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Afmob
 Post subject: Assassin 194
PostPosted: Thu May 20, 2010 10:57 pm 
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
The original plan was to create a Killer with no preliminaries. I succeeded but that Killer was way too difficult for a V1. So I changed some cages and this puzzle was the result. Despite it's SS Score it can be solved with steps of rating 1.0.

V2 will be posted on Monday, if V1 was solved with a proper walkthrough. To give you a teaser:

Ratings for V2:
SS Score (v3.3.1): 3.10
Estimated rating: At least 1.75!


Assassin 194

Image

3x3::k:3841:3841:4355:4355:6406:3588:3588:3847:3847:3841:3330:4355:3330:6406:4613:3588:4613:3847:3592:3592:3330:6406:6406:6406:4613:4617:4617:3592:5130:5130:5130:3340:6411:6411:6411:4617:4109:3599:5130:3340:4625:3340:6411:3088:3086:4109:4109:3599:4625:1561:4625:3088:3086:3086:3858:3608:3599:1561:5146:5146:3088:1815:3859:4372:3858:3608:4118:5146:4118:1815:3859:4117:4372:4372:3858:3608:4118:1815:3859:4117:4117:

Solution:
8 3 9 7 4 5 2 6 1
4 5 1 2 3 6 7 9 8
2 7 6 1 8 9 3 5 4
5 2 3 8 1 4 6 7 9
1 4 7 9 6 3 8 2 5
6 9 8 5 2 7 1 4 3
3 6 2 4 5 8 9 1 7
9 8 5 6 7 1 4 3 2
7 1 4 3 9 2 5 8 6


SS Score (v3.3.1): 1.44
Estimated rating: 1.0 - Hard 1.0.

Please do not use this thread for posting different images!
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mhparker
 Post subject: Re: Assassin 194
PostPosted: Sat May 22, 2010 8:46 pm 
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Joined: Mon Apr 21, 2008 6:23 am
Posts: 113
Location: Germany
Hi folks,

Unfortunately, I wasn't around to attempt Ronnie's A193X, due to being "stuck" on a beach in Turkey :sun: . So thought I'd give this one a try first. Thanks, Afmob, for an enjoyable puzzle with an interesting cage pattern (which I admittedly took some time to get used to! :scratch: ).

Assassin 194 Walkthrough:
Prelims

a) 6(2) at R6C5 = {15/24} (no 3,6..9)
b) 20(3) at R7C5 = {389/479/569/578} (no 1,2)
c) 7(3) at R7C8 = {124}


1. Naked triple (NT) at R7C8+R8C7+R9C6
1a. -> no 1,2,4 in R9C789 (common peer elimination (CPE))

2. Innies N8: R7C4+R9C46 = 9(3) = {126/135/234} (no 7..9)
2a. must have one of {36}, only available in R9C4
2b. -> R9C4 = {36}

3. Outies R123: R4C19 = 14(2) = {59/68} (no 1..4,7)

4. Innies N5689: R4C49+R9C4 = 20(2+1)
4a. R4C49 cannot sum to 14 (combo crossover clash (CCC), step 3)
4b. -> R9C4 <> 6
4c. -> R9C4 = 3
4d. -> R4C49 = 17(2) = {89}, locked for R4

5. Innies N7: R7C3 = 2
5a. split 12(2) at R5C2+R6C3 = {39/48/57} (no 1,6)
5b. cleanup: no 4 in R6C5

6. Split 6(2) at R7C4+R9C6 (step 2) = [42/51] (no 1 in R7C4, no 4 in R9C6)
6a. R7C8+R9C6 cannot also sum to 6 (CCC)
6b. -> no 1 in R8C7
6c. cleanup: no 5 in R6C5

7. 16(3) at R8C4 = {169/178/268} (no 4,5)
(Note: {259} blocked by R7C4+R9C6 (step 6), {457} blocked by R7C4)

8. 4 in R9 locked in R9C123 for N7

9. Split 11(2) at R7C2+R8C3 = {56} (last combo), locked for N7

10. 15(3) at R7C1 = {348} (last combo)
10a. -> R9C3 = 4, R7C1+R8C2 = {38}, locked for N7

11. Innie/outie difference (IOD), N9: R7C7 = R9C6 + 7
11a. -> R7C7+R9C6 = [81/92]
11b. -> R7C7 = {89}

12. {28} in R9 locked in R9C56789
12a. R9C5789 cannot have both of {28} (blocked by R7C7+R9C6 (step 11a))
12b. -> one of {28} must be in R9C6
12c. -> R9C6 = 2
12d. -> R7C7 = 9 (step 11a)
12e. -> split 3(2) at R5C8+R6C7 = {12}, locked for N6

13. Naked single (NS) at R8C7 = 4
13a. -> R7C8 = 1
13b. -> R5C8 = 2
13c. -> R6C7 = 1
13d. -> R6C5 = 2
13e. -> R7C4 = 4 (cage sum)

14. Hidden single (HS) in R8/N9 at R8C9 = 2
14a. -> split 14(2) at R9C89 = {68} (last combo), locked for R9 and N9

15. HS in R9 at R9C7 = 5

16. 12(3) at R5C9 = {345} (last combo), locked for N6

17. Naked pair (NP) at R4C78 = {67}, locked for R4 and N6
17a. -> split 12(2) at R4C6+R5C7 = [48]

18. R4C19 = [59]
18a. -> R4C4 = 8; split 9(2) at R3C12 = {18/27/36} (no 4,9);
split 9(2) at R3C89 = {36/45}/[81] (no 7, no 8 in R3C9)

19. HS in R4/N4 at R4C2 = 2
19a. -> split 10(2) at R45C3 = [19/37] (no 1,3,6 in R5C3)

20. 6 in N4 locked in 16(3) at R5C1 = {169/367} (no 4,8)

21. HS in R6/N4 at R6C3 = 8
21a. -> R5C2 = 4 (cage sum)

22. Outies N1: R12C4 = 9(2) = {27} (last combo), locked for C4 and N2

23. 17(3) at R1C3 = {179/269} (no 3,5)
(Note: {359} blocked because {359} only available in R12C3)
23a. 9 locked in R12C3 for C3 and N1
23b. 7 of {179} must go in R1C4
23c. -> no 7 in R12C3

24. NS at R5C3 = 7
24a. -> R4C3 = 3 (cage sum)
24b. -> R4C5 = 1
24c. -> split 12(2) at R5C46 = [93] (last permutation)
24d. -> R5C9 == 5
24e. -> R5C5 = 6
24f. -> R5C1 = 1, R6C4 = 5
24g. -> R6C6 = 7

25. 15(3) at R1C8 = {168/348/456} (no 7,9)
(Note: {159} unplaceable, because {59} only available in R1C8; {357} blocked by R7C9)

26. HS in C8/N3 at R2C8 = 9
26a. -> split 9(2) at R2C6+R3C7 = [63] (last permutation)

Rest is naked singles and cage sums.

From Afmob's comments, it loks like the V2 will make a good team challenge... ;)

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Mike
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h3lix
 Post subject: Re: Assassin 194
PostPosted: Sun May 23, 2010 3:24 am 
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Joined: Sun May 18, 2008 6:22 pm
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Had a lot of fun with this one! I only have some vague notes now, but I'll try to flesh them out into a full solve path tomorrow hopefully.

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Andrew
 Post subject: Re: Assassin 194
PostPosted: Mon May 24, 2010 5:37 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
h3lix wrote:
Had a lot of fun with this one! I only have some vague notes now, but I'll try to flesh them out into a full solve path tomorrow hopefully.
I hope that posting my walkthrough won't put you off posting your solving path. Maybe you've found a different way than both Mike and I did.

Thanks Afmob for a nice Assassin and Mike for an interesting walkthrough; I liked your CCC moves.

Afmob wrote:
The original plan was to create a Killer with no preliminaries.
You came pretty close; there were only three of them.

