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 Post subject: Pinata Killer Sudoku 12
PostPosted: Sun Oct 07, 2012 6:43 pm 
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Pinata Killer Sudoku 11 Solution
Hidden Text:
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Pinata Killer Sudoku 12
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Jsudoku Code: 3x3::k:4864:4864:4864:3585:3585:3585:4866:4866:4866:4864:4355:5380:5380:2565:3846:3846:6151:4866:4355:4355:5380:2824:2565:2313:3846:6151:6151:4355:6154:2824:2824:5131:2313:2313:5900:6151:6154:6154:1549:1549:5131:1294:1294:5900:5900:5391:6154:3344:3344:5131:4881:4881:5900:4882:5391:5391:3091:3344:2836:4881:4885:4882:4882:4886:5391:3091:3091:2836:4885:4885:4882:4375:4886:4886:4886:4632:4632:4632:4375:4375:4375:

Sudoku Solver Score: 1.30


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PostPosted: Tue Oct 09, 2012 3:40 am 
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Joined: Tue Jun 16, 2009 9:31 pm
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Easier than the Sudoku Solver score I think.

Thanks Pinata! Keep them coming...
Hidden Text:
Innies c1234 -> r19c4 = +17 = {89}
Innies c5 -> r19c5 = +4 = {13}
Innies c6789 r19c6 = +11

-> 2 in c5 must be in 10/2@r2c5 or 11/2@r7c5
-> Either r23c5 = {28} or r78c5 = {29}

Regardless of which it is - r19c4 cannot be [89]
-> r19c4 = [98]

-> r19c6 = [47] or [29]
But whether r23c5 = {28} or r78c5 = {29} r19c6 cannot be [29]

-> r1c456 = [914] and r9c456 = [837]

6/2 @r5c3 and 5/2@r5c6 -> r5c34 = {15} and r5c67 = {23}.

4 in c5 must be in n5 -> 20/3@r4c5 = {479}
-> 10/2@r2c5 (28)
-> 11/2@r7c5 = {56}

HS 1 in c6 -> r4c6 = 1.
HS 8 in c6 -> r6c6 = 8.

->Outies n9 = +10 -> r6c9 = 1, r8c6 = 9
-> 19/3@r6c6 = [892]
-> 5/2@r5c6 = [32]
-> 9/3@r3c6 = [513]
-> 6/2@r5c3 = [15]
Also r2c6 = 6
Also r23c4 = [73]

-> r46c4 = {26}
-> r78c4 = {14}

Regardless of whether r6c4 is 2 or 6, r7c4 cannot be 1.
-> r78c4 = [41]
-> Outies n7 -> r6c1 = 6
-> r46c4 = [62]

etc. etc.


Last edited by wellbeback on Wed Oct 10, 2012 5:03 pm, edited 1 time in total.

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PostPosted: Wed Oct 10, 2012 4:03 am 
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Location: Lethbridge, Alberta, Canada
Thanks Pinata for posting a killer with a lower SS score. It was still hard enough to be interesting. I also liked the fact that it was a symmetrical cage pattern; we don't get many of them.

As wellbeback said "Keep them coming ..." :D

My solving path was very different from wellbeback's:
which made interesting use of locking-out cages to give early placements. Mine was more routine until I found an interesting use of combined cages in step 26 which cracked this puzzle.

Congratulations Pinata for creating a cage pattern and totals which allowed wellbeback's locking-out cages and also my combined cages to be done so simply.

Here is my walkthrough for Pinata #12:
Prelims

a) R23C5 = {19/28/37/46}, no 5
b) R5C34 = {15/24}
c) R5C67 = {14/23}
d) R78C5 = {29/38/47/56}, no 1
e) 21(3) cage at R2C3 = {489/579/678}, no 1,2,3
f) 11(3) cage at R3C4 = {128/137/146/236/245}, no 9
g) 9(3) cage at R3C6 = {126/135/234}, no 7,8,9
h) 20(3) cage at R4C5 = {389/479/569/578}, no 1,2
i) 19(3) cage at R6C6 = {289/379/469/478/568}, no 1
j) 19(3) cage at R7C7 = {289/379/469/478/568}, no 1

1. R5C34 = {15} (cannot be {24} which clashes with R5C67), locked for R5, clean-up: no 4 in R5C67
1a. Naked pair {23} in R5C67, locked for R5

