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 Post subject: Assassin 284
PostPosted: Fri Feb 07, 2014 7:12 am 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Assassin 284

A serendipity one - the SS score is 1.45 which seems about right.

Image

JS Code:
3x3::k:3329:5890:5890:5890:5890:2819:2819:3844:3844:3329:5890:4101:2310:2310:2819:6663:6663:6663:3336:3616:4101:4101:4874:4874:4874:6663:6663:3336:3616:3616:3851:4874:2572:2572:8476:6663:2335:2335:3851:3851:6685:6685:8476:8476:8476:1552:4369:4369:3851:6685:6685:8476:8476:6420:1552:4369:3349:3349:4888:3614:3614:6420:6420:1302:7959:3349:4888:4888:3353:6420:6420:6420:1302:7959:7959:7959:7959:3353:3353:2586:2586:

Solution:
645932178
721458639
938716452
492583761
817264395
563179284
186345927
254697813
379821546


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PostPosted: Fri Feb 07, 2014 8:29 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! It took me quite some time to solve it which was due to missing step 2h and trying to avoid step 3b.

A284 Walkthrough:
1. C123
a) Innie C1 = R5C1 = 8
b) Cage sum: R5C2 = 1
c) Both 13(2) = {49/67} locked for C1
d) 6(2) = {15} -> R6C1 = 5, R7C1 = 1
e) 5(2) = {23} locked for N7
f) 13(3) = {247/256/346} <> 8,9 because 2,3 only possible @ R7C4 -> R7C4 = (23)

2. R789+N6 !
a) Innies+Outies N6: -2 = R4C6 - R46C9 -> R6C9 <> 2 (IOU @ R4)
b) Outies R9 = 14(3) <> 1 because R8C1 = (23)
c) 1 locked in 25(6) @ R8 for N9+25(6)
d) Innies+Outies R789: -4 = R6C9 - R7C2 -> R6C9 = (34), R7C2 = (78)
e) 25(6) = 12{3469/3478/3568/4567} -> 2 locked for N9
f) 10(2) <> 8,9
g) Killer pair (67) locked in 10(2) + 25(6) for N9
h) ! Hidden Killer pair (45) in 31(5) @ N7 because 13(3) can only have one of them -> 31(5) <> 1
i) Hidden Single: R9C6 = 1 @ N8

3. R789 !
a) 13(3) @ N9: R8C6 <> 2,5,6
b) ! Consider placement of R7C4 -> R8C456 <> 3
- i) R7C4 = 2 -> 2 locked in R8C789 @ N9 for R8 -> R8C1 = 3
- ii) R7C4 = 3
c) ! Innies N78 = 20(2+1) = 7[58/67/94] / 8[57] -> CPE: R8C23 <> 7
d) Outies R9 = 14(3) <> 6,9 because 5,6 only possible @ R8C2 and R8C26 <> 2,3
e) 31(5) = 79{258/348/456} because {35689} blocked by Killer pair (36) of 10(2) -> 7,9 locked for R9
f) 10(2) = {46} locked for R9+N9
g) 25(6) = {123478} -> R6C9 = 4; 3,8 locked for N9
h) R9C7 = 5 -> R8C6 = 7, R7C7 = 9 -> R7C6 = 5, R9C9 = 6
i) Innie R789 = R7C2 = 8

4. R456
a) 17(3) <> 9
b) 15(4): R5C3 <> 9 because {1239} blocked by R7C4 = (23)
c) 9 locked in R4C123 @ N4 for R4
d) 10(2) <> 1
e) Innies N6 = 8(2) = [35/62/71]
f) 10(2) = [37/46]
g) Innies N6 = 8(2) = [62/71]
h) Innies R1234 = 11(2) = {38/56} because (47) is a Killer pair of 10(2)
i) Killer pair (36) locked in Innies R1234 + 10(2) for R4

5. R456
a) 14(3) = 2{39/57} because 3{47} blocked by Killer pair (47) of 10(2) and R4C23 <> 3,5 -> R3C2 = (35); 2 locked for R4+N4
b) Innies N6 = 8(2) = {17} -> R4C7 = 7, R4C9 = 1
c) Cage sum: R4C6 = 3
d) 14(3) = {239} -> R3C2 = 3; 9 locked for N4
e) R4C1 = 4 -> R3C1 = 9

6. R123+N47
a) 13(2) @ R1 = {67} locked for N1
b) Killer pair (67) locked in R1C1 + 15(2) for R1
c) 23(5) = 239{18/45} -> R1C45 = {39} locked for R1+N2
d) 11(3) = 1{28/46} -> R1C7 = 1
e) 23(5) = {23459} -> 2,4,5 locked for N1
f) 16(3) = {178} because R23C3 = (18) -> R3C4 = 7
g) 9(2) = {45} locked for R2+N2 because {18} is blocked by R2C3 = (18)
h) 17(3) = {367} -> R6C2 = 6, R6C3 = 3
i) 15(4) = {1257} because R5C3 = 7 -> R5C3 = 7, R4C4 = 5, R5C4 = 2, R6C4 = 1
j) 13(3) = {346}

7. Rest is singles.

Rating:
(Easy?) 1.5. I used a small forcing chain.


