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Ed
 Post subject: Assassin 281
PostPosted: Thu Jan 02, 2014 10:40 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Happy puzzling 2014! Easy start but then a really good tussle. I used one advanced step, a really nice move. It gets a SudokuSolver score of 1.35. Wasted lots of time on previous versions of this puzzle but just wasn't happy to give them the A tag. Fortunately, that doesn't happen very often with the initial vetting that JSudoku and SS provide. Hats off to HATMAN for making some of his puzzles that don't have any software to provide a filter....

Assassin 281

Image
code: paste into solver:
3x3::k:5888:2561:2561:3330:3330:5635:5635:4356:4356:5888:7429:7429:7429:3330:1542:5635:4356:2311:5888:7429:7949:7429:6153:1542:5635:2311:2311:5888:7949:7949:6153:6153:6153:7688:1291:1291:8471:7949:7949:3596:3596:3596:7688:7688:7688:8471:8471:7949:4622:4622:4622:7688:5905:5905:1296:8471:8471:2834:4622:2835:5905:5905:3604:1296:8471:3864:2834:2837:2835:2582:5905:3604:3087:3087:3864:3864:2837:2582:2582:2314:2314:
solution: 
+-------+-------+-------+
| 1 8 2 | 5 7 3 | 4 9 6 |
| 9 5 7 | 6 1 4 | 8 2 3 |
| 6 3 4 | 8 9 2 | 7 5 1 |
+-------+-------+-------+
| 7 6 3 | 2 5 8 | 9 1 4 |
| 5 1 9 | 3 4 7 | 2 6 8 |
| 4 2 8 | 1 6 9 | 5 3 7 |
+-------+-------+-------+
| 3 7 6 | 4 2 5 | 1 8 9 |
| 2 9 1 | 7 8 6 | 3 4 5 |
| 8 4 5 | 9 3 1 | 6 7 2 |
+-------+-------+-------+
Cheerio
Ed
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Afmob
 Post subject:
PostPosted: Sat Jan 04, 2014 10:37 am 
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Happy new year, everybody! This puzzle was quite fun to solve and can be cracked by one advanced move early on.

A281 Walkthrough:
1. C456
a) Outie N3 = R1C6 = 3
b) Outie N69 = R9C6 = 1
c) 6(2) = {24} locked for C6+N2
d) 11(2) @ C6 = {56} locked for C6+N8
e) 13(3) = {157} locked for N2
f) Outies N5 = 11(2) = [83/92]
g) Innies N8 = 11(2) = [29/38]
h) Naked triple (689) locked in R239C4 for C4
i) 11(2) @ C4 = {47} locked for C4+N8

2. R789 !
a) 15(3) = {159/168/258} <> 3,4,7 since R9C4 = (89) and 4{29/38} blocked by Killer pairs (24,34) of 5(2); R89C3 <> 8,9
b) Outies R9 = 12(3): R8C7 <> 5,6 since R8C5 <> 1,4,5,6 and R8C3 <> 3,4
c) 10(3): R9C7 <> 3,4
d) ! Killer quad (2567) locked in R9C37+9(2) for R9 -> 12(2) can have at most one of (57) -> 12(2) <> 5,7
e) Killer pair (89) locked in 12(2)+R9C4 for R9
f) 11(2) @ C5 = [83/92]
g) Outies R9 = 12(3) = 1[83/92] since R8C5 = (89) -> R8C3 = 1
h) 5(2) = {23} locked for C1+N7
i) 12(2) = {48} locked for R9+N7

3. N589
a) R9C4 = 9 -> R9C3 = 5, R8C5 = 8 -> R9C5 = 3, R7C5 = 2, R3C5 = 9
b) 9(2) = {27} locked for N9
c) R9C7 = 6, R8C7 = 3
d) 14(2) = {59} locked for C9+N9
e) 23(5) = {13478} since R7C78+R8C8 = {148} -> R6C89 = {37} locked for R6+N6
f) 5(2) = {14} locked for R4+N6
g) 18(4) = {1269} -> R6C6 = 9, R6C5 = 6, R6C4 = 1

4. N3569
a) 7 locked in 22(4) for C7 -> 22(4) = {3478} -> 4,7,8 locked for C7+N3
b) Hidden Single: R5C9 = 8 @ C9
c) R5C6 = 7, R4C6 = 8, R4C5 = 5 -> R4C4 = 2, R4C7 = 9
d) 17(3) = {269} locked for N3 since R1C9 <> 3,5,9

