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Pinata
 Post subject: Pinata Killer Sudoku 18
PostPosted: Sun Nov 18, 2012 8:41 am 
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Pinata Killer Sudoku 17 Solution
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Pinata Killer Sudoku 18
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Jsudoku code: 3x3::k:8192:8192:8192:3073:3073:3073:3842:3842:3842:4355:2052:8192:8192:2565:4102:4102:4102:3591:4355:2052:11528:2565:2565:7945:7945:3591:3591:4355:2826:11528:11528:11528:7945:7945:7945:7945:7179:2826:3084:3084:11528:3597:3597:2830:7945:7179:7179:7179:7179:11528:11528:11528:2830:3343:5136:5136:7179:7179:3089:3089:11528:3346:3343:5136:4115:4115:4115:3089:6676:6676:3346:3343:2325:2325:2325:5142:5142:5142:6676:6676:6676:

Sudoku Solver Score: 1.25
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Andrew
PostPosted: Fri Nov 23, 2012 12:36 am 
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Thanks Pinata for another nice killer. It started fairly easily, with some interesting steps, but then suddenly became difficult; maybe I missed something.

Here is my walkthrough for Pinata Killer #18:
Prelims

a) R23C2 = {17/26/35}, no 4,8,9
b) R45C2 = {29/38/47/56}, no 1
c) R5C34 = {39/48/57}, no 1,2,5
d) R5C67 = {59/68}
e) R56C8 = {29/38/47/56}, no 1
f) R78C8 = {49/58/67}, no 1,2,3
g) 10(3) cage at R2C5 = {127/136/145/235}, no 8,9
h) 20(3) cage at R7C1 = {389/479/569/578}, no 1,2
i) 9(3) cage at R9C1 = {126/135/234}, no 7,8,9
j) 20(3) cage at R9C4 = {389/479/569/578}, no 1,2
k) 32(5) cage at R1C1 = {26789/35789/45689}, no 1
l) 28(7) cage at R5C1 = {1234567}, no 8,9
m) and, of course, 45(9) cage at R3C1 = {123456789}

1. 32(5) cage at R1C1 = {26789/35789/45689}, CPE no 8,9 in R2C1

2. 45 rule on R1 2 outies R2C34 = 14 = {59/68}

3. 45 rule on R9 2 outies R8C67 = 10 = {19/28/37/46}, no 5

4. 45 rule on N2 3 innies R2C46 + R3C6 = 23 = {689}, locked for N2, clean-up: no 9 in R2C3 (step 2)
4a. 9 of {689} must be in R2C46 (R2C46 cannot total 14, which clashes with R2C45, CCC), locked for R2 and N2

5. R3C6 = {68} -> 31(7) cage at R3C6 = {1234678} (only remaining combination), no 5,9

6. 45 rule on N3 1 outie R2C6 = 1 innie R3C7 -> R2C6 = R3C7 = {68}
6a. Naked pair {68} in R23C6, locked for C6 and N2 -> R2C4 = 9, R2C3 = 5, clean-up: no 3 in R23C2, no 3 in R5C3, no 7 in R5C4, no 6,8 in R5C7, no 2,4 in R8C7 (step 3)
6b. Naked pair 6,8 in R3C67, locked for R3 and 31(7) cage at R3C6, no 6,8 in R4C789 + R5C9, clean-up: no 2 in R2C2
6c. Naked pair {59} in R5C67, locked for R5, clean-up: no 2,6 in R4C2, no 7 in R5C3, no 3 in R5C4, no 2,6 in R6C8
6d. Naked pair {48} in R5C34, locked for R5, clean-up: no 3,7 in R4C2, no 3,7 in R6C8
6e. 31(7) cage at R3C6 = {1234678}, 4 locked for R4, clean-up: no 7 in R5C2
6f. 8 in N6 only in R6C789, locked for R6

7. R2C34 = [59] -> 32(5) cage at R1C1 = {35789/45689}, no 2, 8 locked for R1
7a. Killer pair 6,7 in 32(5) cage and R23C2, locked for N1

8. 9 in R1 only in 15(3) cage at R1C7, locked for N3
8a. 15(3) cage = {159/249}, no 3,6,7
8b. 12(3) cage at R1C4 = {237} (only remaining combination, cannot be {147/345} which clash with 15(3) cage), locked for R1 and N2
8c. Naked triple {468} in R1C123, locked for R1 and N1, clean-up: no 2 in R3C2
8d. Naked pair {17} in R23C2, locked for C2 and N1
8e. Naked triple {159} in 15(3) cage at R1C7, locked for N3

