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 Post subject: Assassin 145
PostPosted: Thu Mar 05, 2009 10:01 pm 
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Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
After all those rather hard V1s I wanted to make an Assassin with a moderate difficulty and despite SudokuSolver's rating I think I succeeded. I hope you have as much fun in solving this Killer as I had!

Assassin 145

Image

3x3::k:5377:5377:5377:4866:7184:7184:7184:3606:3606:3843:3843:5377:4866:4111:7184:3603:4375:3606:3843:3076:4866:4866:4111:4111:3603:3603:4375:3076:3076:3590:3083:3083:4111:4120:5401:4375:2821:2821:3590:2573:2573:2573:4120:5401:5401:4359:4359:3590:2828:2828:4622:4120:5401:2581:4361:4359:6920:6920:4622:4622:2834:2834:2581:4361:4361:4362:6920:4622:4369:2834:2581:5140:4362:4362:4362:6920:4369:4369:4369:5140:5140:

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

SS Score: 1.20
Estimated rating: 1.0 - Hard 1.0

I haven't planned a V2 (yet?) but there are lots of other V2s which should have more walkthroughs so that should keep you busy.


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 Post subject: Re: Assassin 145
PostPosted: Fri Mar 06, 2009 4:59 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1703
Location: Lethbridge, Alberta, Canada
Thanks Afmob. I enjoyed that this one. I hope we'll see some walkthroughs from solvers who don't usually post them.

I'll rate A145 at 1.0. I hope that step 9c, which made things a bit quicker but wasn't a key breakthrough, counts within this rating. Edit. Ed's message below suggests that my walkthrough should be rated 1.25; he's probably right. However Ed also shows an alternative step at this stage so a rating of 1.0 is valid for A145.

Here is my walkthrough. I've simplified steps 19 and 25.

Prelims

a) R4C45 = {39/48/57}, no 1,2,6
b) R5C12 = {29/38/47/56}, no 1
c) R6C45 = {29/38/47/56}, no 1
d) R5C456 = {127/136/145/235}, no 8,9
e) 10(3) cage at R6C9 = {127/136/145/235}, no 8,9
f) 11(3) cage in N9 = {128/137/146/236/245}, no 9
g) 20(3) cage in N9 = {389/479/569/578}, no 1,2
h) 28(4) cage at R1C5 = {4789/5689}, no 1,2,3
i) 27(4) cage at R7C3 = {3789/4689/5679}, no 1,2

1. 45 rule on N1 2 innies R3C23 = 9 = {18/27/36/45}, no 9

2. 45 rule on N4 2 outies R37C2 = 9 = {18/27/36/45}, no 9

3. 45 rule on N5 2 innies R46C6 = 12 = {39/48/57}, no 1,2,6
3a. 1 in N5 locked in R5C456, locked for R5

4. 45 rule on N6 2 innies R46C9 = 8 = {17/26/35}, no 4,8,9

5. 45 rule on N7 2 innies R7C23 = 11 = [29]/{38/47/56}, no 1, clean-up: no 8 in R3C2 (step 2), no 1 in R3C3 (step 1)

6. 45 rule on N3 1 innie R1C7 = 1 outie R4C9, no 4,8,9 in R1C7, no 1,2,3 in R4C9, no 5,6,7 in R6C9 (step 4)
6a. 8,9 in 28(4) cage locked in R1C56 + R2C6, locked for N2

7. 45 rule on C789 = R19C7 = 12 = {57}, locked for C7, clean-up: no 6 in R4C9 (step 6), no 2 in R6C9 (step 4)
7a. 28(4) cage at R1C5 = {4789/5689}
7b. R1C7 = {57}, no 5,7 in R1C56 + R2C6

8. R4C45 = {39/48} (cannot be {57} which clashes with R4C9), no 5,7
8a. R6C45 = {29/47/56} (cannot be {38} which clashes with R4C45), no 3,8

9. 45 rule on C1234 3 innies R456C4 = 10 = {136/145/235} (cannot be {127} because no 1,2,7 in R4C4), no 7,8,9, clean-up: no 3,4 in R4C5, no 2,4 in R6C5
9a. R4C4 = {34} -> no 3,4 in R56C4, clean-up: no 7 in R6C5
9b. 1 of {136} must be in R5C4, no 6 in R5C4
9c. 2 of {235} must be in R5C4 (R456C4 cannot be [352] because R46C5 would both be 9), no 2 in R6C4, clean-up: no 9 in R6C5

10. Naked pair {56} in R6C56, locked for R6 and N5, clean-up: no 7 in R46C6 (step 3)
10a. R5C456 = {127} (hidden triple in N5), locked for R5, clean-up: no 4,9 in R5C12

