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Assassin 75
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Andrew
Grandmaster
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Joined: 11 Aug 2006
Posts: 300
Location: Lethbridge, Alberta

PostPosted: Sun Nov 04, 2007 12:13 am    Post subject: Reply with quote

It looks like Susan's intuitive leap, if that's what it was, must have been an inspired one. Solving any Assassin in 45 minutes is excellent! I'm not sure if I've ever done that; maybe on one of the very early ones.

I've only had a glance at the posted walkthroughs, I'll go through them properly later, but I think my solving method was different.

On going through the posted walkthroughs I particularly liked Susan's use of innies/outies that are in the same columns, C3 for N14 and C7 for N69.

I must admit I missed Gary's first step; that would probably have made my solving path quicker. On checking while editing typos, I found that step 10 gave the same result.

My main technique for this puzzle was the one outlined in my previous message. Once I realised it was there and I reworked some of the earlier stages more rigorously, the puzzle fell out fairly quickly. However I'll still rate it 1.25 because the technique was hard to spot.

Here is my walkthrough for A75 (corrections in red, original step 31 delete as unnecessary). Thanks Ed for your feedback, added after step 6.

Prelims

a) R12C1 = {29/38/47/56}, no 1
b) R1C89 = {17/26/35}, no 4,8,9
c) R23C2 = {13}, locked for C2 and N1, clean-up: no 8 in R12C1
d) R2C78 = {89}, locked for R2 and N3, clean-up: no 2 in R1C1
e) R78C8 = {29/38/47/56}, no 1
f) R8C23 = {48/57}/[93], no 1,2,6, no 9 in R8C3
g) R89C9 = {18/27/36/45}, no 9
h) R9C12 = [19/37]/{28/46}, no 5, no 7,9 in R9C1
i) 22(3) cage in N4 = 9{58/67}, 9 locked for N4
j) 10(3) cage at R5C6 = {127/136/145/235}, no 8,9
k) 19(3) cage at R8C4 = {289/379/469/478/568}, no 1
l) 11(3) cage in N9 = {128/137/146/236/245}, no 9
[I missed 21(3) cage at R2C6 = {489/579/678}, no 1,2,3]

1. 45 rule on R12 3 innies R2C259 = 9 = {126/135/234}, no 7

2. 45 rule on R789 3 innies R7C349 = 19 = {289/379/469/478/568}, no 1
2a. 1 in N7 locked in R789C1, locked for C1

3. 45 rule on C89 3 innies R259C8 = 19 = {289/379/469/478/568}, no 1

4. 45 rule on N1 2 innies R3C13 = 15 = {69/78}

5. 45 rule on N3 2 innies R13C7 = 10 = {37/46}, no 1,2,5
5a. 10(3) cage in N3 = {127/145/235} (cannot be {136} which clashes with R13C7), no 6

6. 45 rule on N7 2 innies R79C3 = 8 = {26/35}, no 4,7,8,9
6a. 9 in C3 locked in R13C3, locked for N1, clean-up: no 2 in R2C1, no 6 in R3C3 (step 4)
6b. 15(3) cage in N7 = {159/168/249/267/348/357} (cannot be {258/456} which clash with R79C3)
[Ed. I went a step further with this one: {168} clashes with h8(2) & 10(2) -> 1 in 15(3) must have 9. 1 in 10(2) -> must have 9. -> no 9 in 12(2). You get rid of it pretty soon anyway, so not much of a short cut.
When I discussed this clash with Ed, he pointed out the use of "combining cages". It's a technique I've used occasionally but haven't yet reached the stage of instinctively looking for them.]


7. 2 in N1 locked in 15(3) cage = 2{49/58} (cannot be {267} which clashes with R12C1), no 6,7
7a. 6 in N1 locked in R123C1, locked for C1, clean-up: no 7 in R6C2, no 4 in R9C2

8. 45 rule on N9 2 innies R7C79 = 14 = {59/68}
8a. R78C8 = {29/38/47} (cannot be {56} which clashes with R7C79), no 5,6

9. R7C349 (step 2) = {289/379/469/568} (cannot be {478} because no 4,7,8 in R7C3)
9a. 2,3 of {289/379} must be in R7C3 -> no 2,3 in R7C4
9b. 6 of R7C349 = {568} must be in R7C3, here’s how
9ba. If R7C3 = 5 => R7C49 = {68} clashes with R7C79 = {68}
9bb. -> no 5 in R7C3, clean-up: no 3 in R9C3 (step 6)
[Note that R7C349 = [685] is still valid but [658] gives clash between R7C3 and R7C7.]

10. 45 rule on C12 3 innies R158C2 = 13 = {247/256} = 2{47/56}, no 8,9, 2 locked for C2, clean-up: no 3,4 in R8C3, no 8 in R9C1
10a. 5 on {256} must be in R8C2 -> no 5 in R15C2

11. 15(3) cage in N1 (step 7) = 2{49/58}
11a. 8,9 only in R1C3 -> R1C3 = {89}

12. 45 rule on R123 3 innies R3C167 = 18 = {468/567} (cannot be {189} because no 1,8,9 in R3C7, cannot be {279} because 2,9 only in R3C6, cannot be {369} because R3C167 = [693] clashes with R1C13 = [69], cannot be {378} because 7/8 in R3C67 clashes with R3C13 = {78}, cannot be {459} because no 4,5,9 in R3C1) = 6{48/57}, no 1,2,3,9, 6 locked for R3, clean-up: no 7 in R1C7 (step 5)
12a. 5 of {567} must be in R3C6 -> no 7 in R3C6
[If I’d included the 21(3) in the Prelims, then I wouldn’t have needed to eliminate {279} from R3C167 which wouldn’t contain a 2.]