9. 45 rule on N1 1 remaining outie R4C1 = 1 innie R3C3 + 3 -> R3C3 = {23}, R4C1 = {56}
9a. R3C1 = 9 (hidden single in N1)
9b. R45C2 = [83/92] (cannot be [56] which clashes with R4C1), no 5,6
9c. 9 in N4 only in R4C23, locked for R4

10. 14(3) cage at R2C9 = {248/347}, no 6, 4 locked for N3
10a. 8 of {248} must be in R2C9 -> no 2 in R2C9

11. 1 in R2 only in R2C25
11a. 45 rule on R12 4 innies R2C1259 = 15 = {1248/1347}
11b. R2C1 = {23} -> no 3 in R2C9

12. 45 rule on N7 1 outie R8C4 = 1 innie R7C3, no 5,8 in R8C4

13. Caged X-Wing for 4 in 45(9) cage at R3C3 and 28(7) cage at R5C1 in R67, no other 4 in R67, clean-up: no 7 in R5C8, no 9 in R8C8

14. Caged X-Wing for 5 in 45(9) cage at R3C3 and R5C67 in C7 + N5, no other 5 in C7 + N5

15. 20(3) cage at R7C1 = {389/479/578} (cannot be {569} which clashes with R4C1), no 6
15a. 9 of {389} must be in R7C2 -> no 3 in R7C2

16. 1 in C1 only in R569C1, CPE no 1 in R7C3, clean-up: no 1 in R8C4 (step 12)

17. 45 rule on N8 3 innies R7C4 + R8C46 = 13 = {139/157/247/256/346}
17a. 1 of {139} must be in R7C4, 3 of {346} must be in R8C46 (R8C46 cannot total 10 which clashes with R8C67, CCC), no 3 in R7C4

18. Caged X-Wing for 4 in 28(7) cage at R5C1 and R5C34 in C4 + N4, no other 4 in C4, clean-up: no 4 in R7C3 (step 12)

19. Naked triple {145} in 10(3) cage at R2C5, 4 locked for C5

20. 45 rule on N7 3 innies R7C3 + R8C23 = 16 = {169/268/349/358/457} (cannot be {178/259/367} which clash with 20(3) cage at R7C1)
20a. 2 of {268} must be R78C3 (R78C3 cannot be [68] which clashes with R15C3, ALS block), no 2 in R8C2
20b. 3 of {349/358} must be in R7C3 -> no 3 in R8C23
20c. 7 of {457} must be in R7C3 -> no 7 in R8C3

21. 4 in N8 only in R7C4 + R8C46 (step 17) = {247/346} and 20(3) cage at R9C4 = {479} -> R7C4 + R8C46 = {139/247/256/346} (cannot be {157}, locking-out cages)
21a. 12(3) cage at R7C5 = {129/138/156} (cannot be {237} which clashes with R7C4 + R8C46), no 7, 1 locked for N8, clean-up: no 9 in R8C7 (step 3)
21b. R7C4 + R8C46 = {247/256/346}, no 9, clean-up: no 1 in R8C7 (step 3)

[There ought to be a better way forward but the only way I could see to make progress was …]
22. R7C4 + R8C46 (step 21b) = {247/256/346}
22a. Consider placements for R8C6
R8C6 = 2 => R8C7 = 8 (step 3) => 8 in R9 only in 20(3) cage at R9C4 = {389/578}, no 4
or R8C6 = {347} => R7C4 + R8C46 = {247/346}, 4 locked for N8
-> 20(3) cage at R9C4 = {389/569/578}, no 4
22b. 4 in N8 only in R7C4 + R8C6 -> R7C4 + R8C46 = {247/346}, no 5
[The rest is fairly straightforward]

23. 28(7) cage at R5C1 = {1234567}, 5 locked for N4 -> R4C1 = 6, R2C1 = 2 (cage sum), R3C3 = 3, clean-up: no 3 in R8C4 (step 12)
23a. 3,6 in R2 only in 16(3) cage at R2C6 = {367} -> R2C6 = 6, R2C78 = {37}, locked for R2 and N3, R23C2 = [17], R2C5 = 4, R3C67 = [86], clean-up: no 4 in R8C6 (step 3)