Rating Comment:
I'll rate my walkthrough for A194 at 1.25 because of steps 20 and 26; apart from those steps the ALS block in step 35a would have made it Easy 1.25.

The key move I missed was Afmob's step 3i. As he has shown later in this thread, with that move this puzzle is in the 1.0 range.

Here is my walkthrough for A194.

Prelims

a) 6(2) cage at R6C5 = {15/24}
b) 20(3) cage at R7C5 = {389/479/569/578}, no 1,2
c) 7(3) cage at R7C8 = {124}, CPE no 1,2,4 in R9C789

1. 45 rule on N9 1 innie R7C7 = 1 outie R9C6 + 7, R7C7 = {89}, R9C6 = {12}
1a. 7(3) cage at R7C8 = {124}, 4 locked for N9
1b. Min R9C89 = 8 -> max R8C9 = 8

2. 12(3) cage at R5C8 = {129/138}, 1 locked for N6
2a. 12(3) cage at R5C9 = {246/345} (cannot be {237} which clashes with 12(3) cage at R5C8), no 7,8,9, 4 locked for N6
2b. Killer pair 2,3 in 12(3) cage at R5C8 and 12(3) cage at R5C9, locked for N6

3. 45 rule on N69 1 innie R4C9 = 2 outies R49C6 + 3
3a. Min R49C6 = 3 -> min R4C9 = 6

4. 25(4) cage at R4C6 = {1789/2689/3589/3679/4579/4678}
4a. 1,2,3,4 only in R4C6 -> R4C6 = {1234}

5. 45 rule on C789 4 outies R1249C6 = 17 = {1259/1268/1349/1358/1367/1457/2348/2357/2456}
5a. 1,2 of {1259/1268} must be in R49C6, 1,2 of other combinations must be in R9C6 -> no 1,2 in R12C6

6. 45 rule on R123 2 outies R4C19 = 14 = [59/68/86], R4C1 = {568}, no 7 in R4C9
6a. Min R4C1 = 5 -> max R3C12 = 9, no 9 in R3C12

7. 45 rule on N47 2 outies R49C4 = 1 innie R4C1 + 6, IOU no 6 in R9C4
7a. Min R4C1 = 5 -> min R49C4 = 11, no 1 in R49C4

8. 45 rule on N7 1 outie R9C4 = 1 innie R7C3 + 1, no 5,9 in R7C3

9. 7 in N6 only in 25(4) cage at R4C6 (step 4) = {1789/3679/4579/4678}, no 2

10. 45 rule on N5 3 innies R4C46 + R6C5 = 14 = {149/158/167/239/248/257/347/356}
10a. 6,7,8,9 only in R4C4 -> R4C4 = {6789}
10b. Naked quint {56789} in R4C14789, locked for R4

11. R49C4 = 1 innie R4C1 + 6 (step 7)
11a. Max R4C1 = 8 -> max R49C4 = 14, no 9 in R9C4, clean-up: no 8 in R7C3 (step 8)

12. 45 rule on R1234 2 outies R5C37 = 1 innie R4C5 + 14
12a. Max R5C37 = 17 -> max R4C5 = 3
12b. Min R5C37 = 15, no 1,2,3,4,5 in R5C37

13. 45 rule on R789 3 innies R7C347 = 15
13a. Min R7C47 = 9 -> max R7C3 = 6, clean-up: no 8 in R9C4 (step 8)

14. 45 rule on N8 3 innies R7C4 + R9C46 = 9 = {135/234} -> R9C4 = 3, R7C3 = 2 (step 8), R7C4 = {45}, clean-up: no 4,5 in R6C5
[I ought to have spotted this step earlier.]
14a. Killer pair 4,5 in R7C4 and 20(3) cage, locked for N8
14b. 2 in R9 only in R9C56, locked for N8
14c. 4 in R9 only in R9C123, locked for N7

15. R7C3 = 2 -> R5C2 + R6C3 = 12 = {39/48/57}, no 1,6

16. R9C4 = 3 -> R7C2 + R8C3 = 11 = {56} (only remaining combination), locked for N7

17. 17(3) cage in N7 = {179} (only remaining combination), locked for N7
17a. R9C3 = 4 (hidden single in R9), clean-up: no 8 in R5C2 (step 15)
17b. 5 in R9 only in R9C789, locked for N9
17c. Min R9C89 = 11 -> no 6,7,8 in R8C9

18. R4C46 + R6C5 = 14 (step 10)
18a. Max R4C4 + R6C5 = 11 -> no 1 in R4C6
18b. Max R4C6 + R6C5 = 6 -> min R4C4 = 8

19. R4C9 = R49C6 + 3 (step 3)
19a. Min R49C6 = 4 -> no 6 in R4C9
19b. Naked pair {89} in R4C49, locked for R4
19c. R4C9 + R5C7 = {89} (hidden pair in N6)
19d. Naked pair {89} in R57C7, locked for C7

20. R4C9 + R5C7 = {89}, R57C7 = {89} -> R4C9 = R7C7
20a. 45 rule on N6 2(1+1) outies R4C6 + R7C7 = 1 innie R4C9 + 4, R4C9 = R7C7 -> R4C6 = 4

21. 45 rule on N14 3 remaining outies R124C4 = 17 = {179/269/278} (cannot be {458} which clashes with R7C4, cannot be {467} because R4C4 only contains 8,9), no 4,5
21a. R4C4 = {89} -> no 8,9 in R12C4

22. 17(3) cage at R1C3 = {179/269/278/368} (cannot be {359} because no 3,5,9 in R1C4), no 5

23. 13(3) cage in N5 = {139/157/238/256}
23a. Killer pair 1,2 in 13(3) cage and R6C5, locked for N5

24. 15(3) cage in N9 = {159/168/258/267/357}
24a. 6 of {168} must be in R9C7, 2 of {267} must be in R8C8 -> no 6 in R8C8

25. 45 rule on N47 4 innies R4C123 + R5C3 = 17 = {1259/1268/1358/1367/2357}
25a. 7,8,9 only in R5C3 -> R5C3 = {789}
[One of the combinations for R4C123 + R5C3 can be eliminated because of interactions between R4C1 and the 20(4) cage but I’ll leave that for now.]

26. 45 rule on N8 1 outie R6C5 = 1 remaining innie R9C6
26a. 2 in R9 only in R9C56 -> 2 in R69C5, locked for C5

27. Naked pair {13} in R4C35, locked for R4 -> R4C2 = 2
27a. R5C37 = R4C5 + 14 (step 12)
27b. R4C5 = {13} -> R5C37 = 15,17 = {78/89}, 8 locked for R5

28. 13(3) cage in N5 (step 23) = {139/157} (cannot be {256} because R4C5 only contains 1,3), no 2,6, 1 locked for N5 -> R6C5 = 2, R7C4 = 4, R7C8 = 1, R9C6 = 2, R8C7 = 4, R7C7 = 9 (step 1), R5C7 = 8, R4C9 = 9, R4C1 = 5 (step 6), R4C4 = 8, clean-up: no 7 in R5C2 + R6C3 (step 15)

29. 12(3) cage at R5C8 (step 2) = {129} (only remaining combination) -> R6C7 = 1, R5C8 = 2
29a. Naked pair {67} in R4C78, locked for N6

30. R8C9 = 2 (hidden single in R8), R9C89 = 14 = {68}, locked for R9 and N9
30a. R9C7 = 5 (hidden single in R9)

31. 45 rule on N1 2 remaining outies R12C4 = 9 = {27}, locked for C4 and N2, CPE no 7 in R2C3
31a. 45 rule on N3 2 remaining outies R12C6 = 11 = {38/56}, no 9

32. R4C1 = 5 -> R3C12 = 9 = {18/36}/[27], no 4, no 7 in R3C1

33. 3 in C7 only in R123C7, locked for N3
33a. R4C9 = 9 -> R3C89 = 9 = [45/54/81], no 6,7, no 8 in R3C9

