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 Post subject: Assassin 316
PostPosted: Thu Apr 16, 2015 9:50 pm 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 829
Location: Sydney, Australia
This is my 101st V1 Assassin! Messed this up the first few times I tried it. A real good struggle when it did finally come out. A bit nit-picky for my taste but well worth the Assassin label. It gets a score of 1.60 JSudoku has a very hard time.

Assassin 316
Image
code: paste into solver:
3x3::k:4608:4608:3585:3585:4610:4355:1796:1796:6149:4608:2310:2310:4610:4610:4355:4355:6149:6149:2823:2310:5648:2063:2057:2057:2826:2826:6149:2823:3339:5648:2063:6924:6924:1037:6670:6149:3339:3339:5648:6924:6924:4888:1037:6670:6670:3857:3857:5648:6924:4888:4888:4888:6670:8978:2835:3857:2836:3607:3607:3607:4886:4886:8978:2835:6165:2836:5128:5128:5128:4886:4886:8978:6165:6165:6165:6165:5128:8978:8978:8978:8978:
solution:
+-------+-------+-------+
| 9 7 8 | 6 5 2 | 4 3 1 |
| 2 1 3 | 9 4 8 | 7 5 6 |
| 4 5 6 | 3 1 7 | 2 9 8 |
+-------+-------+-------+
| 7 3 9 | 5 2 6 | 1 8 4 |
| 6 4 5 | 8 7 1 | 3 2 9 |
| 1 8 2 | 4 3 9 | 6 7 5 |
+-------+-------+-------+
| 3 6 7 | 1 8 5 | 9 4 2 |
| 8 9 4 | 2 6 3 | 5 1 7 |
| 5 2 1 | 7 9 4 | 8 6 3 |
+-------+-------+-------+
Cheers
Ed


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PostPosted: Fri Apr 17, 2015 5:52 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 Assassin, Ed! It wasn't as hard as I initially thought it was but it took me quite some time to solve. Once I had my first walkthrough finished I could easily cut down a lot of steps. It was also interesting that there were some regions which you could completely ignore with regards to cracking this Killer.

A316 Walkthrough:
1. N2356 !
a) 4(2) = {13} locked for C7+N6
b) Innies N2356 = 11(1+1) = {56}/[92]
c) ! Hidden Killer quad (1234) in 18(3) + 17(3) + both 8(2) @ N2 since each can only have one of them -> 18(3) <> {567}; 8(2) @ C4 = [17/26/35]; 17(3): R2C7 <> 2,4
d) Outies N5 = 9(1+1) = [18/27/36]
e) 14(2) = {59}/[86]
f) Outies N23 = 17(2+1): R4C9 <> 6 since R4C4 = (567) and R1C3 <> 4,6
g) Innies+Outies N3: -3 = R4C9 - R2C7 -> R4C9 = (245); R2C8 <> 6,9
h) Outies N25 = 21(2+1): R1C3 <> 5 since R26C7 <> 9
i) 14(2) = [86/95]

2. C123
a) Outies C123 = 13(2) = [58/67]
b) Outies C12 = 11(2+1) = 7+{13} / 8+{12} -> R29C3 = 1{2/3} -> 1 locked for C3
c) Innies N1 = 18(3): R3C13 <> 8,9 since R1C3 = (89) and R3C13 <> 1

3. R123 !
a) Hidden Killer pair (89) locked in 11(2) @ R3C7 + R3C9 @ R3 for N3 since 11(2) can only have one of them -> 11(2) = {29}/[83]; R3C9 = (89)
b) Innies+Outies N3: -3 = R4C9 - R2C7 -> R4C9 <> 5
c) ! 24(5) can only have one of (124) @ N3 since R4C9 = (24) and 8,9 only possible @ R3C9
d) ! Hidden Killer triple (124) in 11(2) @ N3 since each of 7(2) and 24(5) can only have one of them @ N3 -> 11(2) = {29} locked for R3+N3
e) 18(3) @ N1 <> 1 since {189} blocked by R1C3 = (89)
f) 1 locked in 9(3) @ N1 = 1{26/35}
g) 4 locked in Innies N1 = 18(3) @ R3 = 4{59/68} locked for N1
h) 7 locked in 8(2) @ R3C5 @ R3 = {17} locked for N2+R3
i) R3C4 = 3 -> R4C4 = 5, R1C4 = 6 -> R1C3 = 8

4. N356
a) Outie N5 = R6C7 = 6
b) Innies N6 = 9(2) = [45] -> R4C9 = 4, R6C9 = 5
c) 7(2) = [43] -> R1C7 = 4, R1C8 = 3
d) Naked quad (2789) locked in R3456C8 for C8
e) Innies+Outies N3: -3 = R4C9 - R2C7 -> R2C7 = 7
f) 17(3) = {278} -> R1C6 = 2, R2C6 = 8