Last edited by Afmob on Thu Feb 13, 2014 2:22 pm, edited 1 time in total.

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 Post subject: Re: Assassin 284
PostPosted: Mon Feb 10, 2014 12:02 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for your Assassin!

It also took me quite a long time to solve it:
before I found step 16. I spent a long time looking at the 45 which Afmob used for his step 3c. I'm not sure whether I missed his CPE; I may have had more options when I was looking at that 45.

Here is my walkthrough for Assassin 284:
Thanks Afmob and Ed for correcting my typos

Prelims

a) R12C1 = {49/58/67}, no 1,2,3
b) R1C89 = {69/78}
c) R2C45 = {18/27/36/45}, no 9
d) R34C1 = {49/58/67}, no 1,2,3
e) R4C67 = {19/28/37/46}, no 5
f) R5C12 = {18/27/36/45}, no 9
g) R67C1 = {15/24}
h) R7C67 = {59/68}
i) R89C1 = {14/23}
j) R9C89 = {19/28/37/46}, no 5
k) 11(3) cage at R1C6 = {128/137/146/236/245}, no 9
l) 19(3) cage at R8C5 = {289/379/469/478/568}, no 1
m) 26(4) cage at R5C5 = {2789/3689/4589/4679/5678}, no 1

1. 45 rule on C1 1 innie R5C1 = 8, R5C2 = 1, clean-up: no 5 in R12C1, no 5 in R34C1, no 5 in R7C1

2. R6C1 = 5 (hidden single in C1), R7C1 = 1, clean-up: no 4 in R89C1
2a. Naked pair {23} in R89C1, locked for N7

3. 45 rule on R789 1 remaining innie R7C2 = 1 outie R6C9 + 4 -> R6C9 = {1234}, R7C2 = {5678}

4. 45 rule on R1234 2 innies R4C48 = 11 = {29/38/47/56}, no 1

5. 45 rule on N9 2 innies R79C7 = 1 outie R6C9 + 10
5a. Min R79C7 = 11, no 1 in R9C7

6. 45 rule on R9 3 outies R8C126 = 14
6a. Max R8C12 = 12 -> min R8C6 = 2
6b. 1 in N8 only in R9C456, locked for R9, clean-up: no 9 in R9C89

7. 1 in N9 only in R8C789, locked for 25(6) cage at R6C9, no 1 in R6C9, clean-up: no 5 in R7C2 (step 3)
7a. Min R6C9 = 2 -> min R79C7 (step 5) = 12, no 2 in R9C7

8. 45 rule on R789 3 remaining outies R6C239 = 13 = {247/346}, no 9, 4 locked for R6

9. 13(3) cage at R7C3 = {247/256/346} (cannot be {238} because 2,3 only in R7C4), no 8,9
9a. 2,3 only in R7C4 -> R7C4 = {23}
9b. 9 in N7 only in R8C2 + R9C23, locked for 31(5) cage at R8C2, no 9 in R9C45

10. Hidden killer pair 4,5 in 13(3) cage at R7C3 and 31(5) cage at R8C2 for N7, 13(3) cage contains one of 4,5 -> 31(5) cage must contain one of 4,5 in N7 (it may also contain 4 or 5 in N8) -> 31(5) cage = {25789/34789/35689/45679} (cannot be {16789} which doesn’t contain 4 or 5), no 1

11. R9C6 = 1 (hidden single in R9), clean-up: no 9 in R4C7
11a. R9C6 = 1 -> R8C6 + R9C7 = 12 = {39/48/57}, no 2,6
11b. R8C126 = 14 (step 6), min R8C12 = 6 -> max R8C6 = 8, clean-up: no 3 in R9C7
11c. Min R12C6 = 5 -> max R1C7 = 6

12. 45 rule on N6 2 innies R46C9 = 1 outie R4C6 + 2, IOU no 2 in R6C9, clean-up: no 6 in R7C2 (step 3)