34. 17(3) cage at R1C3 (step 22) = {179/269/278} (cannot be {368} because R1C4 only contains 2,7), no 3
34a. 8 of {278} must be in R2C3 -> no 8 in R1C3

35. 20(3) cage in N8 = {569/578}
35a. 9 of {569} must be in R8C5, 5 of {578} must be in R7C56 (R7C56 cannot be {78} which clashes with R7C19, ALS block) -> no 5 in R8C5

36. R8C3 = 5 (hidden single in R8), R7C2 = 6, clean-up: no 3 in R3C1 (step 32)

37. 20(3) cage in N8 (step 35) = {578} (only remaining combination, cannot be {569} because 6,9 only in R8C5), locked for N8
37a. 7 in R9 only in R9C12, locked for N7

38. 6 in N4 only in R56C1, locked for C1, clean-up: no 3 in R3C2 (step 32)
38a. 16(3) cage in N4 = {169/367}, no 4,8

39. R5C2 = 4, R6C3 = 8 (hidden pair in N4)

40. 17(3) cage at R1C3 (step 34) = {179/269}, 9 locked for C3 and N1 -> R5C3 = 7, R4C3 = 3 (step 25)
40a. R6C12 = [69], R5C1 = 1
40b. Naked triple {169} in R123C3, locked for N1, clean-up: no 8 in R3C12 (step 32)
40c. R3C12 = [27]

41. 13(3) cage in N5 (step 28) = {139} (only remaining combination) -> R4C5 = 1, R5C46 = [93], R9C5 = 9

42. 1 in N2 only in R3C46, locked for R3 -> R3C3 = 6, R3C7 = 3, clean-up: no 8 in R3C8 (step 33a)
42a. Naked pair {45} in R3C89, locked for R3 and N3 -> R3C5 = 8, R78C5 = [57], R7C6 = 8, R5C5 = 6

43. R3C3 = 6 -> R2C24 = 7 = [52], R2C6 = 6, R2C8 = 9 (cage sum)

and the rest is naked singles.


Last edited by Andrew on Wed Jun 02, 2010 11:40 pm, edited 1 time in total.

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Afmob
 Post subject: Assassin 194 V2
PostPosted: Mon May 24, 2010 6:15 pm 
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Posts: 310
Location: MV, Germany
Ed told me that he was looking forward to a difficult Assassin, so here it is! No preliminaries and a wicked cage pattern should keep you busy for a while.

Assassin 194 V2

Image

3x3::k:3841:3841:4354:4354:6404:3589:3589:3847:3847:3841:3331:4354:3331:6404:4614:3589:4614:3847:3593:3593:3331:6404:6404:6404:4614:4616:4616:3593:5130:5130:5130:3346:6411:6411:6411:4616:4112:3601:5130:3346:4627:3346:6411:3086:3087:4112:4112:3601:4627:3606:4627:3086:3087:3087:5652:5652:3601:3606:5400:3606:3086:3861:3861:4364:5652:5652:5400:5399:5400:3861:3861:4109:4364:4364:5399:5399:5400:5399:5399:4109:4109:

SS Score (v3.3.1): 3.10
Estimated rating: Hard 1.75.

Same solution as V1.
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mhparker
 Post subject: Re: Assassin 194 V2
PostPosted: Wed May 26, 2010 8:49 am 
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Joined: Mon Apr 21, 2008 6:23 am
Posts: 113
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Afmob wrote:
No preliminaries and a wicked cage pattern should keep you busy for a while.

Thanks, Afmob. :roll:

Fascinating to have an Assassin without any preliminaries (but please don't feel obliged to make a habit of it... ;) ).

Time to get the ball rolling:


Assassin 194 V2 Tag Walkthrough

1. Outies R123: R4C19 = 14(2) = {59/68} (no 1..4,7)

2. Innies N7: R79C3 = 6(2) = {15/24} (no 3,6..9)

3. Innies N9: R79C7 = 14(2) = {59/68} (no 1..4,7)

4. Outies R1234: R5C3467 = 27(4) = {3789/4689/5679} (no 1,2)
4a. 9 locked in R5C3467 for R5

5. Innie/outie difference (IOD) R1234: R5C37 = R4C5 + 14
5a. min. R4C5 = 1 -> min. R5C37 = 15
5b. -> no 1..5 in R5C37
5c. max. R5C37 = 17 -> max. R4C5 = 3
5d. -> no 4..9 in R4C5

6. Outies N1234: R4C49+R7C3 = 19(2+1)
6a. max. R4C49 = 17 -> min. R7C3 = 2
6b. -> no 1 in R7C3
6c. R4C49 cannot sum to 14 (Combo crossover clash (CCC) w/ R4C19 (step 1))
6d. -> no 5 in R7C3
6e. max. R7C3 = 4 -> min. R4C49 = 15
6f. -> no 1..5 in R4C49
6g. cleanup: no 9 in R4C1 (step 1); no 1,5 in R9C3 (step 2)

7. Naked pair (NP) at R79C3 = {24}, locked for C3 and N7

8. Outies N8: R6C5+R9C37 = 11(1+2)
8a. min. R9C37 = 7 -> max. R6C5 = 4
8b. -> no 5..9 in R6C5
8c. min. R6C5+R9C3 = 3 -> max. R9C7 = 8
8d. -> no 9 in R9C7
8e. cleanup: no 5 in R7C7 (step 3)

9. 12(3) at R5C8 can only contain 1 of {6..9}, which must go in R7C7
9a. -> no 6..9 in R5C8+R6C7

10. 25(4) at R4C6 = {1789/2689/3589/3679/4579/4678}
10a. -> must contain exactly one of {1..4} within R4C678
10b. -> R4C235 and R4C678 form hidden killer quad on {1..4} within R4
10c. -> no 5..9 in R4C23

11. Outies N1236: R4C16+R7C7 = 18(2+1) = [549/576/639/648/819/828/846]
11a. -> no 5,6,8,9 in R4C6

Grid state after step 11:

Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 123456789   123456789 | 1356789     123456789 | 123456789 | 123456789   123456789 | 123456789   123456789 |
|           .-----------:           .-----------:           :-----------.           :-----------.           |
| 123456789 | 123456789 | 1356789   | 123456789 | 123456789 | 123456789 | 123456789 | 123456789 | 123456789 |
:-----------'-----------+-----------+-----------'           '-----------+-----------+-----------'-----------:
| 123456789   123456789 | 1356789   | 123456789   123456789   123456789 | 123456789 | 123456789   123456789 |
|           .-----------'-----------'-----------.-----------.-----------'-----------'-----------.           |
| 568       | 1234        13          6789      | 123       | 12347       123456789   123456789 | 689       |
:-----------+-----------.           .-----------+-----------+-----------.           .-----------+-----------:
| 12345678  | 12345678  | 6789      | 3456789   | 12345678  | 3456789   | 6789      | 12345     | 12345678  |
|           '-----------+-----------+-----------+-----------+-----------+-----------+-----------'           |
| 123456789   123456789 | 1356789   | 123456789 | 1234      | 123456789 | 12345     | 123456789   123456789 |
:-----------------------:           :-----------+-----------+-----------:           :-----------------------:
| 1356789     1356789   | 24        | 123456789 | 123456789 | 123456789 | 689       | 123456789   123456789 |
:-----------.           '-----------+-----------+-----------+-----------+-----------'           .-----------:
| 1356789   | 1356789     1356789   | 123456789 | 123456789 | 123456789 | 123456789   123456789 | 123456789 |
|           '-----------.-----------'-----------+-----------+-----------'-----------.-----------'           |
| 1356789     1356789   | 24          123456789 | 123456789 | 123456789   568       | 123456789   123456789 |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'

Now time to become a little more creative...