24. R7C4 = 4 (hidden single in N8), R5C34 = [48]

25. 45(9) cage at R3C3 = {123456789}, 6 locked for C5
25a. 12(3) cage at R8C5 (step 21a) = {129/138}, no 5

26. 5 in N8 only in 20(3) cage at R9C4, locked for R9
26a. 20(3) cage (step 22a) = {569/578}, no 3
26b. 9(3) cage at R9C1 = {126/234}, 2 locked for R9 and N7, clean-up: no 2 in R8C4 (step 12)

27. R7C3 + R8C23 (step 20) = {169} (only remaining combination, cannot be {457} because 4,5 only in R8C2) -> R7C3 = 6, R8C23 = [91], R8C4 = 6 (cage sum), R8C6 = 3 (step 22b), R8C7 = 7 (step 3), R2C78 = [37], R4C2 = 8, R5C2 = 3, clean-up: no 8 in R6C8

28. Naked triple {234} in 9(3) cage at R9C1, locked for R9 and N7

29. R7C1 = 7 (hidden single in N7), R56C1 = [15], R6C8 = 9, R5C8 = 2

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for Pinata #18 at 1.5. I used a short forcing chain as my breakthrough step. Before that I'd used locking-out cages and the "multi-dimensional" caged X-Wings felt as if they should also be in the 1.5 range. Maybe the fairly low SS score is because it's a fairly short solving path?
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Ed
PostPosted: Sat Nov 24, 2012 10:26 am 
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Thanks Pinata! I found this puzzle to be exactly as Andrew described and had to use a surprisingly complicated move to crack it. Fortunately, Andrew's step 20. and 20c. (the key elimination) showed me what I missed and can now see an easier way to go from there. It takes quite a few steps to get it but they are all straightforward once you see them. [Many thanks to Andrew for a nice bit of naming in my step 23 and typos]
Alt ending 12 more steps:
End of Andrew's step 20 to here [edit: added 5 to r7c6, 1 to r7c4, 1 to r8c67, 9 to r8c67] (BTW: v3.6.1 has a bug which doesn't allow these marks to "Paste Into" PKS18, hence I use an older version for everyday solving. I've told Richard so it will get fixed one day)

.-------------------------------.-------------------------------.-------------------------------.
| 468       468       468       | 237       237       237       | 19        159       159       |
| 23        17        5         | 9         14        68        | 23678     23678     478       |
| 9         17        23        | 15        145       68        | 68        2347      2347      |
:-------------------------------+-------------------------------+-------------------------------:
| 56        89        1236789   | 1235678   1235678   12347     | 12347     12347     12347     |
| 12367     23        48        | 48        12367     59        | 59        236       1237      |
| 1234567   23456     123467    | 123467    1235679   1234579   | 123456789 589       12356789  |
:-------------------------------+-------------------------------+-------------------------------:
| 3578      589       2367      | 124567    1235689   12359     | 123456789 56789     12356789  |
| 34578     45689     124689    | 2367      1235689   123479    | 136789    45678     123456789 |
| 123456    23456     12346     | 35678     356789    3479      | 12346789  123456789 123456789 |
'-------------------------------.-------------------------------.-------------------------------'


21. 7 in n4 in 28(7) or r4c3 and r7c3 see all of these -> no 7 in r7c3(CPE)
21a. no 7 in r8c4 (IODn7 = 0)

22. 7 in n7 only in c1: 7 locked for c1
22a. 20(3) must have 7 = {479/578}(no 3)

23. 7 in r45 only in 31(7)r3c6 and 45(9)r3c3 -> 7 locked for 45(9) (Hidden caged x-wing: Like that name - thanks Andrew)
23a. no 7 in r6c567+r7c7

24. 7 in 45(9)r3c3 only in r4c345+r5c5 and r4c6 sees all those -> no 7 in r4c6 (CPE)

25. 31(7)r3c6 must have 7 which is only in n6: 7 locked for n6

26. 7 in r6 only in r6c34 in 28(7)r5c1: locked for that cage
26a. no 7 in r7c4

27. 7 & 9 in r9 only in 26(5)r8c6 or r9c456 and r8c6 sees all these -> no 7 or 9 in r8c6
27a. no 1 or 3 in r8c7 (h10(2)r8c67)

28. h13(3)n8 = {256/346}(no 1)
28a. must have 6 -> 6 locked for c4 and n8
28b. no 9 in r8c7 (h10(2)r8c7)

