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Andrew
 Post subject: Assassin 232
PostPosted: Thu Feb 02, 2012 11:02 pm 
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Many thanks to Andrew for posting this puzzle for me. Out of net world for a little while in the backblocks of Indonesia. This is my first ever "zero" killer. I tried the cage striping approach that HATMAN used for a recent Assassin but this is no-where near as good as the ones he makes. Much easier than my usual Assassins but I hope you still find it satisfying.

Assassin 232

Image

code: paste into solver:
3x3::k:4864:4864:2817:2306:2306:2306:7191:3860:3860:4106:4864:2817:7191:7191:7191:7191:3860:6407:4106:0000:0000:0000:3094:5637:5637:5637:6407:4106:4106:4117:3094:3094:2563:6407:6407:6407:2059:4117:4117:2820:2820:2563:2831:3090:4102:2059:7432:7432:0000:0000:0000:2831:3090:4102:3347:3347:7432:0000:0000:0000:2320:2320:4102:2572:7432:7432:7432:5897:0000:0000:0000:2318:2572:2829:2829:5897:5897:5897:1041:1041:2318:
solution: 
+-------+-------+-------+
| 4 7 9 | 1 3 5 | 2 6 8 |
| 5 8 2 | 6 9 7 | 4 1 3 |
| 3 6 1 | 2 4 8 | 5 9 7 |
+-------+-------+-------+
| 7 1 8 | 3 5 6 | 9 4 2 |
| 6 3 5 | 9 2 4 | 8 7 1 |
| 2 9 4 | 7 8 1 | 3 5 6 |
+-------+-------+-------+
| 8 5 6 | 4 1 3 | 7 2 9 |
| 1 2 3 | 5 7 9 | 6 8 4 |
| 9 4 7 | 8 6 2 | 1 3 5 |
+-------+-------+-------+
Cheerio
Ed

[Edit Andrew]I'll post Ed's walkthrough in about a week.
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HATMAN
 Post subject: Re: Assassin 232
PostPosted: Fri Feb 03, 2012 6:25 pm 
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Ed

Thanks for the compliment - if it is easier maybe I can solve it for a change.

Maurice
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Andrew
 Post subject: Re: Assassin 232
PostPosted: Fri Feb 03, 2012 11:10 pm 
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Congratulations Ed on posting your first zero killer! Thanks for an enjoyable puzzle! :D

Yes, Maurice, it is easier than Ed's recent Assassins.

Rating Comment:
I'll rate my walkthrough for A232 at Hard 1.25 mainly based on steps 7 and 24. Then there was a useful hidden killer pair for the final breakthrough.

Here is my walkthrough for A232:
Thanks Ed for pointing out an error in my step 19. I've deleted that step and modified step 20 to give the same result.

Prelims

a) R12C3 = {29/38/47/56}, no 1
b) R45C6 = {19/28/37/46}, no 5
c) R56C1 = {17/26/35}, no 4,8,9
d) R5C45 = {29/38/47/56}, no 1
e) R56C7 = {29/38/47/56}, no 1
f) R56C8 = {39/48/57}, no 1,2,6
g) R7C12 = {49/58/67}, no 1,2,3
h) R7C78 = {18/27/36/45}, no 9
i) R89C1 = {19/28/37/46}, no 5
j) R89C9 = {18/27/36/45}, no 9
k) R9C23 = {29/38/47/56}, no 1
l) R9C78 = {13}
m) 19(3) cage at R1C1 = {289/379/469/478/568}, no 1
n) 9(3) cage at R1C4 = {126/135/234}, no 7,8,9
o) 22(3) cage at R3C6 = {589/679}

1. Naked pair {13} in R9C78, locked for R9 and N9, clean-up: no 6,8 in R7C78, no 7,9 in R8C1, no 6,8 in R89C9, no 8 in R9C23

