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Ed
 Post subject: Assassin 308
PostPosted: Thu Jan 29, 2015 9:51 pm 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
Happy with this one, just. Took 5 solves! Kept making mistakes then finally found what I was missing. Am sure that you guys will find this much easier than I did. SudokuSolver gives it a 1.40.

Assassin 308

Image

code: paste into solver:
3x3::k:2560:2560:3842:3864:3864:3864:4375:2308:2308:5125:5125:3842:4889:4889:4889:4375:4870:4870:5125:5125:3842:5127:4889:3592:4375:4870:4870:5385:5385:5127:5127:1290:3592:3592:4875:4875:5385:5903:2829:2829:1290:3854:3854:5121:4875:5385:5903:5903:2829:4112:3854:5121:5121:4875:3857:3857:5903:2582:4112:2819:5121:4626:4626:3859:3857:2582:3349:3349:3349:2819:4626:5140:3859:3859:3859:3852:3852:3852:5140:5140:5140:
solution: 
+-------+-------+-------+
| 3 7 9 | 8 6 1 | 2 5 4 |
| 1 6 2 | 4 5 7 | 8 3 9 |
| 5 8 4 | 9 3 2 | 7 6 1 |
+-------+-------+-------+
| 8 2 6 | 5 4 9 | 3 1 7 |
| 7 9 3 | 6 1 8 | 4 2 5 |
| 4 1 5 | 2 7 3 | 9 8 6 |
+-------+-------+-------+
| 6 4 8 | 3 9 5 | 1 7 2 |
| 2 5 7 | 1 8 4 | 6 9 3 |
| 9 3 1 | 7 2 6 | 5 4 8 |
+-------+-------+-------+
Cheers
Ed
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Afmob
 Post subject:
PostPosted: Fri Jan 30, 2015 9:29 pm 
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Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Assassin, Ed! You're right that this Killer is not particularly hard but it took me quite some time to solve it. This also shows in my walkthrough which is quite long even after some optimization.

Edit: Ed made me aware that my step 3b is also quite difficult, so I added a "!" and changed my rating comment though I find it hard to rate this move since unlike Andrew I rarely use these types of moves.

A308 Walkthrough:
1. R789
a) Innies N7 = 15(2) = {69/78}
b) Innies N9 = 7(2) = [16]/{25/34}
c) Outies R9 = 5(2) = {14/23}
d) Innies N78 = 22(3) = 9{58/67} -> 9 locked for R7; R7C6 <> 8 since R7C35 <> 5
e) 11(2) <> 3
f) Innies+Outies R89: -16 = R7C6 - R8C238 -> R7C6 <> 9 and R8C28 <> 1,2,3 since R7C6 >= 5

2. R789 !
a) Innies R89 = 27(4) = 69{48/57} -> 6,9 locked for R8
b) ! 13(3) = 8{14/23} -> 8 locked for R8+N8 since {247} blocked by Killer pair (24) of Outies R9 and {157} blocked by Killer pair (57) of 11(2)
c) Innies R89 = 27(4) = {5679}
d) 11(2) = {56} -> CPE: R7C789 <> 5,6
e) Innies N9 = 7(2) = [16/25]
f) Innies N78 = 22(3): R7C3 <> 6 since R7C6 = (56)
g) Innies N7 = 15(2) = [87/96]
h) 10(2) = [37/46]
i) Killer pair (34) locked in R7C4 + 13(3) for N8

3. C789 !
a) 18(3) <> 5 since R7C89 <> 6,9
b) ! Outies C89 = 15(3) <> 8 since 8{16/25} clashes with Innies N9 (CCC)
c) Innies N69 = 13(3) <> 8,9 since R8C7 = (56)
d) 8 locked in 17(3) @ C7 = 8{27/36/45}
e) 9(2) <> 1
f) Innies N69 = 13(3): R45C7 <> 2,5,6 since R8C7 = (56) and {256} is a Killer triple of 17(3)