29. r7c3 = r8c4 and 6 locked in r78c4 -> 6 must be in r7c34: 6 locked for r7 and 28(7)r5c1
29a. no 6 in r5c1+r6c123
29b. no 7 in r8c8

30. 6 in n5 only in c5 in 45(9) -> 6 locked for 45(9)
30a. no 6 in r4c3 or r6c7

31. Hidden single 6 in n4 -> r4c1 = 6
31a. r2c1 = 2 (cage sum)
31b. r3c3 = 3
31c. no 3 in r8c4 (IODn7 = 0)

32. 3 in n7 only in 9(3) = {135/234}(no 6)

33. 7 in n8 is only in 20(3)r9c4, locked for r9
33a. 20(3) = {479/578}, no 3

on from there. It's effectively cracked now. See Andrew's step 23a following
Cheerio
Ed
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Pinata
PostPosted: Sat Nov 24, 2012 1:26 pm 
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I am glad that you both enjoyed this puzzle, and Ed, i thought that you had stopped doing my puzzles as you hadn't done my last few, even though I started posting one or two puzzles with a Sudoku Solver score below 1.50 per month.

I noticed that some of my early ones were extremely/plain hard, so when Andrew asked me to start posting one or two puzzles with a Sudoku Solver score below 1.50 per month, I decided to make my puzzles interesting and hard, instead of tedious and plain hard as a few of my early ones may have been.
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wellbeback
PostPosted: Sat Nov 24, 2012 11:00 pm 
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Adding my thanks to Pinata for continuing the series. We all followed similar lines here. My key steps (678) took me a little while to spot.

Hidden Text:
1. Innies - Outies n3 -> r2c6 = r3c7.
Innies n2 -> r2c46+r3c6 = +23 = {689}
At least one of (68) must be in r3c67 -> 31/7@r3c6 = {1234678}
-> r3c67 = {68} -> r23c6 = {68} and r2c4 = 9
-> Outies r1 r2c3 = 5.

2. Also 9 in r1 in n3 - r1c789
-> (68) in r1 in n1
-> r1 = [{468} {237} {159}]
-> 10/3@r2c5 = {145}
Also 8/2@r2c2 = {17}

3. Also r23c6 = {68} -> 14/2@r5c6 = {59}
-> 12/2@r5c3 = {48}

4. Remaining cells in n1: r23c1 + r3c3 = {239}.
r23c1 cannot be {23} -> r3c1 = 9, r2c1,r3c3 = {23}
-> r4c1 from (56)
-> 11/2@r4c2 = [83] or [92]

5. Outies r9 -> r8c67 = +10 - No 5
Whatever is in r8c6 must go in r9 in n7 - i.e., in the 9/3@r9c1.
-> r8c6 is max 6. But 6 already in c6 and it cannot be a 5
-> r8c6 is max 4.

6. Innies - Outies n7 -> r7c3 = r8c4.
28/7@r5c1 = {1234567}
-> whatever is in r7c3 (and r8c4) must in n4 be in r4c1 or r5c2 - i.e. be from {2356}.
But 5 already in c3 -> r7c3 and r8c4 from (236)

7. Either of (23) in r7c3 would prevent 4 from being in r9c123 and therefore also from r8c6,
and a 6 in r8c4 also prevents a 4 from being in r8c6.
-> r8c6 is max 3.

8. Innies n8 r78c4 + r8c6 = +13.
r7c4 is max 7 and r8c6 is max 3 -> r8c4 is min 4.
-> r8c4 (from (236)) = 6 -> r7c3 = 6 -> r4c1 = 6 -> r2c1 = 2 and r3c3 = 3.

9. Also [r7c4,r8c6] from [52] or [43]
But 5 in r7c4 would leave no place for 5 in n4
-> [r7c4,r8c6] = [43]
-> 12/2@r7c5 = {129}
-> 20/3@r9c4 = {578}
-> 9/3@r9c1 (must include a 3) = {234} -> r9c789 = {169}
Also r8c23 = [91]
-> 11/2@r4c2 = [83]
-> r6c4 = 3.

10. Also 12/2@r5c3 = [48]
Also r8c7 = 7
Also 13/2@r7c8 = {58}
Also r8c9 = 4
Also r7c79 = [23] -> r6c9 = 6.
Also 2 in n5 can only go in r4c6
-> 11/2@r5c8 = [29]
-> 14/2@r5c6 = [95]

etc. etc.
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