5. C123
a) 33(6) = 2679{18/45} since R7C23+R8C2 = {679} -> R6C2 = 2; R5C1 = (145)
b) Killer pair (48) locked in 33(5)+R9C1 for C1
c) 23(4) = {1679} -> 1,9 locked for C1+N1
d) 29(5) = {35678} -> R2C23+R3C2 = {357} locked for N1, 5 locked for C2
e) Hidden Single: R1C9 = 6 @ C9
f) 10(2) = [82]

6. Rest is singles.

Rating:
1.25. I used a Killer quad.
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Andrew
 Post subject: Re: Assassin 281
PostPosted: Mon Jan 06, 2014 12:20 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for another nice Assassin.

Welcome back Afmob! It's good to see one of your walkthroughs again. Loved your breakthrough step!

My breakthrough was in the same area, but seen in a very different way.

Here is my walkthrough for Assassin 281:
Prelims

a) R1C23 = {19/28/37/46}, no 5
b) R23C6 = {15/24}
c) R4C89 = {14/23}
d) R78C1 = {14/23}
e) R78C4 = {29/38/47/56}, no 1
f) R78C6 = {29/38/47/56}, no 1
g) R78C9 = {59/68}
h) R89C5 = {29/38/47/56}, no 1
i) R9C12 = {39/48/57}, no 1,2,6
j) R9C89 = {18/27/36/45}, no 9
k) 9(3) cage at R2C9 = {126/135/234}, no 7,8,9
l) 10(3) cage at R8C7 = {127/136/145/235}, no 8,9

1. 45 rule on N3 1 outie R1C6 = 3, clean-up: no 7 in R1C23, no 8 in R78C6
1a. R1C6 = 3 -> R123C7 = 19 = {289/469/478/568}, no 1

2. 45 rule on N69 1 outie R9C6 = 1, clean-up: no 5 in R23C6, no 8 in R9C89
2a. 1 in N9 only in R7C78 + R8C8, locked for 23(5) cage at R6C8, no 1 in R6C89
2b. 8,9 in N9 only in R7C789 + R8C89, CPE no 8,9 in R6C9

3. Naked pair {24} in R23C6, locked for C6 and N2, clean-up: no 7,9 in R78C6
3a. Naked pair {56} in R78C6, locked for C6 and N8
3b. Naked triple {789} in R456C6, locked for N5

4. 45 rule on N5 2 outies R37C5 = 11 = [74/83/92]

5. 45 rule on N8 2 remaining innies R7C5 + R9C4 = 11 = [29/38/47]
5a. 15(3) cage at R8C3 cannot contain more than one of 7,8,9 -> no 7,8,9 in R89C3

6. 45 rule on N2 3 remaining innies R23C4 + R3C5 = 23 = {689}, locked for N2, 6 also locked for C4 and 29(5) cage at R2C2, no 6 in R2C23 + R3C2, clean-up: no 4 in R7C5 (step 4), no 7 in R9C4 (step 5)
6a. R23C4 + R3C5 = {689}, CPE no 8,9 in R3C2

7. Naked triple {689} in R239C4, locked for C4, clean-up: no 2,3 in R78C4
7a. Naked pair {47} in R78C4, locked for C4 and N8
7b. Naked quad {2389} in R3789C5, locked for C5

8. 15(3) cage at R8C3 = {159/168/258} (cannot be {249/348} which clash with R78C1, cannot be {267/357/456} because R9C4 only contains 8,9), no 3,4 in R89C3
8a. 1 of {168} must be in R8C3 -> no 6 in R8C3
8b. Killer pair 1,2 in R78C1 and 15(3) cage, locked for N7

9. 45 rule on N6 2 innies R6C89 = 10 = {37/46}/[82], no 5,9, no 2 in R6C8

10. 45 rule on N7 3 innies R7C23 + R8C2 = 1 outie R9C4 + 13
10a. Min R9C4 = 8 -> min R7C23 + R8C2 = 21, no 3 in R7C23 + R8C2
10b. The number in R9C4 must also be in R7C23 + R8C2 (only remaining place in N7), R9C4 = {89} -> R7C23 + R8C2 = 21,22 = {489/678/679} (cannot be {579} which doesn’t contain 8, cannot be {589} which clashes with R9C12), no 5 in R7C23 + R8C2

