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Ed
 Post subject: Assassin 305
PostPosted: Fri Dec 05, 2014 7:04 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Came to a stand-still fairly early but then after a breakthrough wondered if it might be a touch easy for an Assassin. Then came the middle....! Finally worked out what I missed. Before finding that, a very hard puzzle and very resistant but as with most of my puzzles, lots of areas to explore..it gets a SudokuSolver score of 1.40

Assassin 305

Image

Code: paste into solver:
3x3::k:2304:4353:5378:5378:5891:5891:5891:4612:4612:2304:4353:4353:5378:5378:3077:5891:4612:4612:3334:3334:7687:3848:3077:3077:1289:1289:5386:7435:7435:7687:3848:3848:3848:6668:5386:5386:7435:7687:7687:7687:3085:3085:6668:6668:6668:7435:7435:7687:4366:3599:3599:6668:6160:6160:2321:2321:7687:4366:3090:3090:6160:6160:6160:2323:4628:4628:4366:4366:3090:5653:4886:4886:2323:4628:2583:2583:5653:5653:5653:4886:4886:
Solution: 
+-------+-------+-------+
| 6 1 2 | 7 3 5 | 9 4 8 |
| 3 9 7 | 8 4 2 | 6 1 5 |
| 8 5 4 | 6 1 9 | 3 2 7 |
+-------+-------+-------+
| 7 8 6 | 3 2 4 | 1 5 9 |
| 1 2 3 | 9 5 7 | 8 6 4 |
| 9 4 5 | 1 6 8 | 7 3 2 |
+-------+-------+-------+
| 2 7 1 | 5 8 3 | 4 9 6 |
| 5 6 9 | 4 7 1 | 2 8 3 |
| 4 3 8 | 2 9 6 | 5 7 1 |
+-------+-------+-------+
Cheers
Ed
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Afmob
 Post subject:
PostPosted: Fri Dec 05, 2014 8:16 pm 
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for this fun Killer, Ed! I've solved it fairly quickly despite a false start but it took some time to optimize the walkthrough.

A305 Walkthrough:
1. R123 !
a) Innie R12 = R2C6 = 2
b) 12(3) = 2{19/37/46} <> 5,8
c) Innies N1 = 6(2) = {15/24}
d) 9(2) <> {45} since it's a Killer pair of Innies N1
e) Innies R123 = 17(3)
f) ! Killer quad (1234) locked in 12(3) + 5(2) + Innies R123 for R3
g) 13(2) <> 9
h) 9 locked in 17(3) @ N1 = 9{17/26/35} <> 4,8
i) 4 locked in Innies N1 = 6(2) = {24} locked for C3+N1

2. C123+N5 !
a) Innies+Outies C12: 14 = R28C3 - R5C2 -> R5C2 = (123), R28C3 <> 1,3,5
b) ! Innies+Outies N5: -4 = R3C4 - R56C4 -> R56C4 <> 4 (IOU @ C4)
c) 30(7) = 12345{69/78} -> R3C3 = 4; 2 locked for R5
d) Innies N7 = 9(2) = {18/36}
e) Outies N4 = 10(2) = [28/73/91]
f) 9 locked in 29(5) @ C1 for N4
g) Outies C1 = 24(4) = 78{36/45} -> 7,8 locked for C2
h) 17(3) = {179} since {35}9 blocked by Killer pair (35) of Outies C1 -> R2C3 = 7; 1,9 locked for C2+N1

3. R123
a) 5(2) = {23} locked for R3+N3
b) 12(3) = {129} -> 1,9 locked for R3+N2
c) 13(2) = {58} locked for R3+N1
d) Innies N3 = 22(3) = {679} locked for N3 since R3C9 = (67); 9 also locked for C7
e) 9 locked in 23(4) @ N3 = 39{47/56} -> 3 locked for R1+N2; R1C56 = (345)