13. 45 rule on N6 3 innies R4C79 + R6C9 = 12 = {138/147/237/246/345} (cannot be {129/156} because R6C9 only contains 3 and 4), no 9
13a. 5 of {345} must be in R4C9, 3 or 4 of other combinations must be in R6C9 -> no 3,4 in R4C9

14. 25(6) cage at R6C9 = {123469/123478/123568/124567}, 2 locked for N9, clean-up: no 8 in R9C89
14a. 25(6) cage = {123469/123478/123568} (cannot be {124567} which clashes with R9C89)
14b. 25(6) cage = {123469/123478/123568}, CPE no 3 in R9C9, clean-up: no 7 in R9C8
14c. Killer pair 6,7 in 25(6) cage and R9C89, locked for N9, clean-up: no 8 in R7C6, no 5 in R8C6 (step 11a)

15. 15(4) cage at R4C4 = {1239/1248/1257/1347/1356/2346}
15a. 9 of {1239} must be in R45C4 (R456C4 cannot be {23}1 which clashes with R7C4), no 9 in R5C3
15b. 1 in R6C4 or 15(4) cage = {2346} -> R6C4 = {1236}
15c. 9 in N4 only in R4C123, locked for R4, clean-up: no 2 in R4C48 (step 4), no 1 in R4C7

[I don’t know whether this counts as a “serendipity” step.]
16. 31(5) cage at R8C2 (step 10) = {25789/34789/35689/45679}
16a. Consider permutations for R6C9 + R7C2 (step 3) = [37/48]
R6C9 + R7C2 = [37] => 8 in N7 only in 31(5) cage
or R6C9 + R7C2 = [48] => 4 in N9 only in R9C78, locked for R9 => 31(5) cage cannot be 4{5679} which clashes with R9C89
-> 31(5) cage = {25789/34789/35689}
16b. 31(5) cage must contain one of 4,5 in N7 (step 10) -> no 4,5 in R9C45
16c. Killer pair 2,3 in R7C4 and 31(5) cage, locked for N8, clean-up: no 9 in R9C7 (step 11a)
16d. Killer pair 2,3 in R9C1 and 31(5) cage, locked for R9, clean-up: no 7 in R9C9
16e. Naked pair {46} in R9C89, locked for R9 and N9, clean-up: no 8 in R8C6 (step 11a)
16f. 7,9 in R9 only in R9C2345, locked for 31(5) cage, no 7,9 in R8C2

17. R79C7 = R6C9 + 10 (step 5)
17a. R6C9 = {34} -> R79C7 = 13,14 = {58}/[95], 5 locked for C7 and N9

18. 31(5) cage at R8C2 (step 16a) = {25789/34789} (cannot be {35689} which clashes with R9C7), no 6
[Ed pointed out Ed that 31(5) cage contains both of 7,9 (step 16f) is simpler.]
18a. 6 in N7 only in R78C3, locked for C3
18b. 13(3) cage at R7C3 (step 9) = {256/346}, no 7

19. R6C239 (step 8) = {247/346}
19a. 6 of {346} must be in R6C2, 4 of {247} must be in R6C9 -> no 3,4 in R6C2

20. 19(3) cage at R7C5 = {469/568} (cannot be {478} which clashes with R8C6), no 7, 6 locked for N8, clean-up: no 8 in R7C7
20a. Naked pair {59} in R7C67, locked for R7
20b. R7C35 = {46} (hidden pair in R7)

21. 25(6) cage at R6C9 (step 14a) = {123478} (only remaining combination), 8 locked for N9 -> R9C7 = 5, R8C6 = 7 (step 11a), R7C67 = [59], clean-up: no 3 in R4C7
21a. 25(6) cage = {123478} -> R6C9 = 4, R7C2 = 8 (step 3), R9C89 = [46], clean-up: no 9 in R1C8, no 6 in R4C6
21b. R6C9 = 4 -> R4C79 (step 13) = 8 = [62/71], R4C6 = {34}
21c. Naked triple {238} in R7C4 + R9C45, 8 locked for R9 and N8

22. 45 rule on N3 2 innies R13C7 = 1 outie R4C9 + 4
22a. R4C9 = {12} -> R13C7 = 5,6 = {14/24} (cannot be {23} because whichever value is in R4C9 must also be in one of R13C7), 4 locked for N3

23. 11(3) cage at R1C6 = {128/146/236}
23a. 1 of {146} must be in R1C7 -> no 4 in R1C7

24. R3C7 = 4 (hidden single in N3), clean-up: no 9 in R4C1

25. 9 in R4 only in 14(3) cage at R3C2 = {239}, R3C2 = {23}
25a. Killer pair 2,3 in 14(3) cage and 17(3) cage at R6C2, locked for N4

26. 45 rule on N5 2 innies R4C56 = 1 outie R5C3 + 4
26a. R5C3 = {47} -> R4C56 = 8,11 = [53/74/83]
26b. R4C9 = 1 (hidden single in R4), R4C7 = 7 (step 21b), R4C6 = 3, clean-up: no 6 in R3C1
[I forgot about clean-up for R4C48 (step 4) but this isn’t important, so I haven’t re-worked.]