2. 45 rule on R1 2 outies R2C19 = 7 = {16/25/34}, no 7,8,9

3. 45 rule on R9 2 outies R8C19 = 9 = {18/27/36/45}, no 9

4. 45 rule on C5 2 innies R19C5 = 4 = {13}, locked for C5, clean-up: no 7,9 in R23C5, no 8 in R78C5
4a. 18(3) cage at R9C7 = {189/369/378} (only combinations containing 1 or 3), R9C5 = {13} -> R9C46 = {69/78/89}

5. 45 rule on N1 2(1+1) outies R2C4 + R4C1 = 12, no 1,2,9 in R4C1

6. 45 rule on N3 2(1+1) outies R2C6 + R4C9 = 13 = {49/58/67}, no 1,2,3

7. 45 rule on N7 2(1+1) outies R6C1 + R8C4 = 7 = {16/25/34}

8. 45 rule on N9 2(1+1) outies R6C9 + R8C6 = 10, no 9 in R6C9

9. 45 rule on C1234 2 innies R19C4 = 17 = {89}, locked for C4, clean-up: no 3,4 in R4C1 (step 5)
9a. 21(3) cage at R2C3 = {489/579/678}
9b. 4 of {489} must be in R2C4 -> no 4 in R23C3

10. 45 rule on C6789 2 innies R19C6 = 11 = [29/38/47/56]

11. 14(3) cage at R1C4 = {149/158/239} (cannot be {248} because R1C5 only contains 1,3)
11a. R1C5 = {13} -> no 3 in R1C6, clean-up: no 8 in R9C6 (step 10)

12. 45 rule on C12 2 outies R19C3 = 10 = {19/28/37/45}, no 5

13. 45 rule on C89 2 outies R19C7 = 12 = {39/48/57}, no 1,2,6

14. 45 rule on R1234 3 innies R4C258 = 21 = {489/579/678}, no 1,2,3

15. 1 in C6 only in R34C6, locked for 9(3) cage at R3C6, no 1 in R4C7
15a. 9(3) cage = {126/135}, no 4

16. 1 in N6 only in R6C89, locked for R6, clean-up: no 6 in R8C4 (step 7)
16a. 1 in N4 only in R45C3, locked for C3, clean-up: no 9 in R19C3 (step 12)
16b. 1 in N6 only in R6C89, CPE no 1 in R78C8

17. 1 in C7 only in R23C7, locked for N3, clean-up: no 6 in R2C1 (step 2)
17a. 1 in C7 only in 15(3) cage at R2C6 = {159/168}, no 2,3,4,7, clean-up: no 6,9 in R4C9 (step 6)
17b. 7 in N2 only in R23C4, locked for C4
17c. 7 in N2 only in R23C4, CPE no 7 in R3C3

18. 9 in R4 only in R4C258 (step 14) = {489/579}, no 6

19. 45 rule on N2 R23C46 = 21 contains 7 = {1578/2379/3567} (cannot be {1479/2478} which clash with 14(3) cage at R1C4), no 4, clean-up: no 8 in R4C1 (step 5)
[Can make a further elimination, using interactions with R2C4 + R4C1 and R2C6 + R4C9, but that’s beyond the SS score so I’ll leave it for now.]

20. 21(3) cage at R2C3 = {579/678}, 7 locked for R2

21. Hidden killer pair 8,9 in 20(3) cage at R4C5 and R6C6 for N5, 20(3) cage contains one of 8,9 -> R6C6 = {89}
21a. 7 in N5 only in 20(3) cage, locked for C5, clean-up: no 4 in R78C5
21b. 20(3) cage = {479/578}, no 6

22. 18(3) cage at R9C7 (step 4a) = {189/378} (cannot be {369} which clashes with R78C5), no 6 -> R9C4 = 8, R1C4 = 9, clean-up: no 2 in R1C3 (step 12), no 5 in R1C6 (step 10), no 4 in R4C9 (step 6), no 2 in R6C9 (step 8)
22a. Killer pair 2,4 in R1C6 and R23C5, locked for N2

23. 15(3) cage at R2C6 (step 17a) = {159/168}
23a. 5 of {159} must be in R2C6 -> no 5 in R23C7

24. Hidden killer pair 4,7 in R19C6 and R78C6 for C6, R19C6 contains both or neither of 4,7 -> R78C6 must contain both or neither of 4,7
24a. 45 rule on N8 4 innies R78C46 = 16 = {1249/1456/2347} (cannot be {1267/2356} which clash with R78C5, cannot be {1357} which clashes with R9C5)
24b. 4,7 of {2347} must be in R78C6 -> no 3 in R78C6, clean-up: no 7 in R6C9 (step 8)
24c. 5,6 of {1456} must be in R78C6 -> no 5,6 in R78C4, clean-up: no 2 in R6C1 (step 7)
24d. 1,4 of {1249} must be in R78C4
24e. R78C4 = {14/23}