4. C1234
a) Innies N7 = 9(2) = {18}/[36]
b) 3 locked in 30(7) @ C3 for 30(7)
c) Innies+Outies C12: 7 = R8C3 - R5C2: R5C2 = 2, R8C3 = 9
d) 7 locked in R13C4 @ N2 for C4
e) Outies N4 = 10(2) = [91] -> R5C4 = 9, R7C3 = 1
f) 30(7) = {1234569} -> 3,5,6 locked for C3+N4
g) R9C3 = 8 -> R9C4 = 2

5. N35689
a) 14(2) = {68} locked for R6+N5
b) 12(2) = {57} locked for R5+N5
c) 2 locked in 15(4) @ N5 = {2346} -> R3C4 = 6, R4C5 = 2; 3,4 locked for R4+N5
d) Outies N69 = 22(2+1) -> R3C9 = 7; 6,9 locked for R9+N8+22(4)
e) 22(4) = 69{25/34}
f) Killer pair (23) locked in R3C7 + 22(4) for C7
g) 2 locked in 24(5) @ R6 for 24(5) <> {13569}
h) Hidden Single: R7C1 = 2 @ R7 -> R7C2 = 7
i) 6,9 locked in 24(5) @ R7 for N9+24(5) -> 24(5) = {23469}
j) 22(4) = {2569} since {3469} blocked by R7C789 = (3469) -> R9C7 = 5, R8C7 = 2
k) R6C4 = 1
l) 1 locked in 12(3) @ N8 = {138} since R7C56 <> 1,7

6. Rest is singles.

Rating:
1.25. I used IOU and a Killer quad.
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Andrew
 Post subject: Re: Assassin 305
PostPosted: Mon Dec 08, 2014 10:07 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for an interesting Assassin. I enjoyed the early steps, particularly step 10b which simplified step 11, but struggled to find my final breakthrough.

Afmob found a quicker way to get into this puzzle. I'd seen his step 1e, but hadn't spotted the follow-on step 1f which I ought to have seen. Then steps 2g and 2h, even though not marked by !, made his later steps much shorter and simpler than mine were after the first three placements.

Here is my walkthrough for Assassin 305:
Thanks Afmob for the corrections.

Prelims

a) R12C1 = {18/27/36/45}, no 9
b) R3C12 = {49/58/67}, no 1,2,3
c) R3C78 = {14/23}
d) R5C56 = {39/48/57}, no 1,2,6
e) R6C56 = {59/68}
f) R7C12 = {18/27/36/45}, no 9
g) R89C1 = {18/27/36/45}, no 9
h) R9C34 = {19/28/37/46}, no 5
i) 21(3) cage at R3C9 = {489/579/678}, no 1,2,3

1. 45 rule on R12 1 innie R2C6 = 2, clean-up: no 7 in R1C1
1a. R2C6 = 2 -> R3C56 = 10 = {19/37/46}, no 5,8

2. 45 rule on N1 2 innies R13C3 = 6 = {15/24}
2a. R12C1 = {18/36}/[27] (cannot be {45} which clashes with R13C3), no 4,5

3. 45 rule on N3 3 innies R12C7 + R3C9 = 22 = {589/679}, 9 locked for N3

4. 45 rule on N7 2 innies R79C3 = 9 = {18/27/36} (cannot be [54] which clashes with R13C3), no 4,5,9, clean-up: no 1,6 in R9C4

5. 45 rule on N69 1 outie R3C9 = 2 innies R89C7, max R89C7 = 9, no 9 in R89C7
5a. 45 rule on N69 3(2+1) outies R3C9 + R9C56 = 22 -> min R9C56 = 13, no 1,2,3 in R9C56

6. 45 rule on N5 2 innies R56C4 = 1 outie R3C4, IOU no 4 in R56C4

7. R5C56 = {39/48/57}, R6C56 = {59/68} -> combined cage R56C56 = {39}{68}/{48}{59}/{57}{68}, 8 locked for N5

8. 45 rule on C12 2 outies R28C3 = 1 innie R5C2 + 14
8a. Max R28C3 = 17 -> max R5C2 = 3
8b. Min R28C3 = 15, no 1,2,3,4,5 in R28C3