13. 45 rule on C123 3 innies R349C3 = 16 = {169/259/367/457} (cannot be {178/349} because R9C3 only contains 2,5,6, cannot be {268} because R49C3 = {26} clashes with R79C3 = {26}, cannot be {358} because R49C3 = [35] clashes with R79C3 = [35]), no 8, clean-up: no 7 in R3C1 (step 4)
13a. 7 of {367/457} must be in R3C3 -> no 7 in R4C3
13b. 1,3 of {169/367} must be in R4C3 -> no 6 in R4C3

14. 45 rule on C789 3 innies R167C7 = 13 = {139/148/157/238/256/346} (cannot be {247} because no 2,4,7 in R7C7)
14a. 1,2 of {157/256} must be in R6C7
14b. 6 of {346} must be in R7C7
14c. -> no 5,6,7 in R6C7
14d. 3 of {139/238/346} must be in R1C7 (3 of {346} in R6C7 would make R13C7 = [46] clash with R7C7 = 6), no 3 in R6C7

15. 15(3) cage at R3C1 = {258/267/348/456} (cannot be {357} because R3C1 only contains 6,8)
15a. 8 of {258/348} must be in R3C1 -> no 8 in R4C12
15b. 2 of {267} must be in R4C1 -> no 7 in R4C1
15c. 6 of {267/456} must be in R3C1 -> no 6 in R4C2

16. 15(4) cage at R5C2 = {1248/1347/2346} (cannot be {1257} because {157} in N4 clashes with 22(3) cage, cannot be {1356} because 6 must be in R7C3 to avoid clash with 22(3) cage and then there’s no 1,3,5 in R5C2) = 4{128/137/236), no 5, 4 locked for N4 because there’s no 4 in R7C3

17. 15(3) cage at R3C1 (step 15) = {258/267} = 2{58/67} -> R4C1 = 2, clean-up: no 8 in R9C2

18. Killer pair 5,7 in R4C2 and 22(3) cage, locked for N4

19. 15(4) cage at R5C2 (step 16) = {1248/2346} = 24{18/36} -> R7C3 = 2, R9C3 = 6 (step 6), clean-up: no 9 in R8C8, no 3 in R8C9, no 4 in R9C1
19a. R9C3 = 6 -> R34C3 (step 13) = 10 = {19/37}
19b. R89C4 = 13 = {49/58}, no 2,3,7

20. R1C2 = 2 (hidden single in C2), clean-up: no 6 in R1C89

21. 45 rule on C3 R12C3 = 13, R34C3 = 10, R79C3 = 8 -> R568C3 = 14 = {158/347}
21a. 5,7 only in R8C3 = {57}, no 8, clean-up: no 4 in R8C2
21b. Naked pair {57} in R8C23, locked for R8 and N7 -> R9C2 = 9, R9C1 = 1, clean-up: no 4 in R7C8, no 4 in R8C4 (step 19b), no 8 in R8C9, no 8 in R9C4 (step 19b), no 2,4 in R9C9
21c. Naked pair {57} in R48C2, locked for C2, clean-up: no 8 in R56C1

22. R7C3 = 2 -> R7C49 = {89} (step 9)
22a. Naked pair {89} in R7C49, locked for R7 -> R7C2 = 4, R78C1 = [38], R7C8 = 7, R8C8 = 4, R8C4 = 9, R9C4 = 4 (step 19b), R7C4 = 8, R7C9 = 9, R7C7 = 5 (step 8), clean-up: no 1 in R1C9, no 2 in R8C9

23. R3C1 = 6 (naked single), R3C3 = 9 (step 4), R4C2 = 7, R8C23 = [57], clean-up: no 5 in R12C1

24. R1C3 = 8 (naked single), R2C3 = 5

25. R5C2 = 6 (naked single), R6C2 = 8, R56C3 = {34} (step 19)
25a. R4C3 = 1 (hidden single in C3)

26. R1C7 = 6 (hidden single in N3), R3C7 = 4 (step 5), R6C7 = 2 (step 14)
26a. R12C6 = 7 = [34/43/52], no 1,7,9

27. 11(3) cage in N9 = {128} (only remaining combination) -> R8C7 = 1, R9C78 = [82], R89C9 = [63], R2C78 = [98], R45C7 = [37], R5C8 = 9 (cage sum), R45C1 = [59], clean-up: no 5 in R1C8

28. R7C7 = 5, R7C56 = {16} -> R8C5 = 3 (cage sum), R8C6 = 2, clean-up: no 5 in R1C6 (step 26a)

29. Naked pair {34} in R12C6, locked for C6 and N2 -> R5C6 = 1, R6C6 = 7, R7C56 = [16], R9C56 = [75], R34C6 = [89], R4C5 = 4

30. Naked pair {56} in R4C48, locked for R4 -> R4C9 = 8, R5C9 = 4, R4C8 = 5, R4C4 = 6, R6C45 = [35], R5C45 = [28], R56C3 = [34]

31. R1C5 = 9 (naked single), R12C4 = 8 = {17} (only remaining combination)
31a. Naked pair {17} in R12C4, locked for C4

and the rest is naked singles and simple cage sums


Last edited by Andrew on Wed Nov 21, 2007 9:27 pm; edited 2 times in total
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azpaull
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Joined: 27 Aug 2007
Posts: 14
Location: Arizona

PostPosted: Sun Nov 11, 2007 6:31 pm    Post subject: Reply with quote

Well, I'm glad to see that this gave (or is giving) others problems, too. I've had limited time to work it this week, and I don't think I'm close to breaking through. I think this will go into my growing bank of "ones to come back to" for now!
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