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Ed
 Post subject: Assassin 317
PostPosted: Fri May 01, 2015 11:33 pm 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
Been so absorbed in trying to solve ixsetf's last few puzzles forgot I hadn't done a validation solve on my next Assassin so a day late. It's quite tricky but enjoyed it a lot. Always felt like I was getting somewhere. It gets a score of 1.65

Assassin 317

Image
code: paste into solver:
3x3::k:9472:9472:9472:9472:4097:4097:2306:1283:1283:9472:4356:4356:3589:3589:4102:2306:5895:5895:9472:4356:4356:3589:9992:4102:4102:4102:5895:9472:5129:5129:9992:9992:3850:3850:3850:5895:3595:5129:9992:9992:4364:4364:3085:3850:5134:3595:6159:6159:9992:4364:4364:3085:5134:5134:3595:3595:6159:9992:7440:7440:5393:5393:5134:2578:5651:6159:1812:1812:7440:5393:5393:4629:2578:5651:5651:5651:7440:7440:7440:4629:4629:
solution: 
+-------+-------+-------+
| 8 5 2 | 3 7 9 | 6 1 4 |
| 4 1 6 | 2 8 5 | 3 7 9 |
| 9 3 7 | 4 6 1 | 2 8 5 |
+-------+-------+-------+
| 6 7 4 | 8 9 3 | 1 5 2 |
| 5 9 3 | 1 2 4 | 8 6 7 |
| 1 2 8 | 7 5 6 | 4 9 3 |
+-------+-------+-------+
| 2 6 9 | 5 4 8 | 7 3 1 |
| 3 4 5 | 6 1 7 | 9 2 8 |
| 7 8 1 | 9 3 2 | 5 4 6 |
+-------+-------+-------+
Cheers
Ed
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Afmob
 Post subject:
PostPosted: Sat May 02, 2015 7:02 pm 
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Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Killer, Ed! I'm quite surprised by SudokuSolver's score since this Assassin doesn't need any particular hard moves to crack it. I'll have to check its solving path.

A317 Walkthrough:
1. C789+N8
a) Innies+Outies N6: 2 = R4C6+R7C9 - R4C9 -> R4C6+R7C9 <> 2 (IOU @ R4+C9)
b) Innies+Outies C789: 4 = R234C6 - R9C7 -> R9C7 <> 1
c) Innies N9 = 6(2) = [15/42]
d) Innies N89 = 15(2+1): R9C4 <> 1,7 and R7C4 <> 1,4 since R7C9 = (14)

2. C456 !
a) 16(2) = {79} locked for R1+N2
b) R4C5 <> 7 since it sees all 7 of C4
c) ! Outies C1234 = 24(4) must have one of (79) -> R4C5 = 9
d) Hidden Single: R9C4 = 9 @ C4
e) Innies+Outies N8: R7C4 = R9C7 = (25)
f) 39(7) = 36789{15/24} -> R3C5+R456C4+R5C3 <> 2,5 since R7C4 = (25)
g) Innies+Outies C123: R1C4 = R5C3 <> 2,5,7
h) 7(2) <> {25} since it's blocked by R7C4 = (25)

3. C456 !
a) R3C5 <> 8 since it sees all 8 of C4
b) Outies C1234 = 24(4) = 9{168/348/456} since R38C5 <> 2,5 -> R2C5 = (58)
c) ! Hidden Killer pair (25) in 14(3) @ C4 = 8{15/24} since R2C5 = (58) -> R2C5 = 8
d) Innies+Outies C123: R1C4 = R5C3 <> 8
e) 39(7) = 36789{15/24} -> 7,8 locked for N5
f) 17(4) = {2456} locked for N5

4. N1236
a) Innies+Outies N6: 2 = R4C6+R7C9 - R4C9: R4C9 = (235) since R4C6+R7C9 = (134)
b) Outies N3 = 8(2+1) <> 6 since R4C9 >= 2
c) 6 locked in R1C4+R3C5 @ N2 -> Innies+Outies N23: -7 = R4C9 - (R1C4+R3C5) = 2-{36} / 3-{46} <> 1,5
d) Outies N1 = 9(2) = {36}/[45]