4. R789 !
a) Outies N8 = 20(2+1) = 7+[76] / 9+{56} -> 6 locked for R8
b) 18(3) <> 4
c) Innies R789 = 18(3) = 9{18/27}
d) Killer pair (28) locked in Innies R789 + 18(3) for R7
e) 15(3) @ N7 = 5{19/37/46} -> 5 locked for N7
f) ! Hidden Killer pair (56) in 20(4) for N9
g) 4 locked in 20(4) @ N9 @ R8C9 = 4{259/268/358/367} <> 1 because of step 4f and {1469} blocked by Killer pair (69) of 15(3) @ N8
h) 1 locked in R7C789 @ N9 for R7
i) 15(3) @ N7 <> 9
j) Hidden Single: R8C8 = 9 @ R8, R6C7 = 9 @ C7

5. C789
a) R6C5 = 7, R7C5 = 9, R7C3 = 8
b) 15(3) @ N8 = {267} locked for R9+N8
c) 18(3) = {279} -> 2,7 locked for R7+N9
d) 2 locked in 17(3) @ C7 = {278} locked for C7+N3
e) R7C6 = 5, R8C7 = 6, R7C7 = 1, R8C3 = 7 -> R7C4 = 3
f) Naked pair (34) locked in R45C7 for C7+N6
g) 20(4) @ N6 = {1289} -> 2,8 locked for C8+N6

6. C123+R1
a) Outies C12 = 6(2) = [24/51]
b) 15(3) @ N1 = 9{15/24} -> 9 locked for C3+N1 since {456} blocked by Killer pair (45) of Outies C12
c) Killer pair (25) locked in 15(3) @ C3 + R6C3 for C3
d) Killer pair (14) locked in 15(3) @ C3 + R9C3 for C3
e) 10(2) <> 1
f) Innies R1 = 11(2) = [47/92]
g) 1 locked in 15(3) @ R1 = 1{59/68} for N2
h) 20(3) = 9{38/56} since R4C3 = (36) -> 9 locked for C4; R34C4 <> 6
i) Naked pair (36) locked in R45C3 for N4
j) 23(4) = 89{15/24} -> R5C2 = 9; R6C2 = (14)

7. N25
a) 15(3) @ N5 = {348} since R5C7 = (34) -> 8 locked for C6+N5; CPE: R5C45 <> 3,4
b) 14(3) <> 6 since R4C7 = (34)
c) Innies N2 = 11(2) = [83/92]
d) 14(3) = {239} since R3C6+R4C7 = (234) -> R4C7 = 3, R3C6 = 2, R4C6 = 9
e) 5(2) = {14} -> R5C5 = 1, R4C5 = 4
f) 11(3) = {236} -> R5C3 = 3; 2,6 locked for C4
g) R5C6 = 8, R5C8 = 2, R5C4 = 6, R6C4 = 2, R6C3 = 5 -> R6C2 = 1
h) 15(3) @ N2 = {168} locked for R1+N2

8. Rest is singles.

Rating:
Hard 1.0 - Easy 1.25. I used a lot of Killer pairs and a combo crossover clash (CCC).
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Andrew
 Post subject: Re: Assassin 308
PostPosted: Sun Feb 01, 2015 5:25 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin! The way I solved it the two diagonal cages made it a fun puzzle with some interesting steps.

Here is my walkthrough for Assassin 308:
Typos corrected. Thanks Afmob and Ed; also for pointing out the CCCs.

Prelims

a) R1C12 = {19/28/37/46}, no 5
b) R1C89 = {18/27/36/45}, no 9
c) R45C5 = {14/23}
d) R67C6 = {79}
e) 10(2) cage at R7C4 = {19/28/37/46}, no 5
f) 11(2) cage at R7C6 = {29/38/47/56}, no 1
g) 20(3) cage at R3C4 = {389/479/569/578}, no 1,2
h) 11(3) cage at R5C3 = {128/137/146/236/245}, no 9

1. Naked pair {79} in R67C5, locked for C5

2. 45 rule on N2 2 innies R3C46 = 11 = {38/47/56}/[92], no 1,9 in R3C6

3. 45 rule on N7 2 innies R78C3 = 15 = {69/78}, clean-up: no 6,7,8,9 in R7C4

4. 45 rule on N9 2 innies R78C7 = 7 = [16]/{25/34}, no 7,8,9, no 6 in R7C7, clean-up: no 2,3,4 in R7C6

