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 Post subject: Pinata Killer Sudoku 19
PostPosted: Mon Nov 26, 2012 11:33 am 
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Joined: Sat Jul 28, 2012 11:05 pm
Posts: 92
Pinata Killer Sudoku 18 Solution:
Image

Pinata Killer Sudoku 19
Image

Jsudoku Code: 3x3::k:5128:3079:3079:3079:6661:6661:4614:4614:4614:5128:2057:2057:6154:1795:6661:1284:2330:2330:5128:5128:6154:6154:1795:6661:1284:3353:3353:6925:1548:1548:6154:6914:6914:6914:2840:2840:6925:3851:3851:3851:3851:6914:6914:6166:2840:6925:5136:5136:3345:3345:5377:5377:6166:6166:6925:1807:5136:3346:3346:5377:5377:6166:2583:9486:1807:9486:9486:2323:1812:1812:6166:2583:9486:9486:9486:9486:2323:4117:4117:4117:4117:

Sudoku Solver Score: 1.40


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PostPosted: Wed Nov 28, 2012 3:19 am 
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Thanks Pinata for your latest killer.

Thanks Ed for pointing out that there’s a flaw in my walkthrough at step 22a. I’ll need to see whether I can rework my later steps.
That’s the second time in a few weeks that I’ve missed out a combination. :oops:
I've now had another look and found a short re-work.
In his post below, Ed wrote:
Finally found Andrew's step 17c which then opens up a really neat way to crack it.
Interestingly it also led to my short re-work.

Here is my walkthrough for Pinata Killer #19:
Prelims

a) R2C23 = {17/26/35}, no 4,8,9
b) R23C5 = {16/25/34}, no 7,8,9
c) R23C7 = {14/23}
d) R2C89 = {18/27/36/45}, no 9
e) R3C89 = {49/58/67}, no 1,2,3
f) R4C23 = {15/24}
g) R6C45 = {49/58/67}, no 1,2,3
h) R78C2 = {16/25/34}, no 7,8,9
i) R7C45 = {49/58/67}, no 1,2,3
j) R78C9 = {19/28/37/46}, no 5
k) R89C5 = {18/27/36/45}, no 9
l) R8C67 = {16/25/34}, no 7,8,9
m) 11(3) cage at R4C8 = {128/137/146/236/245}, no 9
n) 20(3) cage at R6C2 = {389/479/569/578}, no 1,2
o) 26(4) cage at R1C5 = {2789/3689/4589/4679/5678}, no 1
p) 27(4) cage at R4C1 = {3789/4689/5679}, no 1,2

Steps resulting from Prelims
1a. 27(4) cage at R4C1 = {3789/4689/5679}, 9 locked for C1
1b. 9 in R2 only in R2C46, locked for N2

2. 45 rule on R123 (or, if preferred, on N12) 1 outie R4C4 = 7, clean-up: no 6 in R6C45, no 6 in R7C5
2a. 24(4) cage at R2C4 contains 7 = {2679/3579/3678/4578}, no 1
2b. 7 in N2 only in 26(4) cage at R1C5 = {2789/4679/5678}, no 3
2c. 9 of {2789/4679} must be in R2C6 -> no 2,4 in R2C6

3. 45 rule on N1 1 innie R3C3 = 1 outie R1C4 + 5, R1C4 = {134}, R3C3 = {689}

4. 45 rule on C1 1 outie R3C2 = 2 innies R89C1 + 2
4a. Min R89C1 = 3 -> min R3C2 = 5
4b. Max R89C1 = 7, no 7,8

5. 45 rule on R89 3 innies R8C289 = 21 = {489/578/678}, no 1,2,3, clean-up: no 4,5,6 in R7C2, no 7,8,9 in R7C9
5a. R8C2 = {456} -> no 4,5,6 in R8C89, clean-up: no 4,6 in R7C9

6. 20(3) cage at R6C2 = {389/479/569/578}
6a. 3,6 of {389/569} must be in R6C23 (R6C23 cannot be {59/89} which clash with R6C45), no 3,6 in R7C3

7. 45 rule on C89 3(1+2) outies R1C7 + R9C67 = 11
7a. Min R19C7 = 3 -> max R9C6 = 8
7b. Min R9C67 = 3 -> max R1C7 = 8

8. 45 rule on R6789 3(2+1) outies R45C1 + R5C8 = 24
8a. Max R45C1 = 17 -> min R5C8 = 7
8b. Min R45C1 = 15, no 3,4,5
8c. Max R5C18 = 17 -> no 6 in R4C1

9. Min R58C8 = 15 -> max R6C89 + R7C8 = 9, no 7,8,9

10. 45 rule on N2 3 innies R123C4 = 12 = {129/138/345} (cannot be {156} because 24(4) cage at R2C4 cannot contain both of 5,6, cannot be {246} which clashes with R23C5), no 6
10a. 9 of {129} must be in R2C4 -> no 2 in R2C4