5. R456 !
a) 37(7) = 489{1267/1357/2356} -> 8,9 locked for N1; 9 also locked for C1
b) 9 locked in 24(4) @ C3 for 24(4)
c) Hidden Single: R5C2 = 9 @ C2
d) Using R9C4 = 9: Innies N47 = 9(2) = {36}/[54]
e) 20(3) <> 5,6 since {569} blocked by Killer pair (56) of Innies N47
f) ! Hidden Killer pair (56) in 15(4) for R4 -> 15(4) = 15{27/36} since {2346} blocked by R4C9 = (23) -> 5 locked for N6
g) 4 locked in 20(3) @ R4 = {479} -> 4,7 locked for R4+N4
h) Innies N47 = 9(2) = {36} locked for N4
i) Outies N1 = 9(2) = {36} locked for 37(7)
j) 37(7) = {2345689} since R1C4+R4C1 = (36) -> 2,4,5 locked for N1

6. R123+N6
a) 9(2): R1C7 <> 1
b) 1 locked in 5(2) @ R1 = {14} locked for R1+N3
c) 37(7) = {2345689} -> R23C1 = (49) locked for C1; 2,5,8 locked for R1
d) 9(2) = {36} locked for C7+N3
e) 12(2) = {48} locked for C7+N6

7. C123
a) 10(2) = {37} locked for C1+N7 since {28} blocked by R156C1 = (1258)
b) R4C1 = 6, XR1C4 = 3, R5C3 = 3
c) 14(4) = {1256} -> R7C2 = 6; 2,5 locked for C1
d) 22(4) = {1489} -> 1,4,8 locked for N7
e) 39(7) = {1356789} since R456C4 = (178) -> R3C5 = 6, R7C4 = 5; 1 locked for C4+N5

8. N69
a) 15(4) = {1356} since R4C6 = 3 -> R4C6 = 3, R5C8 = 6; 1 locked for R4+N6
b) 20(4) = {1379} -> R5C9 = 7, R7C9 = 1
c) 23(4) = {2579} -> R4C9 = 2, R2C8 = 7; 5,9 locked for C9+N3
d) 18(3) = {468} locked for N9

9. Rest is singles.

Rating:
Hard 1.0. I used two Hidden Killer pairs.
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Andrew
 Post subject: Re: Assassin 317
PostPosted: Tue May 05, 2015 4:51 pm 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin. It took me quite a long time and my solving path is longer and harder than Afmob's optimised walkthrough.

I'm also surprised at the SS score. I didn't use any technically difficult steps.

Here is my walkthrough for Assassin 317:
Prelims

a) R1C56 = {79}
b) R12C7 = {18/27/36/45}, no 9
c) R1C89 = {14/23}
d) R56C7 = {39/48/57}, no 1,2,6
e) R89C1 = {19/28/37/46}, no 5
f) R8C45 = {16/25/34}, no 7,8,9
g) 20(3) cage at R4C2 = {389/479/569/578}, no 1,2
h) 14(4) cage at R5C1 = {1238/1247/1256/1346/2345}, no 9

1. Naked pair {79} in R1C56, locked for R1 and N2, clean-up: no 2 in R2C7

2. 45 rule on N1 2 outies R1C4 + R4C1 = 9 = {18/36/45}/[27], no 2,9 in R4C1
2a. 37(7) cage at R1C1 must contain 9, locked for C1 and N1, clean-up: no 1 in R89C1

3. 45 rule on N9 2 innies R7C9 + R9C7 = 6 = {15/24}

4. 14(4) cage at R5C1 = {1238/1256/1346/2345} (cannot be {1247} which clashes with R89C1), no 7
[Note. All the cells of 14(4) cage at R5C1 and R89C1 ‘see’ each other, so form combined 24(6) cage but that’s not needed for my solving path.]