12. {3589} combo for 25(4) at R4C6 (step 9) blocked by combined 14(2) at R4C19 (step 1) and 14(2) at R79C7 (step 3)
(Explanation: because R4C78 see 14(2) at R4C19 and R45C7 see 14(2) at R79C7, R4C78+R5C7 can only accommodate
one killer digit pair of 14(2), which would then have to go in R4C8+R5C7. However, {589} contains TWO killer
digit pairs of 14(2) (namely {58} and {89}), so a clash with one of the 14(2) cages is inevitable)
12a. -> 25(4) at R4C6 = {1789/2689/3679/4579/4678} (no eliminations)

13. 5 in R4 locked in R4C178
13a. -> either R4C19 (step 1) = [59] -> 25(4) at R4C6 <> {9..}
13b. or 25(4) at R4C6 = {5..}
13c. -> 25(4) at R4C6 (step 12a) = {4579/4678} (no 1..3)
13d. 4 locked in R4C678 for R4

14. IOD N6: R4C6 + R7C7 = R4C9 + 4
14a. -> R4C69+R7C7 = [466/488/499/796] (no eliminations)
14b. Now combine this cage with the hidden 14(2) cage at R79C7 (step 3)
14c. -> R4C69+R79C7 = [4668/4886/4995] ([7968] blocked by R5C7!)
14d. -> R4C6 = 4
14e. R4C9 = R7C7 (no eliminations)
14f. split 21(3) at R4C78+R5C7 (step 13c) = {579/678}
14g. 7 locked in R4C78+R5C7 for N6

Grid state after step 14:

Code:
.-----------------------.-----------------------.-----------.-----------------------.-----------------------.
| 123456789   123456789 | 1356789     123456789 | 123456789 | 12356789    123456789 | 123456789   123456789 |
|           .-----------:           .-----------:           :-----------.           :-----------.           |
| 123456789 | 123456789 | 1356789   | 123456789 | 123456789 | 12356789  | 123456789 | 123456789 | 123456789 |
:-----------'-----------+-----------+-----------'           '-----------+-----------+-----------'-----------:
| 123456789   123456789 | 1356789   | 123456789   123456789   12356789  | 123456789 | 123456789   123456789 |
|           .-----------'-----------'-----------.-----------.-----------'-----------'-----------.           |
| 568       | 123         13          6789      | 123       | 4           56789       56789     | 689       |
:-----------+-----------.           .-----------+-----------+-----------.           .-----------+-----------:
| 12345678  | 12345678  | 6789      | 356789    | 1235678   | 356789    | 6789      | 12345     | 1234568   |
|           '-----------+-----------+-----------+-----------+-----------+-----------+-----------'           |
| 123456789   123456789 | 1356789   | 12356789  | 123       | 12356789  | 12345     | 12345689    12345689  |
:-----------------------:           :-----------+-----------+-----------:           :-----------------------:
| 1356789     1356789   | 24        | 123456789 | 123456789 | 12356789  | 689       | 123456789   123456789 |
:-----------.           '-----------+-----------+-----------+-----------+-----------'           .-----------:
| 1356789   | 1356789     1356789   | 123456789 | 123456789 | 12356789  | 123456789   123456789 | 123456789 |
|           '-----------.-----------'-----------+-----------+-----------'-----------.-----------'           |
| 1356789     1356789   | 24          123456789 | 123456789 | 12356789    568       | 123456789   123456789 |
'-----------------------'-----------------------'-----------'-----------------------'-----------------------'

Maybe someone else can take over from here?

_________________
Cheers,
Mike
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Afmob
 Post subject:
PostPosted: Thu May 27, 2010 5:03 pm 
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Here is how I solved A194 with moves of rating 1.0:

A194 Walkthrough:

1. R789
a) Innies+Outies N9: -7 = R9C6 - R7C7 -> R9C6 <> 4; R7C7 = (89)
b) 7(3) = {124} -> 4 locked for N7; CPE: R9C789 <> 1,2
c) Innies N8 = 9(3) must have one of (36) -> R9C4 = (36)
d) Innies+Outies N7: 1 = R9C4 - R7C3: R7C3 = (25)
e) 12(3) = 1{29/38} since R7C7 = (89) -> R5C8+R6C7 = 1{2/3} -> 1 locked for N6

2. N478 !
a) ! Innies+Outies N4: 5 = R4C4+R7C3 - R4C1 -> R7C3 <> 5 (IOU @ R4)
-> R7C3 = 2, R9C4 = 3
b) Innies N8 = 6(2) = [42/51]
c) Innies+Outies N4: 3 = R4C4 - R4C1: R4C4 <> 1,2; R4C1 <> 7,8,9
d) Killer pair (45) locked in R7C4 + 20(3) for N8
e) 4 locked in R9C123 @ R9 for N7
f) 14(3) @ R7C2 = {356} -> 5,6 locked for N7
g) 15(3) = {348} -> R9C3 = 4; 3,8 locked for N7

3. R456 !
a) Outies R12 = 14(2) = [59/68]
b) Innies+Outies N4: 3 = R4C4 - R4C1: R4C4 = (89)
c) Naked pair (89) locked in R4C49 for R4
d) 12(3) @ R5C9 = 4{26/35} because {237} blocked by Killer pair (23) of 12(3) @ R5C8
-> 4 locked for N6
e) Killer pair (23) locked in both 12(3) for N6
f) 25(4) = 7{369/459/468} <> 1,2 since (89) only possible @ R5C7 -> R4C6 = (34), R5C7 = (89)
-> 7 locked for R4
g) 6(2) = [15/24]
h) 13(3) <> {346} since it's blocked by R4C6 = (34)
i) ! Outies R1234 = 27(4) = 9{378/468/567} <> 1,2 -> 9 locked for R5
j) 13(3) must have one of (12) -> R4C5 = (12)

4. R456+N8
a) Naked pair (12) locked in R46C5 for C5+N5
b) Hidden Single: R9C6 = 2 @ R9
c) 16(3) @ N8 = 1{69/78} -> 1 locked for R8
d) R8C7 = 4, R7C8 = 1
e) Hidden Single: R6C7 = 1 @ N6
f) R6C5 = 2 -> R7C4 = 4, R4C5 = 1
g) Hidden Single: R4C2 = 2 @ R4, R4C6 = 4 @ R4, R4C3 = 3 @ R4
h) Innie N5 = R4C4 = 8
i) Cage sum: R5C3 = 7
j) 14(3) = {248} -> R6C3 = 8, R5C2 = 4

5. N45
a) Innie N4 = R4C1 = 5
b) 13(3) = {139} -> R5C4 = 9, R5C6 = 3
c) R5C8 = 2 -> R7C7 = 9, R4C9 = 9

6. R123+N8
a) Outies N1 = 9(2) = {27} locked for C4+N2
b) Outies N3 = 11(2) = {56} locked for C6+N2
c) R3C4 = 1, R8C4 = 6, R8C3 = 5
d) 16(3) = {169} -> R9C5 = 9, R8C6 = 1
e) 13(3) = {256} since R2C4 = (27) and R3C3 = (69) -> R2C4 = 2, R3C3 = 6, R2C2 = 5
f) Hidden Single: R8C9 = 2 @ N9
g) 18(3) @ R3C8 = {459} -> 4,5 locked for R3+N3
h) 15(3) @ N3 = {168} locked for N3

7. Rest is singles

Nice start from Mike on A194 V2! I don't know why I didn't see your step 10. I'll borrow your move to make my wt shorter and (a bit) easier. :cheesey:
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Ed
 Post subject: Re: Assassin 194 V2
PostPosted: Fri May 28, 2010 1:20 pm 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Afmob wrote:
Ed told me that he was looking forward to a difficult Assassin, so here it is! No preliminaries and a wicked cage pattern should keep you busy for a while.
Me and my big mouth! :pallid: But a wonderful start from Mike! :D

This next batch is mostly pedestrian but can't find anything else.

