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Ed
 Post subject: Assassin 258
PostPosted: Fri Apr 19, 2013 3:23 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
First time doing this I thought it was going to be too hard or at least, not interesting enough. Very stuck. However, as so often happens, perseverance payed off with a very-hard-to-spot-but-not-too-complicated move opening up. Now that I've optimised my solution, it takes two advanced steps. It gets a SudokuSolver score of 1.55.

Assassin 258
Image
code:
3x3::k:1817:1817:3329:3329:1282:4099:4099:3844:3844:5146:5146:5146:3329:1282:4099:3845:3845:2310:6407:5146:5128:5128:4873:4873:4873:3845:2310:6407:5128:5128:2058:2058:6923:4364:4364:4364:6407:4621:4621:4621:6923:6923:6923:2318:2318:6407:6407:5647:5392:5392:2577:6923:3090:3090:2579:2579:5647:5392:3604:2577:6923:4885:3090:3094:4375:5647:5647:3604:3864:4885:4885:4885:3094:4375:4375:4375:3604:3864:3864:2560:2560:
Solution: 
+-------+-------+-------+
| 2 5 8 | 3 1 7 | 4 9 6 |
| 1 6 9 | 2 4 5 | 3 7 8 |
| 7 4 3 | 6 8 9 | 2 5 1 |
+-------+-------+-------+
| 6 9 2 | 1 7 3 | 5 8 4 |
| 4 8 1 | 9 5 2 | 7 6 3 |
| 5 3 7 | 8 6 4 | 9 1 2 |
+-------+-------+-------+
| 8 2 5 | 7 3 6 | 1 4 9 |
| 3 7 6 | 4 9 1 | 8 2 5 |
| 9 1 4 | 5 2 8 | 6 3 7 |
+-------+-------+-------+
Cheerio
Ed
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Andrew
 Post subject: Re: Assassin 258
PostPosted: Tue Apr 23, 2013 1:47 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for another interesting Assassin.

As you suggested, some of the steps were hard to spot. As a result, although this isn't an optimised walkthrough, I've re-written several parts when I spotted steps which simplified what I'd previously done at those stages.

Step 15b+c may possibly be one of Ed's advanced steps. I don't know whether steps 14a and 14c count as advanced steps.

Here is my walkthrough for Assassin 258:
Prelims

a) R1C12 = {16/25/34}, no 7,8,9
b) R12C5 = {14/23}
c) R1C89 = {69/78}
d) R23C9 = {18/27/36/45}, no 9
e) R4C45 = {17/26/35}, no 4,8,9
f) R5C89 = {18/27/36/45}, no 9
g) R67C6 = {19/28/37/46}, no 5
h) R7C12 = {19/28/37/46}, no 5
i) R89C1 = {39/48/57}, no 1,2,6
j) R9C89 = {19/28/37/46}, no 5
k) 19(3) cage at R3C5 = {289/379/469/478/568}, no 1
l) 21(3) cage at R6C4 = {489/579/678}, no 1,2,3

1. 45 rule on R1 2 outies R2C46 = 1 innie R1C5 + 6, IOU no 6 in R2C46
1a. 45 rule on R1 3 outies R2C456 = 11 = {128/137/245}, no 9

2. 45 rule on C1234 2 outies R46C5 = 13 = [58/67/76], clean-up: no 5,6,7 in R4C4

3. 45 rule on C6789 2 outies R35C5 = 13 = {49/58/67}, no 1,2,3

4. 45 rule on R12 3 outies R3C289 = 10 = {127/136/145/235}, no 8,9, clean-up: no 1 in R2C9

[I did step 6 before step 5; their order has been changed to simplify them.]

5. 45 rule on N23 3 innies R123C4 = 11 = {146/236} (cannot be {128/137/245} which clash with R12C5), no 5,7,8,9, 6 locked for C4 and N2
5a. Naked quint {12346} in R123C4 + R12C5, locked for N2
5b. Clean-up: no 7,9 in R5C5 (step 3)

6. 45 rule on N3 2 innies R13C7 = 6 = [15/24/42]
6a. 19(3) cage at R3C5 = {289/478}, no 5, 8 locked for R3 and N2, clean-up: no 1 in R1C7, no 8 in R5C5 (step 3)
6b. Naked pair {24} in R13C7, locked for C7 and N3, clean-up: no 5,7 in R23C9
6c. Killer pair 6,8 in R1C89 and R23C9, locked for N3
6d. 5 in N2 only in R12C6, locked for C6

7. 15(3) cage at R2C7 = {159/357}
7a. 3 of {357} must be in R2C78 (R2C78 cannot be {57} which clashes with R2C6), no 3 in R3C8