5. 45 rule on N8 2 innies R79C4 = 1 outie R9C7 + 9, IOU, no 9 in R7C4

6. 45 rule on C123 2 outies R19C4 = 1 innie R5C3 + 9, max R19C4 = 17 -> max R5C3 = 8

7. 39(7) cage at R3C5 must contain 9, locked for N5

8. 45 rule on N3 3(2+1) outies R23C6 + R4C9 = 8
8a. Min R23C6 = 3 -> max R4C9 = 5
8b. Max R23C6 = 7, no 8 in R23C6

9. 45 rule on C1234 4 outies R2348C5 = 24 = {1689/2589/3489/3678/4569/4578} (cannot be {2679/3579} which clash with R1C5)
9a. 7,9 only in R4C5 -> R4C5 = {79}
9b. Naked pair {79} in R14C5, locked for C5

10. 45 rule on N47 2 innies R4C1+ R5C3 = 1 outie R9C4
10a. Min R4C1 + R5C3 = 3 -> min R9C4 = 3

11. 45 rule on C789 3 outies R234C6 = 1 innie R9C7 + 4
11a. Min R234C6 = 6 -> min R9C7 = 2, clean-up: no 5 in R7C9 (step 3)
11b. Max R9C7 = 5 -> max R234C6 = 9, no 7,8 in R4C6

12. 45 rule on N6 2(1+1) outies R4C6 + R7C9 = 1 innie R4C9 + 2, IOU no 2 in R4C6
[Oops! I missed that this also gives IOU no 2 in R7C9 :oops: , I got it with a different IOU in step 17.]

[Just spotted]
13. Hidden killer pair 7,9 in R4567C4 and R9C4 for C4, R4567C4 cannot contain both of 7,9 -> R9C4 = {79}, R4567C4 must contain one of 7,9
13a. R79C4 = R9C7 + 9 (step 5)
13b. R9C7 = {245} -> R79C4 = 11,13,14 = [29/47/49/67/59] -> R7C4 = {2456}
13c. Killer pair 7,9 in R456C4 and R4C5, locked for N5 and 39(7) cage at R3C5, no 7 in R5C3

14. Hidden killer quad 6,7,8,9 in 15(4) cage at R4C6, R56C7 and 20(4) cage at R5C9 for N6, R56C7 contains one of 7,8,9, 20(4) cage cannot contain more than two of 6,7,8,9 -> 15(4) cage must contain one of 6,7,8,9 in N6, 15(4) cage only contains one of 6,7,8,9 -> no 6 in R4C6

15. Max R234C6 = 9 (step 11b)
15a. R23C6 + R4C9 = 8 (step 8) cannot be [16]1 (because no 2 in R4C6) -> no 6 in R23C6

16. Min R1C23489 = 15 -> min R1C234 = 10
16a. 45 rule on C1 4(3+1) outies R1C234 + R7C2 = 16, min R1C234 = 10 -> max R7C2 = 6

17. 45 rule on N69 2 innies R4C9 + R9C7 = 1 outie R4C6 + 4, IOU no 4 in R9C7, clean-up: no 2 in R7C9 (step 3)
17a. R4C6 = {1345} -> R4C9 + R9C7 = 5,7,8,9 = [32/25/52/35/45], no 1 in R4C9

18. 45 rule on N89 3(2+1) innies R7C49 + R9C4 = 15 = [249/519] (cannot be {26}7 because 2,6 only in R7C4) -> R9C4 = 9, no 4,6 in R7C4
18a. R4C5 = 9 (hidden single in N5)
18b. 9 in N7 only in R78C3, locked for 24(4) cage at R6C2
18c. R5C2 = 9 (hidden single in N4), clean-up: no 3 in R6C7
18d. R8C45 = {16/34} (cannot be {25} which clashes with R7C4), no 2,5 in R8C45

19. 39(7) cage at R3C5 = {1356789/2346789}
19a. R7C4 = {25} -> no 2,5 in R3C5 + R456C4 + R5C3
19b. 2 in R4 only in R4C789, locked for N6