15. "45" on n5: 2 remaining innies r4c4+r6c5 = 10
15a. -> no 6 in r4c4

16. 12(3)r5c8 must have 6,8,9 for r7c7 = {129/138/156/246} = [1/2..]

17. {129} blocked from 12(3)r5c9 by step 17
17a. {156} blocked by [5/6..] in 25(4)n5 (step 13c)
17b. 12(3)r5c9 = {138/246/345}(no 9)
17c. = two of 1..4

18. hidden killer quad in n6; 12(3)r5c9 has two of 1..4 -> 12(3) at r5c8 must have two of 1..4
18a. 12(3)r5c8 = {129/138/246}(no 5)

19. "45" on r1234: 1 outie r5c7 + 6 = 4 innies r4c2345
19a. 1,2 & 3 for r4 are in those 4 innies and sum to 6 -> r4c4 = r5c7 (no 6)

20. h27(4)r5c3467 = {3789/5679}, must have 7
20a. -> 7 locked for r5

21. 13(3)n5 = {139/157/238/256}: must have 1/2
21a. ->r4c5 = (12)

22. 3 in r4 only in n4 in the 20(4) cage
22a. 3 locked for n4

23. 14(3)n4 must have 2/4 for r7c3 = {149/248/347}(no 6)
23a. 8 in {248} must be in r6c3 -> no 8 in r5c2
23b. {149} must be [194] -> no 1 in r6c3
23c. {257} must be [572] -> no 5 in r6c3

24. "45" on r789: 1 outie r6c5 + 9 = 2 innies r7c37 = [1]28/[1]46/[2]29/[3]48] = [3->4;4->6/8..]
25a. 3->4 -> {347} combo blocked from 14(3)n5 (CCC)

25. "45" on r789: 4 innies r7c3467 = 23
25a. must have 2 or 4 for r7c3 = {2489/2579/2678/4568}(no 1,3) ({3479} blocked by no 6/8 in r7c7 from step 24)

26. r4c4 = r5c7 (from step 19a) and r4c4+r6c5 = 10 -> r6c5 + r5c7 = 10 = [73/82/91] = [1/3/8..]
26a. -> [8]{13} blocked from 12(3)r5c9
26b. -> no 8 in r5c9

marks here
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 123456789 123456789 1356789   | 123456789 123456789 12356789  | 123456789 123456789 123456789 |
| 123456789 123456789 1356789   | 123456789 123456789 12356789  | 123456789 123456789 123456789 |
| 123456789 123456789 1356789   | 123456789 123456789 12356789  | 123456789 123456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 568       123       13        | 789       12        4         | 56789     56789     689       |
| 124568    1245      6789      | 356789    123568    356789    | 789       1234      123456    |
| 12456789  12456789  789       | 12356789  123       12356789  | 1234      12345689  12345689  |
:-------------------------------+-------------------------------+-------------------------------:
| 1356789   1356789   24        | 2456789   123456789 256789    | 689       123456789 123456789 |
| 1356789   1356789   1356789   | 123456789 123456789 12356789  | 123456789 123456789 123456789 |
| 1356789   1356789   24        | 123456789 123456789 12356789  | 568       123456789 123456789 |
'-------------------------------.-------------------------------.-------------------------------'


Cheers
Ed
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Andrew
 Post subject: Re: Assassin 194
PostPosted: Sun May 30, 2010 5:00 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Ed wrote:
Me and my big mouth! :pallid:
You shouldn't complain Ed. ;) Afmob gave us exactly what he said he would in the hidden message in the V1 post.

As Ed and Mike already know, I decided to have a try at the V2 myself to see how far I could get before joining the "tag". After struggling for some eliminations I managed to make all the eliminations in their steps and then found some more today. Some of my steps were different from those already posted so I've given my original steps below.

Here are my first 38 steps:
No Prelims

1. 45 rule on N7 2 innies R79C3 = 6 = {15/24}

2. 45 rule on N9 2 innies R79C7 = 14 = {59/68}
2a. Min R7C7 = 5 -> max R5C8 + R6C7 = 7, no 7,8,9 in R5C8 + R6C7

3. 45 rule on R123 2 outies R4C19 = 14 = {59/68}
3a. Min R4C1 = 5 -> max R3C12 = 9, no 9 in R3C12

4. 45 rule on R1234 2 outies R5C37 = 1 innie R4C5 + 14
4a. Max R5C37 = 17 -> max R4C5 = 3
4b. Min R5C37 = 15, no 1,2,3,4,5 in R5C37

5. 45 rule on R1234 4 outies R5C3467 = 27 = {3789/4689/5679}, no 1,2, 9 locked for R5

6. 45 rule on N4 2(1+1) outies R4C4 + R7C3 = 1 innie R4C1 + 5, IOU no 5 in R7C3, clean-up: no 1 in R9C3 (step 1)

7. 45 rule on R789 2 innies R7C37 = 1 outie R6C5 + 9
7a. Max R7C37 = 13 -> max R6C5 = 4
7b. Min R7C37 = 10 -> min R7C7 = 6, clean-up: no 9 in R9C7 (step 2)
7c. Min R7C7 = 6 -> max R5C8 + R6C7 = 6, no 6 in R5C8 + R6C7

8. 45 rule on N1 3(2+1) outies R12C4 + R4C1 = 14
8a. Min R4C1 = 5 -> max R12C4 = 9, no 9 in R12C4

9. 45 rule on N3 3(2+1) outies R12C6 + R4C9 = 20
9a. Min R12C6 = 11, no 1 in R12C6

10. 45 rule on N5689 2 innies R4C49 = 1 outie R9C3 + 13
10a. Min R9C3 = 2 -> min R4C49 = 15, no 1,2,3,4,5 in R4C49, clean-up: no 9 in R4C1 (step 3)
10b. Max R4C49 = 17 -> max R9C3 = 4, clean-up: no 1 in R7C3 (step 1)

11. Naked pair {24} in R79C3, locked for C3 and N7
11a. Max R5C2 + R7C3 = 12 -> no 1 in R6C3

12. 25(4) cage at R4C6 = {1789/2689/3589/3679/4579/4678} contains one of 1,2,3,4 in R4C678
12a. Hidden killer quad 1,2,3,4 in R4C235 and R4C678 for R4 -> R4C235 must contain three of {1234}, no 5,6,7,8,9 in R4C23

13. 45 rule on R789 4 innies R7C3467 = 23
14a. Max R7C3 = 4 -> min R7C467 = 19, no 1 in R7C46

14. 45 rule on N5 3 innies R4C46 + R6C5 = 14
14a. Min R4C4 + R6C5 = 7 -> max R4C6 = 7

15. 45 rule on N6 4 innies R4C789 + R5C7 = 1 outie R7C7 + 21
15a. R7C7 = {689} -> R4C789 + R5C7 = 27,29,30 = {3789/5679/5789/6789} (cannot be {4689} because R79C7 = [68] when R4C789 + R5C7 = 27 and R4C89 cannot be {68} which clashes with R4C19, CCC), no 1,2,4, 7,9 locked for N6, also 7 locked for 25(4) cage at R4C6, no 7 in R4C6

16. 25(4) cage at R4C6 must contain 7 = {1789/3679/4579/4678}, no 2
16a. 4 of {4579} must be in R4C6 -> no 5 in R4C6
16b. 4 of {4678} must be in R4C6, 6 of {3679} must be R4C78 + R5C7 (R4C78 + R5C7 cannot be {379} => R4C69 = [68] clashes with R4C19, CCC) -> no 6 in R4C6

17. Naked quad {1234} in R4C2356, locked for R4

18. R4C789 + R5C7 (step 15a) = {5679/5789/6789}
18a. 12(3) cage at R5C9 = {138/246/345} (cannot be {156} which clashes with R4C789 + R5C7)
18b. 12(3) cage at R5C8 = {129/138/246} (cannot be {345} because R7C7 only contains 6,8,9, cannot be {156} which clashes with R4C789 + R5C7 which must be {5679} when R7C7 = 6), no 5 in R5C8 + R6C7