2. Naked quad {2457} in R7C78 + R89C9, locked for N9

3. 22(3) cage at R3C6 = {589/679}, 9 locked for R3

4. 45 rule on R12 2 innies R2C19 = 8 = {17/26/35}, no 4,8,9

5. 45 rule on N6 3 outies R237C9 = 19 = {289/379/469/568} (cannot be {478} which clashes with R89C9), no 1, clean-up: no 7 in R2C1 (step 4)
5a. 2 of {289} must be in R2C9 -> no 2 in R3C9

6. 45 rule on N7 3 innies R7C3 + R8C23 = 11 = {128/137/146/236} (cannot be {245} which clashes with R9C23), no 5,9

7. R7C3 + R8C23 (step 6) = {128/137/146/236}, R89C1 = {19/28/37/46} -> combined cage R7C3 + R8C23 + R89C1 must contain at least one of 6,7
7a. R7C12 = {49/58} (cannot be {67} which clashes with R7C3 + R8C23 + R89C1), no 6,7

8. R7C78 = {27} (cannot be {45} which clashes with R7C12), locked for R7 and N9

9. Naked pair {45} in R89C9, locked for C9, clean-up: no 3 in R2C1 (step 4)

10. R237C9 (step 5) = {289/379} -> R7C9 = 9, R23C9 = 10 = [28/37/73], no 6, clean-up: no 2 in R2C1 (step 4), no 4 in R7C12
10a. R7C9 = 9 -> R56C9 = 7 = {16} (only remaining combination), locked for C9 and N6, clean-up: no 5 in R56C7
10b. 9 in N7 only in R9C123, locked for R9

11. Naked pair {68} in R8C78, locked for R8, clean-up: no 2,4 in R9C1

12. Naked pair {58} in R7C12, locked for R7 and N7, clean-up: no 2 in R8C1, no 6 in R9C23

13. 45 rule on R9 2 innies R9C19 = 1 outie R8C5 + 7
13a. Min R9C19 = 10 -> min R8C5 = 3
13b. Max R9C19 = 14 -> max R8C5 = 7

14. R7C456 only contain 1,3,4,6
14a. 8 in N8 only in 23(4) cage at R8C5 = {2678/3578} (cannot be {4568} which clashes with R7C456, ALS block), no 4, 7 locked for N8
14b. 3 of {3578} must be in R8C5 -> no 5 in R8C5

15. R9C19 = R8C5 + 7 (step 13)
15a. R8C5 = {37} -> R9C19 = 10,14 = [64/95], no 7 in R9C1, clean-up: no 3 in R8C1

16. 3 in N7 only in R7C3 + R8C23, locked for 29(6) cage at R6C2, no 3 in R6C23 + R8C4
16a. R7C3 + R8C23 (step 6) = {137/236}, no 4
16b. 1 of {137} must be in R8C23 (R8C23 cannot be {37} which clashes with R8C5), no 1 in R7C3
16c. 1,4 in R7 only in R7C456, locked for N8

17. 45 rule on N7 3 outies R6C23 + R8C4 = 18 = {189/459} (cannot be {279/567} which clash with R7C3 + R8C23, cannot be {468} because no 4,6,8 in R8C4), no 2,6,7, CPE no 9 in R6C4

18. 45 rule on C1 2 innies R17C1 = 1 outie R4C2 + 11
18a. Min R17C1 = 12 -> min R1C1 = 4
18b. Max R17C1 = 17 -> max R4C2 = 6
18c. R17C1 cannot total 16 -> no 5 in R4C2
18d. 2,3 in C1 only in R3456C1, CPE no 2,3 in R4C2
18e. R4C2 = {146} -> R17C1 = 12,15,17 = [48/75/78/98] -> R1C1 = {479}

19. Deleted]

20. Killer triple 1,5,6 in R2C1, R56C1 and R89C1 for C1 -> R7C1 = 8, R7C2 = 5

21. 16(4) cage at R2C1 = {1249/1267/1357/2356} (cannot be {1456} because 1,5,6 only in R2C1 + R4C2, cannot be {2347} because R2C1 only contains 1,5,6)
21a. 2,9 of {1249} only in R34C1 -> no 4 in R34C1