20. R234C6 = R9C7 + 4 (step 11)
20a. R9C7 = {25} -> R234C6 = 6,9 = {123/135/234}, 3 locked for C6

21. R4C1+ R5C3 = R9C4 (step 10), R9C4 = 9 -> R4C1 + R5C3 = {18/36}/[54], no 4,7, in R4C1 clean-up: no 2,5 in R1C4 (step 2)

22. 14(3) cage at R2C4 = {158/248/356}
22a. Hidden killer pair 2,5 in 14(3) cage and R7C4 for C4, R7C4 = {25} -> 14(3) cage must contain one of 2,5 in R23C4, no 2,5 in R2C5
22b. Hidden killer pair 2,5 in 14(3) cage and R23C6 for N2, 14(3) cage contains one of 2,5 -> R23C6 must contain one of 2,5
22c. R23C6 + R4C9 = 8 (step 8) = {12}5/{23}3/{15}2/{24}2 (cannot be {13}4 which doesn’t contain one of 2,5), no 4 in R4C9
22d. R234C6 (step 20a) = {123/135/234}
22e. 5 of {135} must be in R23C6 -> no 5 in R4C6

23. 2,5 in N5 only in 17(4) cage at R5C5 = {2456}, locked for N5
23a. 8 in N5 only in R456C4, locked for C4 and 39(7) cage at R3C5, no 8 in R3C5 + R5C3, clean-up: no 1 in R4C1 (step 2)

24. R2C5 = 8 (hidden single in N2) -> R12C4 = 6 = {15/24}, clean-up: no 1 in R1C7

25. 45 rule on N23 2 innies R1C4 + R3C5 = 1 outie R4C9 + 7
25a. Max R1C4 + R3C5 = 10 -> max R4C9 = 3
25b. Min R1C4 + R3C5 = 9, no 1 in R1C4 + R3C5, clean-up: no 8 in R4C1 (step 2), no 1 in R5C3 (step 21)

26. R4C9 + R9C7 = R4C6 + 4 (step 17)
26a. R4C6 = {13} -> R4C9 + R9C7 = 5,7 = [32/25] -> R4C69 + R9C7 = [132/325], 3 locked for R4, clean-up: no 6 in R1C4 (step 2), no 6 in R5C3 (step 21)
26b. 20(3) cage at R4C2 = {479} (only remaining combination, cannot be {569} which clashes with R4C1) -> R4C23 = {47}, locked for R4 and N4 -> R5C3 = 3, R4C1 = 6 (step 21), R1C4 = 3 (step 2)
26c. R1C7 = 6 (hidden single in R1), R2C7 = 3
26d. Naked triple {178} in R456C4, 1 locked for C4 and N5 -> R4C69 = [32], clean-up: no 5 in R23C4 (step 24)
26e. Naked pair {24} in R23C4, locked for C4 and N2 -> R7C4 = 5, R8C4 = 6 -> R8C5 = 1
26f. 2 in N8 locked for 29(6) cage -> R9C7 = 5, R7C9 = 1 (step 3), R1C9 = 4 -> R1C8 = 1
26g. Naked triple {258} in R1C123, locked for N1
26h. 37(7) cage at R1C1 must contain 4,9 -> R23C1 = {49}, locked for C1 and N1

27. 7 in C1 only in R89C1 = {37}, locked for N7

28. Naked pair {15} in R23C6, 5 locked for C6
28a. R23C6 = 6 -> R3C78 = 10 = {28}, locked for R3 and N3

29. R56C7 = {48} (only remaining combination), locked for C7 and N6 -> R3C7 = 2
29a. Naked pair {79} in R78C7, locked for N9
29b. R78C7 = 16 -> R78C8 = 5 = {23}, locked for C8 and N9

30. R4C678 = [315], R5C8 = 6 (cage sum)

31. 14(4) cage at R5C1 (step 4) = {1256} (only remaining combination) -> R56C1 = {15}, locked for C1 and N4, R7C12 = [26]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A317 at Hard 1.25. I used a hidden killer quad. It may not have been necessary, but it was the step I happened to spot at that stage.
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