8. 45 rule on R123 3 innies R3C134 = 16 = {169/259/367/457} (cannot be {349} which clashes with 19(3) cage at R3C5)
8a. 2,4 of {259/457} must be in R3C4 -> no 2,4 in R3C13
8b. R3C289 (step 4) = {136/145/235} (cannot be {127} which clashes with R3C134), no 7
8c. 2,4 of {145/235} must be in R3C2 -> no 5 in R3C2
8d. 4 of {145} must be in R3C2, 1 of {136} must be in R3C8 -> no 1 in R3C2

9. 45 rule on C1234 3 innies R467C4 = 16 = {178/259} (cannot be {349} which clashes with R123C4, cannot be {358} because 21(3) cage at R6C4 cannot contain both of 5,8, cannot be {457} because no 4,5,7 in R4C4), no 3,4, clean-up: no 5 in R4C5, no 8 in R6C5 (step 2)
9a. Killer pair 1,2 in R123C4 and R4C4, locked for C4
9b. Naked pair {67} in R46C5, locked for C5 and N5, clean-up: no 3,4 in R7C6
9c. 21(3) cage at R6C4 = {579/678}
9d. 8 of {678} must be in R6C4 -> no 8 in R7C4
9e. R5C89 = {18/27/36} (cannot be {45} which clashes with R5C5), no 4,5 in R5C89
9f. 7 in C4 only in R789C4, locked for N8, clean-up: no 3 in R6C6
9g. 3 in N5 only in R4C6 + R5C46, CPE no 3 in R5C7

10. Max R12C4 = 10 -> min R1C3 = 3
10a. 13(3) cage at R1C3 = {148/238/256/346} (cannot be {139/247} which clash with R12C5, cannot be {157} because 5,7 only in R1C3), no 7,9
10b. 5 of {256} must be in R1C3, 6 of {346} must be in R1C4 (cannot be 6{34} which clashes with R12C5), no 6 in R1C3
10c. 45 rule on N23 1 outie R1C3 = 1 innie R3C4 + 2, no 4 in R3C4

11. Hidden killer pair 7,9 in R1C6 and R1C89 for R1, R1C89 contains one of 7,9 -> R1C6 = {79}
11a. R2C6 = 5 (hidden single in N2)
11b. R3C8 = 5 (hidden single in N3)
11c. R3C289 (step 8b) = {145/235} -> R3C2 = {24}, R3C9 = {13}, clean-up: no 3 in R2C9
11d. Naked pair {24} in R3C27, locked for R3

12. Killer pair 6,8 in 13(3) cage at R1C3 and R1C89, locked for R1, clean-up: no 1 in R1C12
12a. Killer pair 2,4 in R1C12 and R1C7, locked for R1, clean-up: no 1,3 in R2C5
12b. R2C45 = {24} (hidden pair in N2), locked for R2

13. 1 in R1 only R1C45, locked for N2, clean-up: no 3 in R1C3 (step 10c)

14. 45 rule on N69 3 outies R4C6 + R5C56 = 1 innies R9C7 + 4
14a. Min R4C6 + R5C56 = 8 (cannot be {124} which clashes with R67C6) -> no 1,3 in R9C7
[Ed pointed out to me that {124} clashes with R4C4 is simpler!]
14b. Max R4C6 + R5C56 = 13, min R5C5 = 4 -> max R45C6 = 9, no 9 in R45C6
14c. Max R4C6 + R5C56 = 13, cannot be {148} which clashes with R67C6 -> no 8 in R45C6
14d. Max R4C6 + R5C56 = 12 -> max R9C7 = 8

15. 15(3) cage at R2C7 = {159/357} -> R2C78 = {19/37}
15a. 20(4) cage at R2C1 = {1289/1469/3467} (cannot be {2369/2378/2468} which clash with R1C12, cannot be {1379/1478} which clash with R2C78)
15b. R3C29 = [23/41] (step 11c) -> R2C78 + R3C2 = {19}2/{37}4
15c. 15c. 20(4) cage = {1469} (only remaining combination, cannot be {1289/3467} which clash with R2C78 + R3C2, killer combo blockers) -> R2C123 = {169}, locked for R2 and N1, R3C2 = 4, R2C9 = 8, R3C9 = 1, R3C7 = 2, R1C7 = 4, R1C6 = 7 (cage sum)
15d. R1C3 = 8 (hidden single in R1), R3C4 = 6 (step 10c)
15e. Clean-up: no 3 in R1C12, no 1,8 in R5C8, no 6 in R7C1, no 2,9 in R9C8