11. 1 in N9 only in R7C23 + R8C3
11a. Hidden killer pair 8,9 in R7C23 + R8C3 and R78C9 for N9, R78C9 contains one of 8,9 -> R7C23 + R8C3 must contain one of 8,9
11b. 45 rule on N6 3 outies R7C23 + R8C3 = 13 = {139/148} (cannot be {157} which doesn’t contain 8 or 9), no 2,5,6,7

12. 45 rule on R6789 2 innies R6C37 = 1 outie R5C1 + 8, IOU no 8 in R6C7

13. 5,9 in N6 only in 30(5) cage at R4C7 = {15789/25689/35679}, no 4

14. Max R3C5 + R4C46 = 22 -> no 1 in R4C5

15. 45 rule on C89 2 innies R5C89 = 1 outie R7C7 + 13
15a. Max R5C89 = 17 -> max R7C7 = 4
15b. Min R5C89 = 14, no 1,2,3 in R5C89

16. Hidden killer quad 1,2,3,4 in R123C7, 30(5) cage at R4C7, R7C7 and R89C7 for C7, 30(5) cage contains one of 1,2,3 in C7, R7C7 = {134}, R89C7 contains one of 2,3,4 -> R123C7 (step 1a) must contain one of 2,4 = {289/469/478}, no 5
16a. 9(3) cage at R2C9 = {126/135} (cannot be {234} which clashes with R123C7), no 4, 1 locked for N3

17. 17(3) cage at R1C8 = {269/278/359/467} (cannot be {368/458} which clash with R123C7)
17a. 3 of {359} must be in R2C8 -> no 5 in R2C8

[I was slow in spotting this 45, which I ought to have seen earlier.]
18. 45 rule on R9 3 outies R8C357 = 12 = {129/138/237/345} (cannot be {147} which clashes with R8C4, cannot be {156} which clashes with R8C6, cannot be {246} because 4,6 only in R8C7), no 6
18a. R8C357 = {129/138/237/345} = [192/183/237/534], no 2 in R8C5, no 5 in R8C7, clean-up: no 9 in R9C5
[I was still finding things hard, and continued with other steps, until I found step 18b which cracks the puzzle, so I’ve re-worked from here.]
18b. R8C357 = [192/183] (cannot be [237/534] because 15(3) cage at R8C3 (step 8) = [258/528] clash with R89C5 = [38], killer combo clashes) -> R8C3 = 1, R8C5 = {89}, R8C7 = {23}, clean-up: no 9 in R1C2, no 4 in R78C1, no 8 in R9C5
18c. Naked pair {23} in R78C1, locked for C1 and N7, clean-up: no 9 in R9C12

19. R9C4 = 9 (hidden single in R9), R9C3 = 5 (cage sum), R8C5 = 8, R9C5 = 3, R7C5 = 2, R78C1 = [32], R8C7 = 3, R9C7 = 6 (cage sum), clean-up: no 8 in R7C9, no 7 in R9C12, no 4 in R9C89
19a. Naked pair {59} in R78C9, locked for C9 and N9 -> R8C8 = 4, R7C78 = [18], R78C4 = [47], clean-up: no 1 in R4C9, no 6 in R6C8, no 2,6 in R6C9 (both step 9)
19b. Naked pair {37} in R6C89, locked for R6 and N6, clean-up: no 2 in R4C89
19c. R4C89 = [14]

20. 7 in C7 only in R123C7, locked for N3
20a. R123C7 (step 16) = {478} (only remaining combination), locked for C7 and N3

21. R5C89 = [68] (hidden pair in N6)

22. Naked triple {679} in R7C23 + R8C3, locked for 33(6) cage at R5C1, no 6,7,9 in R5C1 + R6C12
22a. 45 rule on N7 3 remaining outies R5C1 + R6C12 = 11 = {128/245} -> R6C2 = 2, R56C1 = [18]/{45}, clean-up: no 8 in R1C3
22b. 45 rule on C1 3 innies R569C1 = 17 = {458} (only possible combination) -> R56C1 = {45}, locked for C1 and N4, R9C12 = [84], clean-up: no 6 in R1C3