9. 9 in N1 only in 17(3) cage at R1C2 = {179/269/359} or in R3C12 = {49} -> 17(3) cage = {179/269/278/359/368} (cannot be {458/467}, locking-out cages), no 4
9a. 4 in N1 only in R13C3 (step 2) = {24} or R3C12 = {49} -> 17(3) cage = {179/278/359/368} (cannot be {269}, blocking cages)

10. 45 rule on N23 2 innies R3C49 = 1 outie R1C3 + 11
10a. Min R3C49 = 12 -> no 1 in R3C4
10b. R1C3 + R3C49 cannot be 5 + 16 = 5{79} which clashes with R3C12 -> no 5 in R1C3, clean-up: no 1 in R3C3 (step 2)

11. 1 in R3 only in R3C56 (step 1a) = {19} or R3C78 = {14} -> R3C56 = {19/37} (cannot be {46}, locking-out cages), no 4,6
11a. Killer pair 1,3 in R3C56 and R3C78, locked for R3
11b. 1 in R3 only in R3C56 (step 1a) = {19} or R3C78 = {14} -> R3C12 = {58/67} (cannot be {49}, blocking cages), no 4,9

12. 4 in N1 only in R13C3 (step 2) = {24}, locked for C3 and N1, clean-up: no 7 in R2C1, no 7 in R79C3 (step 4), no 3,8 in R9C4

13. 30(7) cage at R3C3 must contain 4 -> R3C3 = 4, R1C3 = 2, clean-up: no 1 in R3C78
13a. Naked pair {23} in R3C78, locked for R3 and N3, clean-up: no 7 in R3C56 (step 1a)
13b. Naked pair {19} in R3C56, locked for R3 and N2
13c. Killer pair 6,8 in R12C1 and R3C12, locked for N1
13d. 9 in N3 only in R12C7, locked for C7
13e. 9 in C1 only in R456C1, locked for N4
13f. R3C9 = R89C7 (step 5), max R3C9 = 8 -> max R89C7 = 8, no 8 in R89C7
13g. R3C9 + R9C56 = 22 (step 5a), max R3C9 = 8 -> min R9C56 = 14, no 4 in R9C56

14. R1C3 = 2 -> 21(4) cage at R1C3 = {2478/2568}, no 3, 8 locked for N2

15. 3 in N2 only in R1C56, locked for R1, clean-up: no 6 in R2C1
15a. 3 in N2 and 9 in N3 both in 23(4) cage at R1C5 = {3479/3569}, no 8
15b. 7,9 of {3479} must be in R12C7 -> no 7 in R1C56
15c. 8 in C7 only in R4567C7, CPE no 8 in R6C89

16. 45 rule on N4 2 remaining outies R5C4 + R7C3 = 10 = [28/73/91], clean-up: no 3 in R9C3 (step 4), no 7 in R9C4

17. 15(4) cage at R3C4 = {1257/1347/1356/2346} (cannot be {1239} because R3C4 only contains 5,6,7), no 9

18. 30(7) cage at R3C3 = {1234569/1234578}, 2 locked for R5, 5 locked for N4

19. 45 rule on C123 2 outies R59C4 = 11
19a. R56C4 = R3C4 + 4 (step 6)
19b. R56C4 cannot total 11 (CCC because R59C4 = 11) -> no 7 in R3C4
19c. R3C4 = {56} -> R56C4 = 9,10 = {27}/[91] (cannot be [73] which clashes with 15(4) cage R3C4), no 3,5,6, no 9 in R6C4
19d. Killer triple 7,8,9 in R56C4, R5C56 and R6C56, locked for N5
19e. Hidden killer pair 7,8 in R3C12 and R3C9 for R3, R3C12 contains one of 7,8 -> R3C9 = {78}

20. 15(4) cage at R3C4 (step 17) = {1356/2346}, 3 locked for R4 and N5, clean-up: no 9 in R5C56
20a. Killer pair 5,8 in R5C56 and R6C56, locked for N5

21. 7 in N2 only in 21(4) cage at R1C3 (step 14) = {2478}, 4 locked for N2
21a. 23(4) cage at R1C5 (step 15a) = {3569}, no 7
21b. 23(4) cage = {3569}, CPE no 5,6 in R1C89