16. R3C4 = 6 -> 20(4) cage at R3C3 = {2369/2567/3467} (cannot be {1469/1568/2468} because R3C3 only contains 3,7), no 1,8
16a. 3,7 of {2369} must be in R3C3, 4 of {3467} must be in R4C3 -> no 3,7, in R4C3

17. 18(3) cage at R5C2 = {189/279/369/468} (cannot be {378/567} which clash with R5C89, cannot be {459} which clashes with R5C5), no 5
17a. 45 rule on N1234 1 outie R5C4 = 1 innie R6C3 + 2 -> R6C3 = {1267}
17b. 18(3) cage = {189/369/468} (cannot be {279} because R5C23 + R6C3 cannot be {27}7), no 2,7 in R5C23
17c. 45 rule on N1234 3 innies R5C23 + R6C3 = 16 = {169/178/268/367} (cannot be {349} because no 3,4,9 in R6C3), no 4
17d. 5 in N5 only in R5C5 + R6C4, CPE no 5 in R6C7

18. 45 rule on C89 3 outies R248C7 = 16 = {178/358/367} (cannot be {169} because R2C7 only contains 3,7), no 9

19. 17(3) cage at R4C7 = {179/359/368/458} (cannot be {269} which clashes with R5C89, cannot be {278} which clashes with R4C45, cannot be {467} which clashes with R4C5), no 2

20. 45 rule on R1234 3(2+1) innies R34C1 + R4C6 = 16
20a. Max R3C1 + R4C6 = 11 -> min R4C1 = 5
20b. R34C1 cannot total 14 -> no 2 in R4C6
20c. R3C1 + R4C6 cannot total 9 -> no 7 in R4C1

[The next step is more useful than expected; it’s cracks the puzzle.]

21. 9 in C7 only in 27(6) cage at R4C6 = {123489/123579/124569} -> R5C6 = 2, R4C4 = 1, R4C5 = 7, R1C4 = 3, R1C5 = 1, R2C5 = 4, R2C4 = 2, R5C5 = 5, clean-up: no 7 in R5C89, no 8 in R6C6, no 8,9 in R7C6
21a. Naked pair {36} in R5C89, locked for R5 and N6
21b. 17(3) cage at R4C7 (step 19) = {458} (only remaining combination), locked for R4 and N6 -> R4C6 = 3
21c. 27(6) cage contains 2,3,5 = {123579} (only remaining combination) -> R567C7 = {179}, locked for C7 -> R2C78 = [37], clean-up: no 3 in R9C9
21d. R4C6 + R5C56 = [352] = 10 -> R9C7 = 6 (step 14), clean-up: no 4 in R9C89
21e. R9C7 = 6 -> R89C6 = 9 = {18}, locked for C6 and N8 -> R3C56 = [89], R67C6 = [46], clean-up: no 4 in R7C1

22. R6C5 = 6 -> R67C4 = 15 = [87], clean-up: no 3 in R7C12
22a. R5C4 = 9, R5C23 = [81], R6C3 = 7 (step 17a), R3C13 = [73], R5C1 = 4, clean-up: no 2 in R7C1, no 5,8 in R89C1

23. Naked pair {29} in R4C23, locked for N4 -> R4C1 = 6
23a. Naked pair {39} in R89C1, locked for C1 and N7 -> R6C12 = [53], R1C12 = [25], R2C1 = 1, R7C1 = 8, R7C2 = 2

24. 12(3) cage at R6C8 = {129} (only remaining combination) -> R7C9 = 9

and the rest is naked singles.

Rating Comment:
The SS score looks good. I think with steps 14 and 15 that my walkthrough should be rated 1.5, rather than Easy 1.5.

I'd better had another try at Pinata's Killer #32 to see whether I can manage to solve it before Ed posts his next Assassin or Pinata's next puzzle is posted.


Last edited by Andrew on Thu Aug 08, 2013 1:00 am, edited 2 times in total.

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Ed
 Post subject: Re: Assassin 258
PostPosted: Fri Apr 26, 2013 9:43 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Andrew's breakthrough move is much better than mine. Now that I look at my step 12 again it is a bit intimidating but great to have two such different ways! I had the feeling that Andrew's neat step 15 must have had an alternative way to do it but couldn't find any. Nicely spotted Andrew! I did some of the early eliminations differently. Then we used completely different areas to crack it. [Big thank you to Andrew for some typos]

A258 Walkthrough
25 steps:
1. "45" on n3: 4 outies r12c6+r3c56 = 29 = {5789} only: all locked for n2

2. "45" on n3: 2 innies r13c7 = 6 = {15/24}(no 3,6,7,8,9)

