78C1 = [73], R7C7 = 4, R4C78 = [64]

34. 18(3) cage at R8C8 (step 28a) = {279} (only remaining combination), 2,7 locked for R8 and N9 -> R9C8 = 8, R8C7 = 5,
34a. 2 in C7 only in R23C7, locked for N3

35. 30(5) cage at R1C8 = {34689} (only remaining combination), no 1,7 -> R4C9 = 8

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A236 at 1.5. I used two short forcing chains but the first one probably wasn't necessary. I also used a derived 45, using the result from an earlier 45.


Last edited by Andrew on Sat Apr 28, 2012 11:52 pm, edited 1 time in total.

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HATMAN
 Post subject: Re: Assassin 236
PostPosted: Tue Apr 17, 2012 5:26 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
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Location: Saudi Arabia
Andrew

Derived 45: I can guess what you mean, so either it is obvious technically but hard to spot or needs to be added to "Killer Techniques".

I suggest it should be added if only for completeness.

Cheers

MAurice
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Ed
 Post subject: Re: Assassin 236
PostPosted: Thu Apr 26, 2012 11:18 pm 
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Location: Sydney, Australia
Frank wrote:
I think you have a sadistic streak in you Ed :).
Thanks for the compliment! :)

I did this puzzle a slightly different way to Andrew though in the same areas. [edit: my way relies on more combo work.] As Andrew mentioned, I also worked with different combinations to Frank to start the puzzle. Andrew does a really good summary of the clean-up.

A236
Hidden Text:
Thanks to Andrew for some good suggested clarifications.

1. "45" on c1234: 2 innies r5c34 = 11 (no 1)
1a. = {29/38/47/56} = [2/4/6/8;3/4/5/9;3/4/6/9..]

2. "45" on r56789: 1 outie r4c6 - 6 = 1 remaining innie r5c5 (remembering h11(2)r5c34)
2a. r4c6 = (789)
2b. r5c5 = (123)

3. "45" on c6789: 2 innies r9c67 = 8 (no 4,8,9)
3a. = {17/26/35} = [1/2/3..]

4. 24(6)r6c5 = {123459/123468/123567} = three of 1,2,3
4a. must have two of in c5
4b. Killer triple 1,2,3 with r5c5: all locked for c5

5. "45" on n3: 2 outies r3c6+r4c9 = 15 = [69]/{78}(no 1..5. no 6 in r4c9, no 9 in r3c6)
5a. no 4..9 in r3c7

6. 6(2)n2 = {15/24}(no 3,6..9)

7. 3 in n2 only in c4: locked for c4
7a. no 8 in r5c3 (h11(2)r5c34)
7b. no 1,8 in 11(2)n8

8. Split-cage 29(5)r12345c5
8a. {24689/34589/34679} clash with h11(2)r5c34 (step 1a)(no eliminations yet)

9. r9c67 see all c5 except r12345c5 -> implied 8(2) between r5c5 + one of r1234c5
9a. ->{15689/23789} blocked from split 29(5)r12345c5 (can't make 8(2))
9b. 29(5)r12345c5 = {14789/25679/35678} only
9c. must have 7 -> 7 locked for c5 and 40(7)r1c5
9d. no 7 in r5c34
9e. no 4 in r5c34 (h11(2)r5c34)

10. Combined half-cage Split 29(5) = {25679} + r4c6 = 8 (IOD with r5c5 = +6) clashes with h11(2)r5c34 = [2/5]/[8]
10a. Split 29(5) = {14789/35678}(no 2)
10b. must have 8 -> 8 locked for c5 & 40(7)r1c5
10c. no 8 in r5c4, no 3 in r5c3 (h11(2)r5c34)
10d. no 8 in r4c6 (IOD r5c5 + 6 = r4c6)
10e. no {26} in r9c56 (step 9)

11. Split-cage 29(5) = {14789/35678}
11a. r123c5 <> {678} because of r3c6 -> {35678} must have 5 in r123c5
11b. -> no 5 in r4c5

12. 5(2)n4 = {14/23}(no 5..9)
12a. 10(2)n6: no 5
12b. 5 in r4 only in r4c34 -> 5 locked for 35(7)r1c2
12c. no 5 in r1c2, r23c34

13. Split-cage 29(5) = {14789/35678} = [1->9] -> {56} in h11(2)r5c34 (similar deal with [3->5]
13a. -> r5c345 = {56}[1]/{29}[3] = [3/5..] (no eliminations yet)

14. "45" on r6789: 3 outies r5c129 = 15
14a. {159/258/267/357} all clash with r5c345 (step 13a)
14b. = {168/249/348/456}(no 7)

15. 7 in r5 only in 25(4)r4c6 -> no 7 in r4c6
15a. r4c6 = 9
15b. r5c5 = 3 (r4c6-6=r5c5)
15c. no 6 in r3c6 (Outies n3 = 15)
15d. no 3 in r3c7
15e. no 1 in 10(2)n6

Missing lots of clean-up from now.
16. r5c5 = 3 -> r5c34 = [92] (step 13a)
16a. r5c5 = 3 -> r9c67 = {35} (step 9): locked for r9 & 24(6)r6c5
16b. 5 in c5 only in n2: locked for n2
16c. -> 6(2)n2 = {24}: both locked for n2 & c6

17. 10(3)n6 (no 8,9)
17a. r6c7 = 9 (hsingle n6)

18. "45" on n47: 2 remaining innies r46c3 = 6
18a. {24} blocked by 5(2)n4 = [2/4.]
18b. r46c3 = {15} only: both locked for n4 and c3 [Andrew noticed that r46c3 immediately becomes [15] if you do Prelims on 19(3)r6c3 first.]
18c. -> 5(2)n4 = {23}: both locked for r4 & n4
18d. -> 10(2)n6 = {46}: both locked for r4 & n6

on from there.
Cheerio
Ed
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