23. 9(3) cage at R2C9 (step 16a) = {135} (cannot be {126} which clashes with R1C9) -> R3C8 = 5, R23C9 = {13}, locked for C9 and N3 -> R6C89 = [37], R9C89 = [72], R1C9 = 6, clean-up: no 4 in R1C3

24. R5C2 = 1 (hidden single in N4), R1C2 = 8, R1C3 = 2, R12C8 = [92], R23C4 = [42]

25. R2C2 = 5 (hidden single in N1), R23C4 = {68} = 14 -> R2C3 + R3C2 = 10 = {37}, locked for N1, R1C1 = 1
25a. R3C5 = 9, R23C1 = [96], R3C3 = 4, R4C1 = 7

26. R3C5 = 9, R4C6 = 8 -> R4C45 = 7 = [25]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A281 at 1.25, as if I'd gone straight from step 7 to step 18 and then filled in the gaps later.
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Ed
 Post subject: Re: Assassin 281
PostPosted: Thu Jan 09, 2014 9:34 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Welcome back Afmob and Azpaull! Really nice solution by Afmob. Had to really think about the "Killer quad" in 2d. Need to think of them as Killer quarters. :) Anyway, step 2d made it seem almost too easy for a 2014 Assassin. Pleased to have Andrew have to search around before seeing the key area. I really like his steps 10b and the cracker, step 18b. I also cracked it in the same area as both the other walkthroughs, but another completely different way.

Alt cracker A281
from end of Afmob's step 2a:
Paste candidates into A281 in SudokuSolver. Alternatively, download the attached file and open with SudokuSolver: 
.-------------------------------.-------------------------------.-------------------------------.
| 12456789  1246789   1246789   | 15        157       3         | 12456789  12456789  12456789  |
| 123456789 123456789 123456789 | 689       157       24        | 12456789  123456789 123456    |
| 123456789 123456789 123456789 | 689       89        24        | 12456789  123456    123456    |
:-------------------------------+-------------------------------+-------------------------------:
| 123456789 123456789 123456789 | 1235      123456789 789       | 123456789 1234      1234      |
| 123456789 123456789 123456789 | 1235      123456789 789       | 123456789 123456789 123456789 |
| 123456789 123456789 123456789 | 1235      123456789 789       | 123456789 123456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 1234      123456789 123456789 | 47        23        56        | 123456789 123456789 5689      |
| 1234      123456789 1256      | 47        2389      56        | 234567    123456789 5689      |
| 345789    345789    256       | 89        2389      1         | 234567    2345678   2345678   |
'-------------------------------.-------------------------------.-------------------------------'


End of Afmob's step 2a. then
3. From step 2a, 15(3)r8c3 = {159/168/258}: ie, cannot have both 5 & 6
3a. also, r9c789 cannot have more than one of 5 or 6 because 14(2)n9 = [5/6] -> r9c123 must have at least one of 5 or 6 for r9 (Hidden killer pair)
3b. -> no 5 in r8c3 since it blocks all 5 and 6 from r9c123 (Locking-out cages)
3c. 15(3)r8c3 = [159/168/258](no 6 in r8c3, no 2 in r9c3)

4. "45" on r9: 3 outies r8c357 = 12
4a. but {147} blocked by r8c4 = (47)
4b. but {156} blocked by r8c6 = (56)
4c. but {246} blocked by 4 and 6 are only in r8c7
4c. Must have 1 or 2 for r8c3 = {129/138/237}(no 4,5,6)
4d. no 3,4,5 in r9c7 (Split 9(2)r89c7)

5. 4 in r9 in 9(2)r9c8 = {45} or in 12(2)r9c1 -> {57} blocked from 12(2) since it would leave no 4 for r9 (Locking-out cages: a simpler form of this technique this time)
5a. 12(2)r9c1 = {39/48}(no 5,7) = [8/9..]

6. 8 and 9 in r9 must be in 12(2)r9c1 and r9c4: both locked for r9 (Killer pair)
6a. no 2,3 in r8c5

7. h12(3)r8c357 (step 4c) must have 8 or 9 for r8c5 = {129/138}(no 7)
7a. must have 1 -> r8c3 = 1
7b. -> 5(2)n7 = {23} only: both locked for c1 and n7

etc, as the other two walkthroughs showed, this cracks the puzzle.
Cheerio
Ed


Attachments:
A281 Afmob WT at end 2a.ssv [84.52 KiB]
Downloaded 625 times
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