5. R789+N4
a) Outie N9 = R9C6 = 4
b) Innie N8 = R9C4 = 7
c) Innies+Outies N7: 1 = R9C4 - R7C2 -> R7C2 = 6
d) R3C2 = 5
e) 11(2) @ N1 = [47] -> R3C1 = 4, R4C1 = 7
f) 15(3) = {168} -> 1,8 locked for R6+N4
g) 22(4) = 69{25/34} -> R3C3 = 6; 9 locked for C3+N4
h) 11(2) @ C3 = {47} locked for C3+N7

6. R789+N5
a) 19(4) @ N5 = {1369} since R56C6 <> 2,4 -> R5C6 = 1; 3,9 locked for R6+N5
b) R1C1 = 9, R1C2 = 7 -> R2C1 = 2, R6C3 = 2
c) 11(2) @ R7C1 = {38} locked for C1+N7
d) R9C3 = 1, R9C8 = 6, R4C6 = 6
e) 5 locked in 19(4) @ C7 for N9
f) 19(4) @ N9 = {1459} locked for N9 since R78C3 = (14); 9 also locked for C7
g) Hidden Single: R8C5 = 6 @ N8, R9C7 = 8 @ C7
h) 20(4) @ N8 = {2369} since R8C6+R9C5 <> 1,8

7. Rest is singles.

Rating:
Hard 1.25. I used some Hidden Killer subsets.


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 Post subject: Re: Assassin 316
PostPosted: Tue Apr 21, 2015 9:31 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1680
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin. Not technically hard, but difficult to find some of the steps. Also when I found the elimination in step 12 it took me some time to find a satisfactory way to describe it.

I loved Afmob's step 1c. Also steps 3c and 3d which were an elegant way to avoid the analysis in my step 20.

Here is my walkthrough for Assassin 316:
Prelims

a) R1C34 = {59/68}
b) R1C78 = {16/25/34}, no 7,8,9
c) R34C1 = {29/38/47/56}, no 1
d) R34C4 = {17/26/35}, no 4,8,9
e) R3C56 = {17/26/35}, no 4,8,9
f) R3C78 = {29/38/47/56}, no 1
g) R45C7 = {13}
h) R78C1 = {29/38/47/56}, no 1
i) R78C3 = {29/38/47/56}, no 1
j) 9(3) cage at R2C2 = {126/135/234}, no 7,8,9
k) 26(4) cage at R4C8 = {2789/3689/4589/4679/5678}, no 1

1. Naked pair {13} in R45C7, locked for C7 and N6, clean-up: no 4,6 in R1C8, no 8 in R3C8

2. 45 rule on C123 2 outies R19C4 = 13 = [58/67/85/94]

3. 45 rule on N7 1 outie R9C4 = 1 innie R7C2 + 1, R9C4 = {4578} -> R7C2 = {3467}

4. 45 rule on N8 2 innies R9C46 = 11 = [47/56/74/83]

5. 45 rule on N9 2 outies R6C9 + R9C6 = 9 = [27/54/63], clean-up: no 5 in R9C4 (step 4), no 8 in R1C4 (step 2), no 6 in R1C3, no 4 in R7C2 (step 3)

6. 45 rule on N5 1 outie R6C7 = 1 innie R4C4 + 1, no 2 in R4C4, no 5,9 in R6C7, clean-up: no 6 in R3C4

7. 45 rule on N3 1 innie R2C7 = 1 outie R4C9 + 3, no 2,4,6 in R2C7, no 7,8,9 in R4C9

8. 45 rule on C3 3 innies R129C3 = 12 = {129/138/156/345} (cannot be {147/237/246} because R1C3 only contains 5,8,9), no 7
8a. R1C3 = {589} -> no 5,8,9 in R29C3

9. 45 rule on R789 3 outies R6C129 = 14
9a. 15(3) cage at R6C1 = {168/267/348/357/456} (cannot be {159/249/258} because R7C2 only contains 3,6,7), no 9
9b. 6 of {168/267/456} must be in R7C2 (R6C12 cannot be {26} because R6C129 cannot be {26}6), no 6 in R6C12

10. 45 rule on N6 3 innies R4C9 + R6C79 = 15 = {258/267/456}
10a. 7,8 of {258/267} must be in R6C7 -> no 2 in R6C7, clean-up: no 1 in R4C4 (step 6), no 7 in R3C4

11. 45 rule on R12 3(2+1) outies R3C2 + R34C9 = 17
11a. Max R3C2 + R4C9 = 12 -> min R3C9 = 5
11b. Max R34C9 = 15 -> min R3C2 = 2

12. R2C7 = R4C9 + 3 (step 7), R6C7 = R4C4 + 1 (step 6), R2C7 cannot be the same as R6C7 -> R4C4 cannot be 2 more than R4C9
12a. 45 rule on N23 3(2+1) outies R1C3 + R4C49 = 17 = [836/854/872/935/962] (cannot be [575] because R4C4 cannot be 2 more than R4C9), no 5 in R1C3, clean-up: no 9 in R1C4, no 4 in R9C4 (step 2), no 7 in R9C6 (step 4), no 2 in R6C9 (step 5), no 3 in R7C2 (step 3)
12b. R129C3 (step 8) = {129/138} -> R29C3 = {12/13}, 1 locked for C3