5. 45 rule on R1 2 innies R1C37 = 11 = {29/38/47/56}, no 1

6. 45 rule on N4 2 innies R45C3 = 1 outie R7C3 + 1, IOU no 1 in R5C3
6a. Max R45C3 = 10, min R5C3 = 2 -> max R4C3 = 8

7. 45 rule on N6 2 innies R45C7 = 1 outie R7C7 + 6, IOU no 6 in R45C7

8. 45 rule on R9 2 outies R8C19 = 5 = {14/23}

9. 45 rule on R89 4 innies R8C2378 = 27 = {3789/4689/5679}, no 1,2, 9 locked for R8, clean-up: no 9 in R7C6, no 5 in R7C7 (step 4)
9a. 3 of {3789} must be in R8C7 -> no 3 in R8C28

10. 45 rule on R789 3 innies R7C357 = 18 = {189/279/369/378} (cannot be {468} because R7C5 only contains 7,9), no 4, clean-up: no 3 in R8C7 (step 4), no 8 in R7C6
10a. R8C2378 (step 9) = {4689/5679}, 6 locked for R8
10b. R45C7 = R7C7 + 6 (step 7), max R7C7 = 3 -> max R45C7 = 9, no 9 in R45C7

11. R78C7 = 7 (step 4), 11(2) cage at R7C6 -> R7C6 = R7C7 + 4
11a. R7C357 (step 10) = {189/279/369} (cannot be {378} which clashes with R7C67 = [73], CCC), 9 locked for R7
11b. R78C3 = 15 (step 3), 10(2) cage at R7C4 -> R7C3 = R7C4 + 5
11c. 7 of {279} must be in R7C5 (cannot be [792] which clashes with R7C34 = [72], CCC), no 7 in R7C3, clean-up: no 8 in R8C3 (step 4), no 2 in R7C4

12. 11(3) cage at R5C3 = {128/137/146/236/245}
12a. 5,7,8 of {128} must be in R56C4 (R56C4 cannot be {12/13/24} which clash with R45C5) -> no 5,7,8 in R5C3

13. 45 rule on N8 3 innies R7C456 = 17 = {179/359/467}
13a. 13(3) cage at R8C4 = {148/238} (cannot be {157} which clashes with R7C456, cannot be {247} which clashes with R8C19), no 5,7, 8 locked for R8 and N8
13b. R8C2378 (step 10a) = {5679} (only remaining combination), no 4, clean-up: no 7 in R7C6, no 3 in R7C7 (step 4)
13c. R7C456 = {359/467} (cannot be {179} because R7C6 only contains 5,6), no 1, clean-up: no 9 in R8C3, no 6 in R7C3 (step 3)
13d. Killer pair 3,4 in R7C4 and 13(3) cage, locked for N8
13e. Naked pair {56} in 11(2) cage at R7C6, CPE no 5,6 in R7C89
13f. R45C7 = R7C7 + 6 (step 7), max R7C7 = 2 -> max R45C7 = 8, no 8 in R45C7

14. R78C3 (step 3) = [87/96]
14a. R45C3 = R7C3 + 1 (step 6)
14b. R7C3 = {89} -> R45C3 = 9,10 = [36/54/63/73/82] (cannot be [72] which clashes with R78C3 = [87], cannot be {46} which clashes with R78C3 = [96]), no 4 in R4C3

15. R78C7 (step 4) = [16/25]
15a. R45C7 = R7C7 + 6 (step 7)
15b. R7C7 = {12} -> R45C7 = 7,8 = {25/34/17} (cannot be {35} which clashes with R78C7 = [25]) -> R457C7 = {25}1/{34}1/{17}2, 1 locked for C7
15c. R457C7 = {25}1/{34}1/{17}2, CPE no 1 in R56C8

16. 45 rule on N8 3(1+2) outies R6C5 + R8C37 = 20
16a. R6C5 = {79} -> R8C37 = 11,13 = [65/76], 6 locked for R8