11. 28(4) cage at R1C5 = {4789/5689}
11a. R1C5 = {89} (R12C6 cannot be {89} which clashes with R46C6)
11b. Naked pair {89} in R14C5, locked for C5
12. 45 rule on C89 2 innies R37C8 = 8 = {17/26/35}, no 4,8,9

13. 45 rule on N9 3 innies R7C9 + R8C8 + R9C7 = 14 = {167/257/356} (cannot be {347} because 10(3) cage at R6C9 cannot contain both of 3,4), no 4

14. 9 in N9 locked in 20(3) cage = {389/479} (cannot be {569} which clashes with R7C9 + R8C8 + R9C7), no 5,6
14a. 11(3) cage in N9 = {128/146/245} (cannot be {137/236} which clash with R7C9 + R8C8 + R9C7), no 3,7

15. 17(3) cage at R2C8 = {179/278/359/458/467} (cannot be {269/368} because R4C9 only contains 5,7)
15a. R4C9 = {57} -> no 5,7 in R2C8 + R3C9

16. 45 rule on R6789 3 innies R6C378 = 15 = {249/348}, no 1,7, 4 locked for R6, clean-up: no 8 in R4C6 (step 3)
16a. 7 in R6 locked in R6C12, locked for N4 and 17(3) cage at R6C1, clean-up: no 2 in R3C2 (step 2), no 7 in R3C3 (step 1), no 4 in R7C3 (step 5)
16b. 17(3) cage at R6C1 = {278} (only remaining combination, cannot be {179} because 1,7,9 only in R6C12, cannot be {467} because 4,6 only in R7C2) -> R6C12 = {278}, R7C2 = {28}, CPE no 8 in R45C2, clean-up: R3C2 = {17} (step 2), R3C3 = {28} (step 1), no 3 in R5C1, R7C3 = {39} (step 5)

17. R6C9 = 1 (hidden single in R6), R4C9 = 7 (step 4), R1C7 = 7 (step 6), R9C7 = 5
17a. 10(3) cage at R6C9 = {127/136}
17b. 7 of {127} must be in R8C8 -> no 2 in R8C8

18. 28(4) cage at R1C5 = {4789}, no 6, 4 locked in R12C6, locked for C6 and N2, clean-up: no 8 in R6C6 (step 3)
18a. Naked pair {39} in R46C6, locked for C6 and N5 -> R4C45 = [48], R1C5 = 9

19. 45 rule on R1234 3 innies R4C378 = 12 = {129/156} -> R4C3 = 1, R4C78 = [29/65/92], no 6 in R4C8

20. 4 in N4 locked in R56C3
20a. R4C3 = 1 -> R56C3 = {49}, locked for C3 and N4 -> R7C3 = 3, R7C2 = 8 (step 4), R3C2 = 1 (step 2), R3C3 = 8 (step 1)

21. Naked pair {27} in R6C12, locked for R6 and N4
21a. R5C1 = 8 (hidden single in N4), R5C2 = 3
21b. Naked pair {56} in R4C12, locked for R4
21c. Naked pair {29} in R4C78, locked for R4 and N6 -> R4C6 = 3, R6C6 = 9, R56C3 = [94]

22. R7C3 = 3 -> R789C4 = 24 = {789}, locked for C4 and N8

23. 17(4) cage at R8C5 = {2456} (only remaining combination) -> R9C5 = 4, R89C6 = {26}, locked for C6 and N8
23a. Naked pair {15} in R7C56, locked for R7 and N8 -> R8C5 = 3

24. Naked pair {26} in R7C89, locked for R7 and N9 -> R7C7 = 4, R5C7 = 6, R8C8 = 7
24a. R5C7 = 6 -> R46C7 = 10 = [28], R46C8 = [93], R8C7 = 1, R7C8 = 6 (step 14a), R7C9 = 2, R9C8 = 8, R89C9 = [93], R8C4 = 8
24b. R23C7 = {39} -> R3C8 = 2 (cage sum)

25. 8 in N3 locked in 14(3) cage = {158} (only remaining combination) -> R1C8 = 1, R2C8 = 4, R3C9 = 6, R5C89 = [54], R12C6 = [48], R12C9 = [85]

26. 19(4) cage at R1C4 = {2368} (only remaining combination) -> R3C4 = 3, R12C4 = {26}, locked for C4 and N2 -> R5C4 = 1, R5C56 = [27], R6C45 = [56], R3C56 = [75], R2C5 = 1, R7C56 = [51], R23C7 = [39], R3C1 = 4

27. 9 in N1 locked in 15(3) cage = {249} (only remaining combination) -> R2C12 = {29}, locked for R2 and N1 -> R12C4 = [26], R2C3 = 7

28. R1C1 = 3, R9C1 = 1 (hidden singles in C1), R8C2 = 4 (hidden single in C2)
28a. R8C2 = 4 -> R78C1 = 13 = [76]

and the rest is naked singles

Afmob wrote:
I haven't planned a V2 (yet?) but there are lots of other V2s which should have more walkthroughs so that should keep you busy.
There certainly are. Ed's A144 V2 and Frank's A142 V2 are two that I haven't yet finished but hope to do so.