13. 45 rule on N2356 2(1+1) innies R1C4 + R6C9 = 11 = {56}, CPE no 5,6 in R1C9 + R6C4

14. 18(3) cage at R1C1 = {279/369/378/459/468/567} (cannot be {189} which clashes with R1C3), no 1
14a. 1 in N1 only in R2C23, locked for R2
14b. 9(3) cage at R2C2 = {126/135}, no 4
14c. 1 in R3 only in R3C456, locked for N2

15. 45 rule on C123 1 innie R1C3 = 1 outie R9C4 + 1 -> R1C3 + R9C4 = [87/98]
15a. R1C3 + R4C49 (step 12a) = [836/854/935/962] (cannot be [872], IOD clash) -> no 7 in R4C4, clean-up: no 1 in R3C4, no 8 in R6C7 (step 6)

16. 1 in N2 only in R3C56 = {17}, locked for R3 and N2, clean-up: no 4 in R3C78, no 4 in R4C1
16a. 18(3) cage at R1C5 = {369/459/468}, no 2
16b. Killer pair 5,6 in R1C4 and 18(3) cage, locked for N2, clean-up: no 3 in R4C4, no 4 in R6C7 (step 6)
16c. Naked pair {56} in R14C4, locked for C4

17. R4C9 + R6C79 (step 10) = {267/456}
17a. 2,4 only in R4C9 -> R4C9 = {24}, clean-up: no 8,9 in R2C7 (step 7)
17b. R4C9 + R6C79 = {267/456}, 6 locked for R6 and N6

18. R3C2 + R34C9 = 17 (step 11)
18a. Max R3C2 + R4C9 = 10 -> no 5,6 in R3C9

19. 4 in R3 only in R3C13, locked for N1
19a. 45 rule on N1 3 innies R1C3 + R3C13 = 18 contains 4 = {459/468}
19b. R1C3 = {89} -> R3C13 = {45/46}, clean-up: R4C1 = {567}
19c. R3C78 = [29/83/92] (cannot be {56} which clashes with R3C13, ALS block), no 5,6 in R3C78
19d. Killer pair 2,3 in R3C4 and R3C78, locked for R3
19e. Killer pair 8,9 in R3C78 and R3C9, locked for N3
19f. Naked triple {456} in R3C123, locked for N1

[I wasn’t sure how much I would get from analysing this cage, but it seemed to be the right thing to try next.]
20. 24(5) cage at R1C9 = {12678/14568/23478} (cannot be {12579/13578/24567} which clash with R2C7, cannot be {12489} because 8,9 only in R3C9, cannot be {13569/23568} which clash with R1C78, cannot be {13479/23469} which clash with R3C78) -> R3C9 = 8, clean-up: no 3 in R3C8
20a. Naked pair {29} in R3C78, locked for R3 and N3 -> R3C4 = 3, R4C4 = 5, R1C4 = 6, R1C3 = 8, R9C4 = 7 (step 2), R9C6 = 4 (step 4), R6C9 = 5 (step 5), R7C2 = 6 (step 3), R3C2 = 5
20b. R1C78 = {34} (only remaining combination) -> R1C7 = 4, R1C8 = 3
20c. R34C1 = {47} (only remaining combination) -> R3C1 = 4, R4C1 = 7
20d. R1C2 = 7 (hidden single in N1) -> R12C1 = 11 = {29}, locked for C1 and N1
20e. R78C1 = {38} (only remaining combination), locked for C1 and N7 -> R6C1 = 1, R6C2 = 8 (cage sum), R9C1 = 5

21. R5C1 = 6 -> R45C2 = 7 = {34}, locked for C2 and N4 -> R2C23 = [13]
21a. Naked pair {29} in R89C2, locked for N7 -> R9C3 = 1

22. 17(3) cage at R1C6 = {278} (only possible combination) -> R1C6 = 2, R2C6 = 8, R2C7 = 7, R12C1 = [92], R1C5 = 5, R6C7 = 6, R4C9 = 4 (step 17), R1C9 = 1, R2C89 = [56]

23. R78C8 = {14} (hidden pair in C8) = 5 -> R78C7 = 14 = {59}, locked for C7 and N9
23a. Naked triple {237} in R789C9, locked for C9 and N9 -> R5C9 = 9, R9C78 = [86]

24. 19(4) cage at R5C6 contains 6 = {1369} (only possible combination, cannot be {2467} because 2,4 only in R6C5) -> R5C6 = 1, R6C56 = {39}, locked for R6 and N5

25. 14(3) cage at R7C4 = {158} (only possible combination, cannot be {239} which clashes with R9C5), locked for R7 and N8 -> R7C4 = 1 (hidden single in C4), R7C5 = 8, R7C6 = 5

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A316 at Hard 1.25 for step 12, which is derived from two innie-outie differences.


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