22. R59C4 = 11 (step 19) = {29} (cannot be [74] which clashes with R12C4, ALS block), locked for C4, clean-up: no 6 in R9C3, no 3 in R7C3 (step 4)
22a. Naked pair {18} in R79C3, locked for C3 and N7
22b. 3 in C3 only in R56C3, locked for N4

23. R3C9 + R9C56 = 22 (step 5a), R3C9 = {78} -> R9C56 = 14,15 = {59/68/69/78}
23a. Killer pair 8,9 in R9C34 and R9C56, locked for R9
23b. 9 in R9 only in R9C456, locked for N8
23c. 9 in R7 only in R7C89, locked for N9 and 24(5) cage at R6C8, no 9 in R6C89

24. 45 rule on N6 1 outie R3C9 = 2 innies R6C89 + 2, max R3C9 = 8 -> max R6C89 = 6, no 6,7 in R6C89

[Took me some time to spot …]
25. R9C56 (step 23) = {59/68/69/78}
25a. 45 rule on N8 3 innies R9C456 = 1 outie R6C4 + 16
25b. R6C4 = {17} -> R9C456 = 17,23 = 2{69}/9{68} (cannot be 2{78} which clashes with R9C34 = [82]), no 5,7, 6 locked for R9, N8 and 22(4) cage at R8C7, no 6 in R8C7, clean-up: no 3 in R8C1

26. 17(4) cage at R6C4 = {1358/1457/2357} (cannot be {2348} because R6C4 only contains 1,7), 5 locked for N8

27. 45 rule on R89 4(3+1) outies R6C4 + R7C456 = 17 = 1{358}/1{457}/7{127}/7{145} (cannot be 1{178} which clashes with R7C3, cannot be 7{235} which clashes with R7C12)
27a. 5 of 1{358}/1{457}/7{145} must be in R7C4, 7{127} must be 7[127] -> R7C4 = {15}
27b. R6C4 + R7C456 = 1{358}/1{457}/7{127}/7{145}, CPE no 1 in R8C4

28. 17(4) cage at R6C4 (step 26) = {1358/1457/2357}
28a. 5 of {1358} must be in R7C4, 2 of {2357} must be in R8C5, 5 of {1457} must be in R78C4 (R678C4 cannot be {147} which clashes with R12C4, ALS block) -> no 5 in R8C5
28b. 5 in N8 only in R78C4, locked for C4
[Cracked, at last.]

29. R3C6 = 6 -> R4C456 = 9 = {234} -> R4C5 = 2, R4C46 = {34}, locked for R4 and N5, R5C4 = 9, R9C4 = 2 -> R9C3 = 8, R7C3 = 1, R5C2 = 2, R7C4 = 5, clean-up: no 7 in R3C12, no 8 in R5C56, no 5 in R6C56, no 4,7 in R7C1, no 4 in R7C2, no 7 in R8C1
29a. Naked pair {58} in R3C12, locked for R3 and N1 -> R3C9 = 7, clean-up: no 1 in R12C1
29b. R12C1 = [63], R7C1 = 2 -> R7C2 = 7
29c. Naked pair {45} in R89C1, locked for C1 and N7 -> R3C12 = [85], R9C2 = 3
29d. Naked pair {19} in R12C2, locked for C2 and N1 -> R2C3 = 7, R8C23 = [69]
29e. Naked pair {35} in R1C56, locked for 23(4) cage at R1C5 -> R12C7 = [96]
29f. Naked pair {48} in R2C45, locked for R2 and N2 -> R16C4 = [71]

30. R3C9 = R6C89 + 2 (step 24), R3C9 = 7 -> R6C89 = 5 = {23}, locked for R6, N6 and 24(5) cage at R6C8, no 3 in R7C789
30a. R7C89 = {69} (hidden pair in R7)
30b. R6C89 = 5, R7C89 = {69} = 15 -> R7C7 = 4 (cage sum)

31. R9C56 = {69} = 15 -> R89C7 = 7 = [25]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A305 at Easy 1.5. I used locking-out cages and blocking cages, also IOU and CCC.
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