22. 45 rule on N236 2 remaining innies R3C45 = 6 = {15/24}
22a. 9(3) cage at R1C4 = {135/234} (cannot be {126} which clashes with R3C45), no 6, 3 locked for R1 and N2, clean-up: no 8 in R2C3
22b. Naked quad {12345} in 9(3) cage and R3C45, locked for N2

23. 3 in C9 only in R234C9, locked for 25(5) cage at R2C9, no 3 in R4C78

24. Min R12C7 = 5 (cannot be 3 because max R2C456 = 24, cannot be 4 = {13} which clashes with R9C7) -> max R2C456 = 23 must contain 6, locked for R2, N2 and 28(5) cage at R1C7, no 6 in R12C7, clean-up: no 5 in R1C3, no 2 in R2C9 (step 4), no 8 in R3C9 (step 10)
24a. Min R2C456 = 21 -> max R12C7 = 7, no 7,8,9

25. Naked pair {37} in R23C9, locked for C1, N3 and 25(5) cage at R2C9, no 7 in R4C78

26. R23C9 = {37} = 10 -> R4C789 = 15 = {249/258}, 2 locked for R4 and N6, clean-up: no 8 in R5C6, no 9 in R56C7
26a. Killer pair 4,8 in R4C789 and R56C7, locked for N6
26b. 7 in R1 only in R1C123, locked for N1, clean-up: no 4 in R1C3

27. 1 in N1 only in R2C1 + R3C23
27a. 45 rule on N1 4 innies R23C1 + R3C23 = 15 contains 1 = {1248/1356}
27b. R3C1 = {23} -> no 2,3 in R3C23
27c. R12C3 = {29/47/56} (cannot be {38} which clashes with R23C1 + R3C23), no 3,8
27d. 19(3) cage at R1C1 = {289/379/478} (cannot be {469} which clashes with R23C1 + R3C23), no 6

28. 15(3) cage at R1C8 = {168/249/258} (cannot be {159/456} because R1C9 only contains 2,8)
28a. Hidden killer pair 6,8 in 15(3) cage and 22(3) cage at R3C6, 22(3) cage cannot contain both of 6,8 -> 15(3) cage must contain at least one of 6,8 -> 15(3) cage = {168/258}, no 4,9

29. 9 in N3 only in R3C78, locked for R3
29a. 9 in N2 only in R2C456, locked for R2, clean-up: no 2 in R1C3

30. 4 in N3 only in R12C7, locked for C7, clean-up: no 7 in R56C7
30a. 28(5) cage at R1C7 contains 4 = {14689/24679}, no 5

31. Naked pair {38} in R56C7, locked for C7 and N6 -> R4C9 = 2, R1C9 = 8, R8C78 = [68], clean-up: no 9 in R56C8

32. Naked pair {57} in R56C8, locked for C8 and N6 -> R4C78 = [94], R7C78 = [72], R3C7 = 5, R12C8 = [61], R2C1 = 5, R2C9 = 3 (step 4), R3C9 = 7, R3C68 = [89], clean-up: no 3 in R56C1, no 1,2,6 in R5C6

33. 9(3) cage at R1C4 (step 22a) = {135} (only remaining combination, cannot be {234} which clashes with R1C7), locked for N2

34. Naked pair {24} in R3C45, locked for R3 -> R3C1 = 3

35. 16(4) cage at R2C1 (step 21) = {1357} (only remaining combination) -> R4C12 = [71], clean-up: no 3,9 in R5C6

36. Naked pair {26} in R56C1, locked for C1 and N4 -> R9C1 = 9, R1C1 = 4, R8C1 = 1, clean-up: no 2 in R9C23

37. Naked pair {47} in R9C23, locked for R9 and N7 -> R9C9 = 5

38. R2C3 = 2, R1C3 = 9, R8C23 = [23], R7C3 = 6, R8C5 = 7, R12C2 = [78], R9C23 = [47], R6C2 = 9, R8C4 = 5, R6C3 = 4 (step 17), R5C2 = 3, R56C7 = [83], R45C3 = [85], R56C8 = [75], R5C6 = 4, R4C6 = 6, R4C45 = [35], R3C5 = 4 (cage sum)

and the rest is naked singles.
I'll be interested to see how Ed solved this puzzle, after I've posted his walkthrough next week.