11. 45 rule on C1234 3 outies R567C5 = 22 = {589/679}, 9 locked for C5, clean-up: no 9 in R6C4, no 9 in R7C4
11a. Min R5C5 = 5 -> max R5C234 = 10, no 8,9 in R5C234

12. 45 rule on C1234 2 innies R67C4 = 1 outie R5C5 + 4
[Sorry, I missed something more here, see step 19]
12a. R5C5 = {5689} -> R67C4 = 9,10,12,13 = {45/46/48/58}
12b. R123C4 (step 10) = {129/138} (cannot be {345} which clashes with R67C4) -> R1C4 = 1, R23C4 = [38/83/92], no 4,5, R3C3 = 6 (step 3), clean-up: no 2 in R2C23, no 6 in R2C5, no 7 in R3C89
12c. Killer pair 2,3 in R23C4 and R23C5, locked for N2
12d. 12(3) cage at R1C2 contains 1 = {129/138/147}, no 5
12e. R2C89 = {18/27/36} (cannot be {45} which clashes with R3C89), no 4,5
12f. R89C5 = {18/27/36} (cannot be {45} which clashes with R23C5), no 4,5

13. 18(3) cage at R1C7 = {279/369/567} (cannot be {378} which clashes with R2C89, cannot be {459/468} which clash with R3C89), no 4,8

14. 45 rule on C6789 2 outies R14C5 = 7 = [43/52/61] -> R1C5 = {456}, R4C5 = {123}
14a. 4 in C5 only in R123C5, locked for N2
14b. 7 in N2 only in R123C6, locked for C6

15. R2C23 = {17/35}, R2C89 = {18/27/36} -> combined cage R2C2389 = {17}{36}/{35}{18}/{35}{27}, 3 locked for R2, clean-up: no 8 in R3C4 (step 12b), no 4 in R3C5, no 2 in R3C7

16. 3 in N2 in R3C45, locked for R3, clean-up: no 2 in R2C7
16a. Naked pair {14} in R23C7, locked for C7 and N3, clean-up: no 8 in R2C89, no 9 in R3C89, no 3,6 in R8C6
16b. Naked pair {58} in R3C89, locked for R3 -> R3C6 = 7, R3C2 = 9, clean-up: no 2 in 12(3) cage at R1C2 (step 12d), no 2 in R2C5
16c. Naked pair {23} in R3C45, locked for R3 + N3
16d. Killer pair 3,7 in 12(3) cage and R2C23, locked for N1
16e. 2 in N1 only in R12C1, locked for C1

17. R3C2 = R89C1 + 2 (step 4), R3C2 = 9 -> R89C1 = 7 = {16/34}, no 5
17a. Killer pair 1,4 in R3C1 and R89C1, locked for C1
17b. 37(7) cage at R8C1 = {1246789/1345789/2345689}
17c. 3 of {1345789/2345689} must be in R89C1 (because these combinations only contain one of 1,6) -> no 3 in R8C34 + R9C234

18. Killer triple 1,4,5 in R2C23, R2C5 and R2C7, locked for R2

19. R67C4 = R5C5 + 4 (step 12), IOU no 4 in R7C4, clean-up: no 9 in R7C5
19a. 9 in C5 only in R56C5, locked for N5

20. R7C45 = {58}/[67], R89C5 = {18/27/36} -> combined cage R7C45 + R89C5 = {58}{27}/{58/36}/[67]{18}, 8 locked for N8

21. 37(7) cage at R8C1 contains 8, locked for N7

22. 45 rule on R6789 2 innies R67C1 = 1 outie R5C8 + 3
22a. R5C8 = {789} -> R67C1 = 10,11,12 = {37/38/39/57}, no 6
[Thanks Ed for pointing out that {56} is still valid. Step 22 deleted and step 23 re-worked.]


23. 45 rule on N4 2 outies R7C13 = 2 innies R5C23 + 8
23a. Min R5C23 = 4 (cannot be {12} which clashes with R4C23) -> min R7C13 = 12 -> R7C13 = 12,13,14,15,16 = {39/49/67/59/69/79} (cannot be {57} which clashes with R7C45)
23b. 45 rule on N9 2 innies R7C13 = 2 outies R89C4 + 1
23c. R89C4 = 11,13,14,15 (cannot total 12 because doesn’t contain 3,7 or 8) -> R7C13 = 12,14,15,16 = {39/59/69/79}, no 4,
9 locked for R7 and N7
[The rest is fairly straightforward.]

24. 9 in N8 only in R89C4, locked for C4 -> R2C4 = 8, R3C4 = 3 (step 12b), R3C5 = 2, R2C5 = 5, R1C56 = [46], R2C6 = 9, R2C1 = 2, clean-up: no 7 in R1C23 (step 12d), no 3 in R2C23, no 7 in R2C89, no 7 in R89C5

25. Naked pair {38} in R1C23, locked for R1 -> R1C1 = 5
25a. R3C1 = 4 (hidden single in N1), clean-up: no 3 in R89C1 (step 17)
25b. Naked pair {16} in R89C1, locked for C1, N7 and 37(7) cage at R8C1, no 6 in R89C4
[6 has now been eliminated from R67C1, without using the incomplete step 22.]