25. 11(3) cage at R3C4 = {137/146/236/245} (cannot be {128} because R34C4 = [12] clashes with R78C4), no 8
25a. 5 of {245} must be in R34C4 -> no 5 in R4C34
25b. 7 of {137} must be in R3C4 (R34C4 cannot be {13} which clashes with R78C4), no 7 in R4C3

26. 1,2,3 in R4 only in R4C3467, R3C46 must contain one of 1,3
26a. Combined cage 11(3) cage at R3C4 and 9(3) cage at R3C6 = 20 must contain 1,2,3 and another of 1,3 = {123167/123356} (cannot be {123347} because 11(3) cage cannot contain both of 4,7), no 4
26b. 11(3) cage at R3C4 (step 25) = {137/236}, no 5
26c. 7 of {137} must be in R3C4 -> no 1 in R3C4

27. 4 in R4 only in R4C258 (step 18) = {489} (only remaining combination), locked for R4, clean-up: no 5 in R2C6 (step 6)
27a. Killer pair 6,8 in R23C5 and R2C6, locked for N2, clean-up: no 6 in R4C1 (step 5)
27b. Naked pair {57} in R4C19, locked for R4

28. 15(3) cage at R2C6 (step 17a) = {168} (only remaining combination), CPE no 6,8 in R2C89, clean-up: no 1 in R2C1 (step 2)

29. 9(3) cage at R3C6 (step 15a) = {126/135}
29a. 3 of {135} must be in R4C7 -> no 3 in R34C6
29b. R5C6 = 3 (hidden single in C6), R5C7 = 2
29c. R4C7 = {36} -> no 6 in R4C6

30. 11(3) cage at R3C4 (step 26b) = {137/236}
30a. 1 of {137} must be in R4C4 -> no 1 in R4C3
30b. 1 in R4 only in R4C46, locked for R4 -> R5C4 = 5, R5C3 = 1, R2C4 = 7, R3C4 = 3, R1C5 = 1, R1C6 = 4 (cage sum), R9C5 = 3, R9C6 = 7 (cage sum), clean-up: no 3,7 in R1C3 (step 12), no 5 in R1C7 (step 13), no 6 in R23C5, no 2 in R78C4 (step 24e), no 6 in R9C3 (step 12), no 4,5 in R6C1 (step 7), no 3,6 in R6C9 (step 8)

31. R3C6 = 5 -> R4C67 = 4 = [13], clean-up: no 5 in R6C9 (step 8), no 9 in R9C7 (step 13)

32. Naked pair {28} in R23C5, locked for C5 and N2 -> R2C6 = 6, R4C9 = 7 (step 6), R4C1 = 5, clean-up: no 2 in R2C9 (step 2), no 4 in R6C9 (step 8), no 9 in R78C5

33. Naked pair {18} in R23C7, locked for C7 and N3 -> R1C7 = 7, R9C7 = 5 (step 13)

34. 45 rule on N6 2 remaining innies R6C79 = 10 = [91], R67C6 = [82], R8C6 = 9
34a. Naked pair {46} in R78C7, locked for N9

35. R9C8 = 1 (hidden single in N9)
35a. R9C78 = [51] = 6 -> R89C9 = 11 = [29] (cannot be {38} because 3,8 only in R8C9), R8C1 = 7 (step 3)
35b. Naked triple {246} in R9C123, locked for N7

36. R6C3 = 7 (hidden single in C3), R67C4 = 6 = [24], R4C34 = [26], R8C4 = 1, R6C1 = 6 (step 7), R78C7 = [64], R78C5 = [56], 20(3) cage at R4C5 = [974], R6C28 = [35], R9C13 = [24], R9C2 = 6, R1C3 = 6 (step 12)

37. R8C4 = 1 -> R78C3 = 11 = {38} (only remaining combination), locked for C3 and N7 -> R23C3 = [59], R8C2 = 5

38. 8 in R1 only in R1C12, locked for N1
38a. 19(4) cage at R1C1 contains 6,8 = {2368} (only remaining combination) -> R1C2 = 2, R12C1 = [83]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough at 1.25, based on my combined cages step.


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