Last edited by Andrew on Thu Mar 12, 2009 11:15 pm, edited 1 time in total.

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 Post subject: Re: Assassin 145
PostPosted: Sun Mar 08, 2009 9:32 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1703
Location: Lethbridge, Alberta, Canada
Afmob suggested to me that there's an easier way than my step 9c so I had another look and found

9. 45 rule on C1234 3 innies R456C4 = 10 = {136/145/235} (cannot be {127} because no 1,2,7 in R4C4), no 7,8,9, clean-up: no 3,4 in R4C5, no 2,4 in R6C5
9a. R4C4 = {34} -> no 3,4 in R56C4, clean-up: no 7 in R6C5
9b. Hidden killer pair 2,6 in R5C456 and R6C45 for N5 -> R5C456 and R6C45 must each contain one of 2,6
9c. 1 locked in R5C456 (step 3a) = {127} (only remaining combination, cannot be {136} because R456C4 cannot contain both of 2,4), locked for R5 and N5, clean-up: no 5 in R46C6 (step 3), no 9 in R6C5

It's a more interesting way but I'm not sure that it's really any simpler than my original step 9c. Maybe I'm still missing something?


Last edited by Andrew on Thu Mar 12, 2009 11:16 pm, edited 1 time in total.

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 Post subject: Re: Assassin 145
PostPosted: Sun Mar 08, 2009 9:41 pm 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 837
Location: Sydney, Australia
Thanks Afmob for a fun puzzle. Lots of areas to explore with lots of eliminations! [edit: for some reason I can't see the puzzle image right now. Can't blame ImageShack this time!]
Andrew wrote:
Afmob suggested to me that there's an easier way than my step 9c
Here's a simpler step 9

A145 Andrew's step 9 ALT 2
Hidden Text:
9. 45 rule on c1234: 1 innie r5c4 + 13 = 2 outies r46c5. Max. 2 outies = 17 -> max. r5c4 = 4
9a. 45 rule on C1234 3 innies R456C4 = 10 = {136/145/235} (cannot be {127} because no 1,2,7 in R4C4), no 7,8,9, clean-up: no 3,4 in R4C5, no 2,4 in R6C5
9b. R4C4 = {34} -> no 3,4 in R56C4, clean-up: no 7 in R6C5
9c. 2 of {235} must be in R5C4, no 2 in R6C4, clean-up: no 9 in R6C5
Andrew's step 13 (& 14 which results) is the trickiest one which I'd rate at least 1.25. However, those steps are not essential to the solution (left them out while going through the WT) so no worries with a 1.0 rating.

I meandered around after the equivalent of Andrew's step 9 before getting to his step 16 so I found this one a 1.25 rating puzzle. Nice feeling being on time with you guys. Think I'll just skip some of the recent V1s I haven't been able to get to.

Cheers
Ed


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 Post subject: Re: Assassin 145
PostPosted: Fri Mar 13, 2009 6:32 am 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Nice solution path, Ed! Your way is easier than mine. I think the way I solved it also justifies a 1.0 rating. I'm glad that despite SudokuSolver's rating this one was easier to solve than recent Assassins.

A145 Walkthrough snippet
Hidden Text:
1. C789
a) Innies N6 = 8(2) <> 4,8,9
b) Innies+Outies N3: R1C7 = R4C9 = (567)
c) Innies C789 = 12(2) = {57} locked for C7
d) 28(4) = 89{47/56} -> 8,9 locked for N2; R1C56+R2C6 <> 5,7 since R1C7 = (57)
e) Innies N69 = 12(1+1) = {57} -> CPE: R789C9 <> 5,7
f) Innies N6 = 8(2) = [53/71]

2. C1234
a) 12(2) <> {57} since it's blocked by R4C9 = (57)
b) Innies C1234 = 10(3) = {136/145/235} <> 7,8,9 because R4C4 = (3489); R56C4 <> 3,4
c) 8,9 locked in 27(4) @ C4 for N8+27(4) -> 27(4) = 89{37/46}
d) Innies C123 = 11(2) = [47/56/74/83]
e) Innies N7 = 11(2) = [47/56/74/83]
f) 11(2) = [29/56/65]

3. N235
a) ! Outies N23 = 18(2+1): R4C6 <> 5,7 because R4C9 = (57) and R3C3 <> 6
b) Innies N5 = 12(2) = {39/48}
c) 7 locked in 10(3) @ N5 = {127} locked for R5+N5
d) 11(2) = {56} locked for R6


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