19. R7C7 = {689} -> R4C789 + R5C7 (step 15a) = {5679/5789/6789}
19a. For R7C7 = {68} => R4C789 + R5C7 = {5679/5789} => R4C19 = {68} => R7C7 = R4C9 because R4C789 + R5C7 only contains one of 6,8
19b. For R7C7 = 9 => R4C789 + R5C7 = {6789} => R4C1 = 5 (hidden single in R4) => R4C9 = 9 (step 3)
19c. From steps 19a and 19b, R4C9 = R7C7 for all three values in R7C7
19d. 45 rule on N6 2(1+1) outies R4C6 + R7C7 = 1 innie R4C9, R4C9 = R7C7 (from above) -> R4C6 = 4
19e. R4C46 + R6C5 = 14 (step 14), R4C6 = 4 -> R4C4 + R6C5 = 10, no 6 in R4C4

20. 13(3) cage in N5 = {139/157/238/256}
20a. 1,2 of {139/238} must be in R4C5 -> no 3 in R4C5
20b. 3 in R4 only in R4C23, locked for N4

21. R5C3467 (step 5) = {3789/5679}, 7 locked for R5

22. 14(3) cage at R5C2 = {149/248/257} (cannot be {158/167} because R7C3 only contains 2,4), no 6
22a. 7,9 only in R6C3, 8 of {248} must be in R6C3 -> R6C3 = {789}, no 8 in R5C2

23. 18(3) cage in N5 = {189/369/378/567} (cannot be {279} which clashes with 13(3) cage), no 2
23a. 2 in N5 only in R46C5, locked for C5

24. R7C3467 = 23 (step 13)
24a. 14(3) cage at R6C5 = {149/158/167/239/248/257} (cannot be {347} because R7C3467 cannot be [4478])
24b. 3 of {239} must be in R6C5 (R7C46 cannot be {39} because R7C37 would both then be even so R7C3467 would be even), no 3 in R7C46

25. 45 rule on R1234 4 innies R4C2345 = 1 outie R5C7 + 6
25a. R4C235 = {123} = 6 -> R4C4 = R5C7, no 6 in R5C7
[Alternatively 25(4) cage = 4{579/678}
4{579} => R4C19 = {68} => R4C478 = {579} => R4C4 = R5C7
4{678} => R4C19 = [59] => R4C478 = {678} => R4C4 = R5C7]

26. 12(3) at R5C9 (step 18a) = {138/246/345}
26a. 8 of {138} must be in R6C89 (R6C89 cannot be {13} => R6C5 = 2, R4C4 = 8 (step 19e) => R5C7 = 8 (step 25a) -> no 8 in R5C9

27. 16(3) cage in N4 = {169/259/457} (cannot be {178} which clashes with 14(3) cage at R5C2, cannot be {268} which clashes with 14(3) cage at R5C2 = [482] because 4 in N4 must be in either 16(3) cage or R5C2), no 8
27a. 4 in N4 only in 16(3) cage and R5C2
27b. 16(3) cage = {169/259} => R5C2 = 4
27c. 16(3) cage = {457} => 14(3) cage at R5C2 (step 22) = {149/248} => R7C3 = 4
27d. From steps 27b and 27c R5C2 = 4 or R7C3 = 4 -> 14(3) cage at R5C2 = {149/248}, no 5,7
[Alternatively for steps 27a to 27d
14(3) cage at R5C2 = {149/248} (cannot be {257} because then cannot place 4 in N4 because 16(3) cage requires {39}/{57} to contain 4), no 5,7]

28. 45 rule on C89 3 innies R245C8 = 1 outie R8C7 + 14
28a. Max R245C8 = 21 -> max R8C7 = 7
28b. But R8C7 cannot be 7, here’s how
R8C7 = 7 => R4C8 = 7 (hidden single in N6) => max R245C8 = [974] = 20
-> max R8C7 = 6
28c. Min R245C8 = 15, max R45C8 = 13 -> min R2C8 = 2

29. 8 in R5 only in R5C34567
29a. R5C3467 (step 21) = {3789/5679}
29b. R5C3467 = {3789} => 3 locked for R5
R5C3467 = {5679} => R5C5 = 8
-> no 3 in R5C5

30. 18(3) cage in N5 (step 23) = {189/369/378/567}
30a. 1 of {189} must be in R6C46 (R6C46 cannot be {89} which clashes with R6C3) -> no 1 in R5C5
30b. 8 of {189/378} must be in R5C5 -> no 8 in R6C46

31. Killer pair 7,9 in 16(3) cage in N4 and 18(3) cage in N5, locked for R6 -> R6C3 = 8, clean-up: no 6 in R4C9 (step 3), no 1 in R5C2 (step 27d), no 6 in R7C7 (step 19d), no 8 in R9C7 (step 2)
[With hindsight this killer pair was available immediately after the first part of step 27 but at the time it seemed natural, the way I work, to continue analysing the cages in N4.]

32. 12(3) cage at R5C8 (step 18b) = {129/138}, no 4, 1 locked for N6

33. Killer pair 5,6 in R4C1 and 16(3) cage, locked for N4

34. R5C37 = R4C5 + 14 (step 4)
34a. R4C5 = {12} -> R5C37 = 15,16 = {78/79}, 7 locked for R5

35. 17(3) cage at R1C3 = {179/269/359/368/467} (cannot be {278/458} because 2,4,8 only in R1C4)
35a. 7 of {179} must be in R1C4 (R12C3 cannot be {79} which clashes with R5C3) -> no 1 in R1C4
35b. 2,4,8 of {269/368/467} must be in R1C4 -> no 6 in R1C4
35c. R12C4 + R4C1 = 14 (step 8), min R1C4 + R4C1 = 7 -> max R2C4 = 7

36. 14(3) cage at R3C1 = {158/167/257/356} (cannot be {248/347} because R4C1 only contains 5,6), no 4

37. 18(3) cage at R3C8 = {189/279/369/378/459/468} (cannot be {567} because R3C9 only contains 8,9)
37a. 15(3) cage in N3 must contain at least one of 1,2,3,4
37b. Hidden killer quad for 1,2,3,4 in R123C7 + R2C8, 15(3) cage and 18(3) cage at R3C8, 15(3) cage and 18(3) cage must contain at least two of 1,2,3,4 for N3 -> R123C7 + R2C8 cannot contain more than two of 1,2,3,4
37c. Hidden killer quad for 1,2,3,4 in R123C7, R6C7 and R8C7 for C7, R123C7 cannot contain more than two of 1,2,3,4 -> R6C7 and R8C7 must each contain one of 1,2,3,4 and R123C7 must contain two of R123C7, no 5,6 in R8C7
37d. R123C7 contains two of 1,2,3,4 and R123C7 + R2C8 cannot contain more than two of 1,2,3,4 -> no 2,3,4 in R2C8
37e. 15(3) cage in N3 can only contain one of 1,2,3,4

38. R7C37 = R6C5 + 9 (step 7), R7C3467 = 23 (step 13)
38a. R6C5 = {123} -> R6C5 + R7C3467 = 1[2498/2678/2768]/2[2489/2579/2759]/3[4298/4568/4658/4928] -> no 8 in R7C4

Now, to get into the spirit of the "tag", I think the following are those of my steps which take us further than Ed's marks pic. I've renumbered them to be consistent with the "tag" steps and changed the references in the step 34 clean-up to refer to the original "tag" steps. Thanks Afmob and Mike for your comments; I've done some minor editing to both my original steps and my "tag" steps.