27. Naked pair {29} in R4C23, locked for N4 and 14(3) cage at R3C2 -> R3C2 = 3, R6C3 = 3 (hidden single in N4), R6C2 = 6 (cage sum), R4C1 = 4, R3C1 = 9

28. R5C4 = 7 -> R456C4 = 8 = {125} (only remaining combination) = [521], R4C5 = 8, R4C8 = 6, clean-up: no 9 in R1C9, no 4,7 in R2C5

29. Naked pair {78} in R1C89, locked for R1 and N3

30. R2C6 = 8 (hidden single in C6) -> R1C67 = 3 = [21], R3C6 = 6, R3C5 = 1 (cage sum)
30a. R2C45 = {45} (only remaining combination) = [45]

31. R7C4 = 3 -> R78C3 = 10 = {46}, locked for C3 and N7

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A284 at Easy 1.5; I used a short forcing chain. I was also tempted to write (Easy?) like Afmob did, because it took me a long time to find that step.


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 Post subject: Re: Assassin 284
PostPosted: Thu Feb 13, 2014 9:21 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
Step 8 was a "pleasant surprise" when it popped out so loved this Assassin! Thanks HATMAN! This puzzle took about the normal time being completely stuck.....a long while. So, makes the resolution very satisfying. I found a very different way to get started.

A284 Start
8 steps:
Preliminaries courtesy of SudokuSolver
Cage 5(2) n7 - cells only uses 1234
Cage 6(2) n47 - cells only uses 1245
Cage 14(2) n89 - cells only uses 5689
Cage 15(2) n3 - cells only uses 6789
Cage 13(2) n14 - cells do not use 123
Cage 13(2) n1 - cells do not use 123
Cage 9(2) n2 - cells do not use 9
Cage 9(2) n4 - cells do not use 9
Cage 10(2) n9 - cells do not use 5
Cage 10(2) n56 - cells do not use 5
Cage 11(3) n23 - cells do not use 9
Cage 19(3) n8 - cells do not use 1
Cage 26(4) n5 - cells do not use 1

1. "45" on c1: 1 innie r5c1 = 8, r5c2 = 1
1a. Two 13(2) cages in c1 = {49/67}(no 5)
1b. 5 in c1 only in 6(2)r6c1 -> r6c1 = 5, r7c1 = 1
1c. 5(2)r8c1 = {23} only: both locked for n7

2. "45" on r9: 3 outies r8c126 = 14
2a. Must have 2 or 3 for r8c1 = {239/248/257/347/356}(no 1)

3. 1 in r8 only in r8c789: 1 locked for n9 and 25(6)r6c9
3a. no 1 in r6c9
3b. no 9 in 10(2)n9

4. "45" on n6: 2 innies r46c9 - 2 = 1 outie r4c6
4a. One outie and one innie see each other in r4 -> the 3rd cell cannot equal the Innie Outie difference -> no 2 in r6c9 (IOU)

5. 25(6)r6c9 must have a 2 which is only in n9: 2 locked for n9
5a. no 8 in 10(2)n9

6. "45" on r6789: 1 remaining outie r6c9 + 4 = 1 remaining innie r7c2 = [37/48]

[Saw this next step at the very start of the puzzle but couldn't make it powerful enough until 8b. emerged]
7. "45" on n9: 1 outie r6c9 + 10 = 2 innies r79c7
7a. -> r6c9 cannot repeat in n9 in one of those innies since the other innie can't = 10
7b. -> r6c9 = r9c8 = (34) (Clone)
7c. r9c9 = (67)

8. Combining steps 6 & 7: r7c2 + r9c89 = [7][37]/[8][46]
8a. 31(5)r8c2 = {16789/25789/34789/35689/45679}: ie must have 7 or have 3 in r9c45
8b. -> [7][37] blocked from r7c2+r9c89
8c. -> r7c2 = 8, r9c89 = [46], r6c9 = 4
[Very disappointed I missed the Hidden killer pair 4,5 in n7 (Afmob's 2h, Andrew's 10) which would made step 8a. have one less combo.]

on from there. Just normal hard now.
Cheers
Ed


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