Last edited by Andrew on Sun Feb 19, 2012 5:43 am, edited 3 times in total.

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wellbeback
 Post subject: Re: Assassin 232
PostPosted: Sat Feb 04, 2012 10:49 pm 
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Posts: 282
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It must be easier than normal - I managed to do it without my usual chains :)

Now to read how Andrew did it...

Hidden Text:
1. c9
4/2@r9c7 = {13}
Outies n36 = +39. -> r2c456+r3c6 = {6789} and r7c9=9.
-> Innies n9 -> r8c78 = {68}
Also Outies n6 -> r23c9 = +10 (no 1,5)
-> Innies c9 r14c9 = +10 (no 1,5)
-> r56c9 = {16}
-> 9/2@r8c9 = {45}
-> 9/2@r7c7 = {27}
-> 13/2@r7c1 = {58}

2. r8 and c1
Outies r9 r8c159 = +12. Since r8c9 = (4|5) -> no 9 in r8c15.
Innies n7 r7c3+r8c23 = +11 -> no 9.
-> 9 in r8 in r8c4 or r8c6

8/2 and 10/2 on c1 must between them contain at least one of (13).
-> r23c1 cannot be {13} -> r23c1 not = +4.
Outies n47 r23c1+r8c4 = +13.
-> r8c4 not 9.
-> r8c6 = 9.
-> Innies r89 r8c234 = +10.
-> r7c3 (from 1346) must be 1 more than r8c4.
-> [r7c3,r8c4] = [65] or [32]. (r7c3 = 4 would put two 3s in n8).

But a 29/6 cage has no solution which contains { 3, 2, +8/2, +16/2 }.

-> [r7c3,r8c4] = [65], r6c23 = +13 = {49}, r8c23 = {23}, r89c9 = [45], r89c1 = [19], r9c23 = {47}
r8c5 = 7, r7c456 = {134}, r9c456 = {268}

3. n14
Innies n4 r4c12 = +8, -> r23c1 = +8.
Since r56c1 also = +8 -> r23456c1+r4c2 = {17 26 35}
1 already in c1 -> r4c12=[71]
-> r7c12=[85]
also HS 4 in c1 r1c1 = 4
also Innies n1 r3c23 = +7 must contain a 1 -> r3c23 = [61]
-> r12c2 = {78}, -> r12c3 = {29}, -> r23c1 = {35}, -> r56c1 = {26},
-> r45c3 = {58}, r5c2 = 3, -> r8c23 = [23]

4. n23
9/3@r1c4 can only be {135}
-> r3c45 = {24}
6 in r3c2 -> 22/3@r3c6 = [8{59}]
-> r2c456 = {679}
-> r12c2 = [78], r12c3 = [92]
-> r12c7 = +6 must be [24]
-> r23c9 = {37}
Innies r12 r2c19 = +8 must be [53]
-> r3c19 = [37]
-> 15/3@r1c8 = [681]
-> r8c78 = [68], r9c78 = [13], and r7c78 = [72]

5. n56
3 in n6 can only be 11/2@r5c7 = {38}
As Andrew points out 3 is already in r5 at c2 so 11/2@r5c7 must be [83] which makes some of the below a little more complicated than it need be.
-> 12/2@r5c8 = {57}
-> r4c789 = [942]
-> 9 in n5 -> 11/2@r5c4 = {29}
-> r56c1 = [62]
-> r56c9 = [16]
Also 4 in n5 -> r45c6 = [64]
Since r3c5 = (2|4) -> 8 not in r4c45
-> 8 in n5 in r6c12 -> r56c7 = [83]
-> r45c3 = [85], r56c8 = [75]
-> r4c45 = [35], r3c45 = [24], r1c456 = [135]

etc., etc.