27. 45 rule on N1 3(2+1) outies R12C4 + R4C1 = 14
27a. Min R4C1 = 5 -> max R12C4 = 9, no 9 in R12C4

28. 45 rule on N3 3(2+1) outies R12C6 + R4C9 = 20
28a. Min R12C6 = 11, no 1 in R12C6

29. 13(3) cage in N5 = {139/157/238/256} [Not sure whether this was in the "tag" steps so I've included it for completeness.]
29a. 18(3) cage in N5 = {189/369/378/567} (cannot be {279} which clashes with 13(3) cage), no 2
29b. 2 in N5 only in R46C5, locked for C5

30. 16(3) cage in N4 = {169/259/457} (cannot be {178} which clashes with 14(3) cage at R5C2, cannot be {268} which clashes with 14(3) cage at R5C2 = [482] because 4 in N4 must be in either 16(3) cage or R5C2), no 8
30a. 4 in N4 only in 16(3) cage and R5C2
30b. 16(3) cage = {169/259} => R5C2 = 4
30c. 16(3) cage = {457} => 14(3) cage at R5C2 (step 23) = {149/248} => R7C3 = 4
30d. From steps 30b and 30c R5C2 = 4 or R7C3 = 4 -> 14(3) cage at R5C2 = {149/248}, no 5,7
[Alternatively for steps 30a to 30d
14(3) cage at R5C2 = {149/248} (cannot be {257} because then cannot place 4 in N4 because 16(3) cage requires {39}/{57} to contain 4), no 5,7]

31. 45 rule on C89 3 innies R245C8 = 1 outie R8C7 + 14
31a. Max R245C8 = 21 -> max R8C7 = 7
31b. But R8C7 cannot be 7, here’s how
R8C7 = 7 => R4C8 = 7 (hidden single in N6) => max R245C8 = [974] = 20
-> max R8C7 = 6
31c. Min R245C8 = 15, max R45C8 = 13 -> min R2C8 = 2

32. 8 in R5 only in R5C34567
32a. R5C3467 = {3789/5679}
32b. R5C3467 = {3789} => 3 locked for R5
R5C3467 = {5679} => R5C5 = 8
-> no 3 in R5C5

33. 18(3) cage in N5 = {189/369/378/567}
33a. 1 of {189} must be in R6C46 (R6C46 cannot be {89} which clashes with R6C3) -> no 1 in R5C5
33b. 8 of {189/378} must be in R5C5 -> no 8 in R6C46

34. Killer pair 7,9 in 16(3) cage in N4 and 18(3) cage in N5, locked for R6 -> R6C3 = 8, clean-up: no 6 in R4C9 (step 1), no 1 in R5C2 (step 30d), no 6 in R7C7 (step 14e), no 8 in R9C7 (step 3)
[With hindsight this killer pair was available immediately after the first part of step 30 but at the time it seemed natural, the way I work, to continue analysing the cages in N4.]

35. 12(3) cage at R5C8 = {129/138}, no 4, 1 locked for N6

36. Killer pair 5,6 in R4C1 and 16(3) cage, locked for N4

37. R5C37 = R4C5 + 14 (step 5)
37a. R4C5 = {12} -> R5C37 = 15,16 = {78/79}, 7 locked for R5

38. 17(3) cage at R1C3 = {179/269/359/368/467} (cannot be {278/458} because 2,4,8 only in R1C4)
38a. 7 of {179} must be in R1C4 (R12C3 cannot be {79} which clashes with R5C3) -> no 1 in R1C4
38b. 2,4,8 of {269/368/467} must be in R1C4 -> no 6 in R1C4
38c. R12C4 + R4C1 = 14 (step 27), min R1C4 + R4C1 = 7 -> max R2C4 = 7

39. 14(3) cage at R3C1 = {149/158/167/257/356} (cannot be {248/347} because R4C1 only contains 5,6), no 4,9

40. 18(3) cage at R3C8 = {189/279/369/378/459/468} (cannot be {567} because R3C9 only contains 8,9)
40a. 15(3) cage in N3 must contain at least one of 1,2,3,4
40b. Hidden killer quad for 1,2,3,4 in R123C7 + R2C8, 15(3) cage and 18(3) cage at R3C8, 15(3) cage and 18(3) cage must contain at least two of 1,2,3,4 for N3-> R123C7 + R2C8 cannot contain more than two of 1,2,3,4
40c. Hidden killer quad for 1,2,3,4 in R123C7, R6C7 and R8C7 for C7, R123C7 cannot contain more than two of 1,2,3,4 -> R6C7 and R8C7 must each contain one of 1,2,3,4 and R123C7 must contain two of R123C7, no 5,6 in R8C7
40d. R123C7 contains two of 1,2,3,4 and R123C7 + R2C8 cannot contain more than two of 1,2,3,4 -> no 2,3,4 in R2C8
40e. 15(3) cage in N3 can only contain one of 1,2,3,4

41. R7C37 = R6C5 + 9, R7C3467 = 23
41a. R6C5 = {123} -> R6C5 + R7C3467 = 1[2498/2678/2768]/2[2489/2579/2759]/3[4298/4568/4658/4928] -> no 8 in R7C4

I hope I haven't missed out any steps while editing out ones which already gave the eliminations made by Mike and Ed.

Step 31 could have been omitted, since the same result and more is obtained in step 40 but I've kept it in because that's when I saw it and because that I-O difference for C89 might be useful later.

Here is an updated marks pic, a hand edited version of my Excel worksheet.

Code:
.-------------------------------.-------------------------------.-------------------------------.
| 123456789 123456789 135679    | 234578    13456789  2356789   | 123456789 123456789 123456789 |
| 123456789 123456789 135679    | 1234567   13456789  2356789   | 123456789 56789     123456789 |
| 1235678   1235678   135679    | 123456789 13456789  12356789  | 123456789 123456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 56        123       13        | 789       12        4         | 56789     56789     89        |
| 12456     24        79        | 35689     568       35689     | 789       123       23456     |
| 1245679   1245679   8         | 135679    123       135679    | 123       23456     23456     |
:-------------------------------+-------------------------------+-------------------------------:
| 1356789   1356789   24        | 245679    13456789  256789    | 89        123456789 123456789 |
| 1356789   1356789   135679    | 123456789 13456789  12356789  | 1234      123456789 123456789 |
| 1356789   1356789   24        | 123456789 13456789  12356789  | 56        123456789 123456789 |
'-------------------------------.-------------------------------.-------------------------------'

My feeling is that there's a lot of hard work still needed, probably using some even harder steps than those already used by Mike, Ed and myself.


Last edited by Andrew on Wed Jun 09, 2010 4:34 am, edited 2 times in total.

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mhparker
 Post subject: Re: Assassin 194
PostPosted: Mon May 31, 2010 8:49 pm 
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Joined: Mon Apr 21, 2008 6:23 am
Posts: 113
Location: Germany
Thanks, Andrew. :D

I've taken the liberty of continuing the tag from your step 40, after finding a more direct substitute for your step 41 later (see step 48 below):


Assassin 194 V2 Tag Walkthrough (continued)

...