26. R7C5 = 7 (hidden single in C5), R7C4 = 6, clean-up: no 3 in R89C5
26a. Naked pair {18} in R89C5, locked for C5 and N8 -> R4C5 = 3, R6C5 = 9, R6C4 = 4, clean-up: no 6 in R8C7

27. R5C5 = 6 -> R5C234 = 9 = {135/234}, no 7, 3 locked for R5 and N4
27a. R5C4 = {25} -> no 2,5 in R5C23

28. R7C3 = 9 (hidden single in C3), R7C1 = 3, R7C2 = 2, R8C2 = 5, R7C9 = 1, R8C9 = 9, R8C4 = 2, R8C67 = [43], R7C67 = [58], R78C8 = [47], R8C3 = 8, R1C23 = [83]

29. R5C45 = [56] = 11 -> R5C23 = 4 = [31], R2C23 = [17], R9C23 = [74], R6C23 = [65], R4C23 = [42]

30. R6C1 = 8, R6C7 = 7 (hidden singles in R6), R6C6 = 1 (cage sum)

31. R4C6 = 8, R5C67 = [29], R4C7 = 5 (cage sum)

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for Pinata #19 at Hard 1.25. My technically most difficult steps used combined cages but finding some steps took time so I went for Hard 1.25, rather than 1.25.


Last edited by Andrew on Mon Dec 24, 2012 5:12 am, edited 2 times in total.

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PostPosted: Thu Dec 06, 2012 8:36 pm 
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Joined: Wed Apr 16, 2008 1:16 am
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Location: Sydney, Australia
I really enjoyed this puzzle. Finally found Andrew's step 17c which then opens up a really neat way to crack it. Worth a pic!

Pinata Killer Sudoku 19
11 more steps:
End of Andrew's step 19 is here (select diagram: open PKS19 in SS, File>import>candidates>OK). edit to correct no 5 in r2c6
.-------------------------------.-------------------------------.-------------------------------.
| 258 3478 3478 | 1 456 568 | 2367 23679 23679 |
| 28 1357 1357 | 89 45 689 | 14 2367 2367 |
| 14 9 6 | 23 23 7 | 14 58 58 |
:-------------------------------+-------------------------------+-------------------------------:
| 89 1245 1245 | 7 123 1234568 | 235689 1234568 1234568 |
| 6789 1234567 123457 | 23456 5689 1234568 | 2356789 789 12345678 |
| 356789 345678 345789 | 458 589 1234568 | 2356789 123456 123456 |
:-------------------------------+-------------------------------+-------------------------------:
| 356789 123 45789 | 568 578 12345689 | 2356789 123456 123 |
| 1346 456 1245789 | 245689 123678 1245 | 2356 789 789 |
| 1346 1245678 1245789 | 245689 123678 1234568 | 2356789 123456789 123456789 |
'-------------------------------.-------------------------------.-------------------------------'


20. 1 in c5 in h7(2)r14c5 = [61] or in 9(2)n8
20a. -> {36} blocked from 9(2) since it would block all 1 in c5 (Locking-out cages)
20b. 9(2) = {18/27}(no 3,6)

Now for the crackers
21. 9 in n5 in 13(2) = {49} or is in r5c5 in 15(4)r5c2
21a. but a 15(4) cannot have both 4 & 9 or it would go over the cage sum
21b. -> 4 in r5c4 would block 9 in both the 13(2) and r5c5
21c. -> no 4 in r5c4 (Locking-out cages: Can't remember coming across this variation of L-OC before)

Pic for step 22 below: edit: should have no 5 in r2c6 at this spot. Andrew's step 18 dealt with it
Image

22. 3 in r8 only in h7(2)r89c1 = [34] or in 7(2)r8c6 = [43]: ie, both must have 4 (Locking cages)
22a. -> no 4 in r8c234 and r9c46 (the one in r8c4 because it's the same 37(7) cage as r9c1) because they all see both r8c6 and r9c1
22b. no 3 in r7c2

23. Hidden single 4 in c4 -> r6c4 = 4
23a. r6c5 = 9

24. 4 in n6 only in 11(3) = {146/245}(no 3,7,8)

25. 3 in n8 only in c6: locked for c6

26. 3 in r4 only in 27(5)r4c5 -> no 3 in r5c7

27. 3 in r5 only in 15(4)r5c2 and must have 5/6/8 for r5c5
27a. = {1356/2346}(no 7,8)

28. h22(3)r567c5 = {589/679}: can't have both 5 & 6 -> no 5 in r7c5
28a. no 8 in r7c4

29. Killer pair 7 & 8 in n8 in 13(2) and 9(2): 8 locked for n8

30. r89c4 can't have both 5&6 because of r7c4, must have 2 or 9 -> [92] blocked from r23c4
30a. r23c4 = [83]

cracked
Cheerio
Ed


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