Last edited by wellbeback on Sun Feb 05, 2012 6:48 am, edited 1 time in total.

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Andrew
 Post subject: Re: Assassin 232
PostPosted: Sun Feb 05, 2012 12:32 am 
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Nice start to wellbeback's walkthrough:
Outies n36 = +39. -> r2c456+r3c6 = {6789} and r7c9=9.Outies n36 = +39. -> r2c456+r3c6 = {6789} and r7c9=9 is neat and gets into this Assassin very quickly.

I guess I ought to have looked more closely at the upper right part of the grid, which has several large cages.

I also liked wellbeback's analysis of the 29(6) cage.
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Andrew
 Post subject: Re: Assassin 232
PostPosted: Fri Feb 10, 2012 6:06 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Here is Ed's walkthrough for A232, supplied when he asked me to post this Assassin for him.

Hidden Text:
1. 4(2)n9 = {13}: both locked for n9 and r9
1a. -> the two 9(2) cages in n9 = {27/45}: all locked for n9
1b. no 8 in 11(2)n7
1c. no 7,9 in r8c1

2. 10(2)n7 = [19/37]{28/46} = [2/6/7/9..]
2a. 11(2)n7 = {29/47/56} = both 2,9 or [6/7..]
2c. -> {67} blocked from 13(2)n7 since it would clash with the 10(2) + 11(2) (no 6,7)

3. 13(2)n7 = {49/58} = [4/5..]
3a. -> {45} blocked from 9(2)r7c7
3b. -> 9(2)r7c7 = {27} only: both locked for r7 & n9
3c. -> 9(2)r8c9 = {45}: both locked for c9

4. "45" on r12: 2 innies r2c19 = 8 (no 4,8,9)
4a. no 3 in r2c1

5. 22(3)r3c6 must have 9 -> 9 locked for r3

6. "45" on n6: 3 outies r237c9 = 19(3) = {289/379}(no 1,6)
6a. must have 9 -> r7c9 = 9
6b. no 2,7 in r2c1 (h8(2)r2c19
6c. & 13(2)n7 = {58} only: both locked for r7 and n7
6d. no 2 in 10(2)n7
6e. no 6 in 11(2)n7

7. r7c9 = 9 -> r56c9 = 7 = {16} only: both locked for c9 and n6
7a. no 5 in 11(2)n6

8. r123c9 has three of {2378}
8a. "45" on n3: 4 innies r12c7 + r3c78 = 20
8b. {1379/1478/2369/2378/2468/2567/3458/3467} all blocked by r123c9
8c. = {1289/1469/1568/2459}(no 3,7)

9. 22(3)r3c6 = {589/679}
9a. 7 in {679} must be in r3c6 -> no 6 in r3c6

10. "45" on n36: 4 remaining outies r2c456+r3c6 = 30 = {6789} only: all locked for n2
10a. 6 locked for r2 and 28(5)r1c7 -> no 6 in r1c7
10b. no 2 in r2c9 (h8(2)r2c19)

11. "45" on n6: 2 remaining outies r23c9 = 10 = {37} only: both locked for c9, n3 and 25(5)r2c9
11a. -> no 3,7 in r4c78

12. 15(3)n3 must have 2/8 for r1c9 = {168/249/258} = [1/2..](no eliminations yet)
12a. -> from step 8c, {1289} blocked from h20(4)n3
12b. 22(3)r3c6 = [8]{59}/[7]{69} -> no 9 in r3c6
12c. r3c78 must have 9: 9 locked for n3
12d. -> h20(4)n3 = {1469/2459}(no 8)
12e. must have 4 -> 4 locked for n3 & c7
12f. no 7 in 11(2)n6

13. r7c7 = 7 (hsingle c7)
13a. r7c8 = 2

14. r23c9 = 10 -> r4c789 = 15 = {249/258}
14a. must have 2 -> 2 locked for r4 and n6
14b. -> 11(2)n6 = {38}: both locked for c7 & n6

On from there.
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