41. Outies N89: R5C8+R6C57+R9C3 = 9(1+2+1)
41a. R5C8+R6C57 cannot sum to 6, because R9C3 <> 3
41b. -> R5C8+R6C57 cannot all be distinct (i.e., cannot be {123}), and thus must contain a repeat digit
41c. -> R5C8 = R6C5 ! (only possibility for a repeat with this geometry)
41d. 1 (already) locked in R5C8+R6C7 (step 35)
41e. -> (from step 41c) 1 locked in R6C57 for R6
41f. furthermore, from step 41c, R5C8+R6C5 (being equal) must sum to an even number
41g. R9C3 must also be even (since it only contains even candidates)
41h. -> R6C7 must be odd, in order to get odd 9(1+2+1) outie cage total
41i. -> no 2 in R6C7

42. Hidden pair (HP) in N5 at R46C5 = {12}, locked for C5
42a. cleanup: no 7 in R4C4 (step 15), no 7 in R5C7 (step 19a), no 3 in R5C8 (step 41c)

43. Hidden single (HS) in R5 at R5C3 = 7

44. 9 in N4 locked in 16(3) at R5C1 = {169/259) (no 4)
44a. 9 locked in R6C12 for R6

45. HS in N4 at R5C2 = 4
45a. -> R7C3 = 2
45b. -> R9C3 = 4

46. Naked pair (NP) at R4C49 = {89}, locked for R4

47. NP at R57C7 = {89}, locked for C7

48. Innies N5789: R4C4+R7C7 = 17(1+1) = {89}
48a. -> no 8,9 in R7C4 (CPE)

49. Outies N14: R124C4 = 17(3)
49a. R124C4 cannot contain both of {89}, as this would cause cage sum to be exceeded
49b. -> {89} only in R4C4
49c. -> no 8 in R1C4

50. 17(3) cage at R1C3 (step 38) = {179/269/359} (no 4)
(Note: {467} unplaceable, since {47} only in R1C4)
50a. -> 9 locked in R12C3 for C3 and N1

51. 4 in C1 locked in 15(3) at R1C1 = {348/456} (no 1,2,7)

52. 14(3) at R3C1 (step 39) = {158/167/257} (no 3)
(Note: {356} blocked by 15(3) at R1C1 (step 51))
52a. has only one of {56}, which must go in R4C1
52b. -> no 5,6 in R3C12

53. Innies N2: R12C46 = 20(4)
53a. from step 28, R12C6 must sum to 11 or 12 (because R4C9 = {89}), and thus can only have one of {89}
53b. -> R12C46 cannot contain both of {89}
53c. -> {1289} combo blocked
53d. -> R12C46 cannot contain both of {12} (because this is only possible 20(4) combo with both of {12})
53e. -> 25(5) must contain one of {12}, which must be within R3C46
(Note: can't contain both, because R3C12 requires one of them)
53f. -> R3C12 and R3C46 form killer pair on {12} within R3
53g. -> no 1,2 elsewhere within R3

54. 18(3) at R3C8 (step 40) = {369/378/459/468}
54a. -> only one of {89}, which must go in R4C9
54b. -> no 8,9 in R3C89

55. R2C8 and 15(3) at R1C8 form hidden killer pair on {89} within N3
55a. -> R2C8 = {89}, 15(3) at R1C8 = {(8/9)..} = {159/168/249/258/348} (no 7)

56. 9 in R3 locked in R3C456 for N2

57. 14(3) at R1C6 and 15(3) at R1C8 form hidden killer pair on {12} within N3
57a. -> 14(3) at R1C6 = {(1/2)..} = {158/167/248/257} (no 3),
15(3) at R1C8 = {(1/2)..} = {159/168/249/258/267} (no 3)
57b. no 2 in R1C6

58. 3 in N3 locked in R3C789 for R3

59. 15(3) at R1C1 (step 51) = {348}, locked for N1
(Note: {456} blocked by R3C3)

60. 8 in R3 locked in R3C456 for N2

61. {89} in R3 already locked in 25(5) at R1C5 (steps 56 and 60)
61a. leaves split 8(3) for the remaining three cells = {134}
(Note: not {125} because, due to R3C456 containing both of {89}, there's only room for one of {12})
61b. -> 25(5) at R1C5 = {13489} (last combo)
61c. -> 1 locked in R3C46 for R3 and N2; R12C5 = {34}, locked for C5 and N2

62. NP at R3C12 = {27}, locked for R3 and N1
62a. -> R4C1 = 5 (cage sum)
62b. -> R4C9 = 9 (step 1)
62c. -> R4C4 = 8, R5C7 = 8
62d. -> R7C7 = 9
62e. -> R9C7 = 5 (step 3)
62f. -> R6C5 = 2 (outie cage sum, step 8)
62g. -> R4C5 = 1, R5C8 = 2 (step 41c)
62h. -> R4C3 = 3, R6C7 = 1 (cage sum)
62i. -> R4C2 = 2
62j. -> R3C2 = 7
62k. -> R3C1 = 2

63. NP at R6C12 = {69}, locked for R6 and N4
63a. -> R5C1 = 1

64. 7 in N3 locked in R12C7 for C7 and 14(3)

65. Naked single (NS) at R4C7 = 6
65a. -> R4C8 = 7

66. 14(3) at R1C6 must contain a 7 (step 64) = {257} (last combo)
66a. -> R1C6 = 5, 2 locked in r12C7 for C7 and N3

67. Outie N3: R2C6 = 6

68. Split 12(2) at R5C46 = {39} (last combo), locked for R5 and N5

69. NS at R5C9 = 5
69a. -> R5C5 = 6
69b. -> split 12(2) = [57]
69c. -> R7C6 = 8
69d. -> R7C4 = 4

70. HS in C8 at R3C8 = 5
70a. -> R3C3 = 6, R3C9 = 4 (cage sum)
70b. -> R3C7 = 3, R6C9 = 3
70c. -> R2C8 = 9 (cage sum), R6C8 = 4, R8C7 = 4

71. HS in R1/C3/N1 at R1C3 = 9
71a. -> split 8(2) at R1C4+R2C3 = [71] (last permutation)

72. R12C7 = [27], R2C249 = [528]

73. NS at R8C3 = 5

74. NP at R89C5 = {79}, locked for C5 and N8

75. R37C5 = [85]

76. Split 11(3) at R7C89+R8C8 = {137} (last combo)
76a. -> R7C9 = 7; R78C8 = {13}, locked for C8 and N9

77. NS at R1C8 = 6
77a. -> R1C9 = 1, R9C8 = 8

78. Split 17(3) at R7C12+R8C2 = {368} (last combo)
78a. -> R8C2 = 8;, R7C12 = {36}, locked for R7 and N7

79. NS at R1C2 = 3
79a. -> R1C5 = 4, R2C1 = 4
79b. -> R1C1 = 8, R2C5 = 3, R7C2 = 6
79c. -> R6C2 = 9, R7C1 = 3
79d. -> R6C1 = 6, R9C2 = 1

80. NS at R7C8 = 1
80a. -> R8C8 = 3

81. Split 16(3) at R8C46+R9C5 = [619] (last permutation)

82. NS at R3C6 = 9
82a. -> R3C4 = 1, R5C6 = 3
82b. -> R5C4 = 9

83. R8C5+R9C46 = [732]

84. R89C19 = [9276]

Grid state after step 84:

Code:
.-------.-------.---.-------.-------.
| 8   3 | 9   7 | 4 | 5   2 | 6   1 |
|   .---:   .---:   :---.   :---.   |
| 4 | 5 | 1 | 2 | 3 | 6 | 7 | 9 | 8 |
:---'---+---+---'   '---+---+---'---:
| 2   7 | 6 | 1   8   9 | 3 | 5   4 |
|   .---'---'---.---.---'---'---.   |
| 5 | 2   3   8 | 1 | 4   6   7 | 9 |
:---+---.   .---+---+---.   .---+---:
| 1 | 4 | 7 | 9 | 6 | 3 | 8 | 2 | 5 |
|   '---+---+---+---+---+---+---'   |
| 6   9 | 8 | 5 | 2 | 7 | 1 | 4   3 |
:-------:   :---+---+---:   :-------:
| 3   6 | 2 | 4 | 5 | 8 | 9 | 1   7 |
:---.   '---+---+---+---+---'   .---:
| 9 | 8   5 | 6 | 7 | 1 | 4   3 | 2 |
|   '---.---'---+---+---'---.---'   |
| 7   1 | 4   3 | 9 | 2   5 | 8   6 |
'-------'-------'---'-------'-------'

:cheesey:

Many thanks to Afmob for a great puzzle! :thumbs:

_________________
Cheers,
Mike


Last edited by mhparker on Tue Jun 01, 2010 6:46 am, edited 1 time in total.

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