17. Hidden killer pair 5,6 in 15(3) cage at R7C1 and R7C6 for R7, R7C6 = {56} -> 15(3) cage must contain one of 5,6 in R7 -> 15(3) cage = {159/357/456} (cannot be {249/348} which don’t contain 5 or 6, cannot be {168/258} because R8C2 only contains 5,7,9 and 5 of {258} must be in R7, cannot be {267} which clashes with R8C3), no 2,8 in R7C12, 5 locked for N7
17a. 7 of {357} must be in R8C2 (cannot be {37}5 because R7C12 must contain 5 or 6) -> no 7 in R7C12
17b. R7C357 (step 11a) = {189/279}
17c. 15(3) cage = {357/456} (cannot be {159} which clashes with R7C357 = {279} = [972]), no 1,9
17d. Killer pair 3,4 in 15(3) cage and R7C4, locked for R7
17e. Killer pair 6,7 in 15(3) cage and R8C3, locked for N7

18. R8C8 = 9 (hidden single in R8)
18a. 1,2 in R7 only in R7C789, locked for N9, clean-up: no 3,4 in R8C1 (step 8)

19. R78C7 (step 15) = [16/25], R457C7 (step 15b) = {25}1/{34}1/{17}2 -> R4578C7 = {25}[16]/{34}[16]/{17}[25]
19a. 17(3) cage at R1C7 = {278/368} (cannot be {269/359/458/467} which clash with R4578C7), no 4,5,9, 8 locked for C7 and N3, clean-up: no 1 in R1C89

20. R6C7 = 9 (hidden single in C7), R67C5 = [79], R7C3 = 8, R8C3 = 7 (step 3) -> R7C4 = 3, R8C2 = 5, R8C7 = 6 -> R7C6 = 5, R7C7 = 1 (step 4), clean-up: no 6 in R3C4, no 8 in R3C6 (both step 2)
20a. 17(3) cage at R1C7 (step 19a) = {278} (only remaining combination), locked for C7 and N3
20b. R45C7 = R7C7 + 6 (step 7), R7C7 = 1 -> R45C7 = 7 = {34}, locked for C7 and N6 -> R9C7 = 5
20c. Naked pair {46} in R7C12, locked for N7
20d. Naked pair {27} in R7C89, locked for N9

21. 4,8 in N8 only in 13(3) cage at R8C4 = {148}, locked for R8 and N8 -> R8C1 = 2, R8C9 = 3, clean-up: no 8 in R1C2, no 6 in R1C8

22. R67C7 = [91] = 10 -> R56C8 = 10 = {28}, locked for C8 and N6 -> R7C89 = [72], R9C89 = [48], clean-up: no 5 in R1C9

23. 5 in C5 only in R123C5, locked for N2, clean-up: no 6 in R3C6 (step 2)

24. Max R3C6 + R4C7 = 11 -> min R4C6 = 3
24a. 14(3) cage at R3C6 = {239/248/347}, no 6
24b. 2,7 only in R3C6 -> R3C6 = {27}, clean-up: no 7,8 in R3C4 (step 2)

25. R45C3 = R7C3 + 1 (step 6)
25a. R7C3 = 8 -> R45C3 = 9 = [36/54/63], no 2

26. Grouped double X-Wing for 3,4 in R45C3, R45C5 and R45C7, no other 3,4 in R45

27. 14(3) cage at R3C6 = {239/248} (cannot be {347} because 3,4 only in R4C7) -> R3C6 = 2, R3C4 = 9 (step 2)
27a. R2C9 = 9 (hidden single in N3)

28. 11(3) cage at R5C3 = {146/236/245} (cannot be {128} because R5C3 only contains 3,4,6), no 8
28a. Killer pair 1,2 in R45C5 and 11(3) cage, locked for N5

29. Min R5C7 + R6C6 = 7 -> max R5C6 = 8
29a. R4C6 = 9 (hidden single in N5), R3C6 = 2 -> R4C7 = 3 (cage sum)
29b. R5C7 = 4 -> R56C6 = 11 = [83], R56C8 = [28]
29c. R5C3 = 3 (hidden single in R5) -> R56C4 = 8 = [62], R4C34 = [65], R4C89 = [17]
29d. R4C12 = [82] = 10 -> R56C1 = 11 = [74]

30. 2 in C3 only in 15(3) cage at R1C3 = {249} (only possible combination) -> R1C3 = 9, R3C3 = 4, R2C3 = 2
30a. R1C12 = {37} (only remaining combination) -> R1C1 = 3, R1C2 = 7

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at Easy 1.25. I think the derived differences in step 11 put it in the 1.25 range. Also I used a Grouped double X-Wing to give a quick finish.
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