3. 19(3)r3c5 = {289/478}(no 1,5)
3a. must have 8: 8 locked for r3 and n2

4. h6(2)r13c7 = {24} only: both locked for n3 and c7

5. 8(2)n5: (no 4,8,9)
5a. "45" on c1234: 2 outies r46c5 = 13
5b. {49} blocked since no 4 or 9 in r4c5
5c. h13(2) = [58]/{67}(no 1,2,3,4,9; no 5 in r6c5)
5d. r4c4 = (123)

6. 5(2)n2 = {14/23}(no 6)
6a. 6 in n2 only in c4: 6 locked for c4
6b. "45" on n23: 3 innies r123c4 = 11 and must have 6 = {146/236} = [3/4..](no eliminations yet)

7. "45" on c1234: 3 innies r467c4 = 16
7a. must have 1,2,3 for r4c4 -> {457} blocked
7b. {349} blocked by [3/4] in h123c4 (step 6b)(Killer halves)
7c. [3]{58} blocked by 21(3)r6c4 can't be {588}
7d. h16(3)r467c4 = [1]{78}/[2]{59}(no 3,4; no 1,2 in r67c4)
7e. no 5 in r4c5

8. h13(2)r46c5 = {67} only: both locked for c5 and n5

9. "45" on c6789: 2 outies r35c5 = 13 = [85/94]

10. 5 in n2 only in c6: 5 locked for c6

The first advanced move. Andrew's step 14 gets this elimination very differently.
11. 6 in c6 only in 10(2)r6c6 = [46] or in 15(3)r8c6 -> 4 in r89c6 must also have 6 in r89c6 or else there would be no 6 for c6 (Locking-out cages)
11a. ->{24}[9] blocked from 15(2)r8c6
11b. the only other combination in the 15(3)r8c6 with 9 is {159} but this must be {19}[5]
11c. -> no 9 in r9c7

My key which got me finally unstuck. Its a bit mind boggling with so many combos involved.
12. 27(6)r4c6 must have 4 or 5 for r5c5
12a. = {123489/123579/124569/124578/134568/234567}
12b. the first four options have both 1 & 2 so to avoid clashing with r4c4, must have 1 in c7 (since no 2 in c7)
12c. the last two options {134568/234567} have 6: ie, the 27(6) must have 1 or 6 in c7 (no eliminations yet)

13. "45" on c89: 3 outies r248c7 = 16
13a. {169} is blocked by [1/6] in c7 of 27(6)r4c6 (step 12c)
13b. = {178/358/367}(no 9)

14. 9 in c7 only in 27(6)r4c6
14a. ->no 9 in r45c6
14b. 27(6) must have 9 = {123489/123579/124569}
14c. must have 2: 2 locked for c6 and n5

Much easier from here.
15. r4c45 = [17],
15a. r6c5 = 6 -> r67c4 = 15 = [87] only

16. h11(3)r123c4 = {236} only: locked for c4 and n2
16a. 5(2)n2 = {14} only: locked for c5
16b. r5c5 = 5 -> r3c5 = 8 (h13(2)r35c5)
16c. naked triple {579} in r123c6: locked for c6
16d. 10(2)r6c6 = [46] only permutation
16e. naked pair {23} in r45c6: locked for c6 and 27(6): no 3 in r567c7
16f. naked pair {18} = 9 in r89c6 -> r9c7 = 6

17. r4c6+r5c56 = 10 -> r567c7 = 17 = {179} only: locked for c7 and 7 locked for n6

18. "45" on n9: 2 remaining innies r7c79 = 10 = {19} only: both locked for r7 and n9

19. 12(3)r6c8 = {129} only: 2 locked for r6 and n6

20. Naked quad {1279} in n6 in r5c7+r6c789: locked for n6
20a. 9(2)n6 = {36} only: locked for r5 and n6
20b. r45c6 = [32]
20c. r5c4 = 9 -> r5c23 = 9 = {18} only: locked for r5 and n4
20d. r5c7 = 7, r5c1 = 4

21. 9(2)n3: {36} blocked by r5c9 = (36)
21a. 9(2) = [81] only permutation
21b. r67c9 = [29], r6c8 = 1, r67c7 = [91]
21c. 15(2)n3 = [96] only permutation

22. "45" on r1: 3 outies r2c456 = 11 = [317/245](no 6,9)
22a. naked pair{57} = 12 in r12c6 -> r1c7 = 4
22b. naked pair {23} = 5 in r12c4 -> r1c3 = 8
22c. hidden singles 6 & 9 in n2 -> r3c46 = [69]

23. 7(2)n1 = {25} only: locked for r1 and n1

24. "45" on r12: 2 remaining outies r3c28 = 9 = [45] only
24a. r5c23 = [81]

25. 10(2)n7 = [82] only permutation

etc.
Cheerio
Ed
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