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PostPosted: Mon Aug 13, 2012 8:19 am 
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August 6th 2012 Solution
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13th August 2012
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PostPosted: Mon Aug 13, 2012 11:59 am 
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Location: Saudi Arabia
SS gives 1.5
JS Code:
3x3::k:3329:3855:5390:5390:5390:5390:5390:3085:3852:3329:3855:3855:3855:3346:3603:3603:3085:3852:3329:2576:5649:5649:3346:2324:8729:3085:3852:3330:2576:5649:5649:6168:2324:8729:8729:8729:3330:3330:9751:9751:6168:8729:8729:4886:4886:9751:9751:9751:6168:6168:6168:4886:4886:6923:2819:2819:9751:3861:3861:3861:2569:4362:6923:2309:2820:1543:1543:4360:4360:2569:4362:6923:2309:2820:2566:2566:4360:2569:2569:4362:6923:


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PostPosted: Sat Aug 18, 2012 10:32 pm 
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Another top-notch killer. Thanks a lot Pinata! How do you work out the difficulty level for these?

Saw step 5 quickly but no way did that crack it. Perhaps I missed something. Took a long time to find 14a. which was the key. This optimised walk-through makes it look easier than it felt.

Start to 13th August 2012
31 steps:
Please let me know if anything is not correct or could be clearer. Thanks to Andrew for some helpful suggestions

1. "45" on c9: 2 innies r45c9 = 3 = {12} only: both locked for c9 & n6

2. 10(4)r7c7 = {1234} only

3. "45" on n9: 2 outies r6c9+r9c6 = 9 (no 9)
3a. r9c6 = (1234) -> r6c9 = (5678)

4. 27(4)r6c9 = {3789/4689/5679}
4a. must have 9 -> 9 locked for n9 and c9

5. r6c9 cannot repeat in n9 in r789c7 (no common digits); r9c6 cannot clone in n9 in r789c9 since implied 9(2) with r6c9 (step 3): but remaining two cells (in r789c9) can't sum to 18
5a. -> implied 9(2) in r789c8 in 17(3) -> remaining cell = 8
5b. ->17(3)n9 must have 8 = {278/368/458}(no 1)
5c. 8 locked for c8 and n9

6. 1 in n9 only in c7, 1 locked for c7 and no 1 in r9c6 (same cage)
6a. no 8 in r6c9 (outies n9 = 9)
[Andrew noticed that another way to fix 1 in r789c7 is to do "45" on n78. Certainly easier than what I saw]

7. 27(4)r6c8 = {5679} only: all locked for c9

8. 15(3)n3 = {348} only: all locked for n3
8a. 14(2)r2c6 = {59}[86]
8b. r2c6 = (589), r2c7 = (569)

9. 12(3)n3 = {129/156}(no 7)

10. "45" on n3: 3 innies r123c7 = 18 and must have 7 for n3 and 7 also locked for c7
10a. = {279/567}
10b. 9 in {279} must be in r2c7 -> no 9 in r13c7

11. "45" on n69: 3 outies r3c7+r59c6 = 17
11a. max. r3c7+r9c6 = 11 -> min. r5c6 = 6
11b. max. r59c6 = 13 -> min. r3c7 = 4 (no 2)

12. "45" on c8: 2 outies r5c9+r6c7 = 1 innie r4c8 + 3
12a. max. 2 outies = 11 -> no 9 in r4c8

13. 34(6)r3c7 must have 1/2 for r4c9 = {136789/145789/235789/245689} -> it must have both 8&9 in c67 (important in a sec)

14. "45" on c789: 3 outies r259c6 = 1 innie r1c7+13
14a. the only way for r25c6 to sum to 13 (which would then mean r9c6=r1c7) is [58]: but this forces 9 into c7 in both r2c7+one of r45c7 (step 13, CCC)-> r25c6 <>13 ->r1c7<>r9c6
14b. 2 in c7 only in r1789c7 -> if r9c6 = 2 -> r1c7 = 2: but this means r9c6=r1c7 (IOE) which is not possible -> no 2 in r9c6
14c. no 7 in r6c9 (outies n9 = 9)

15. 2 in 10(4)r7c7 only in r789c7: 2 locked for c7 and n9
15a. h18(3)r123c7 = {567} only: 5&6 locked for c7 & n3
15b. no 5 in r2c6
15c. 12(3)n3 = {129}: 9 locked for c8

16. "45" on n78: 2 innies r7c3+r9c6 = 11 = [83/74] = [3/7..]

17. 6(2)r8c3 = {15/24}(no 3,6,7,8,9)

18. "45" on n8: 3 innies r8c4+r9c46 = 13 and must have 3/4 for r9c6
18a. = {139/148/238/247/346}(no 5)
18b. no 1 in r8c3

19. two 11(2) cages in n7 = {29/38/47/56}(no 1)
19a. 9(2)n7: no 9

20. "45" on n7: 3 innies r789c3 = 14 and must have 7/8 for r7c3
20a. {167} blocked since r8c3 = (245)
20b. {257} blocked since it forces both 11(2) cages in n7 = {38}
20c. = {158/248/347}(no 9) = [3/8..]
20d. no 1 in r9c4

21. two 11(2) cages in n7: {38} blocked by r789c3
21a. = {29/47/56}(no 3,8)

22. 15(3)n8: {348} blocked by r9c6
22b. {357} blocked by innies n78 = [3/7..] (step 16)
22c. = {159/168/249/258/267/456}(no 3)

23. "45" on r89: 4 outies r6c9+r7c789 = 17
23a. min. r67c9 = 11 -> max. r7c78 = 6 -> no 3,4 in r7c7

24. r7c8 = 3 (hidden single r7)

25. r6c9+r9c6 = [63](step 5)
25a. -> r7c3 = 8 (step 16)

26. r7c79 = 8 = [17] (step 23)

27. 15(3)r7c4 = {249/456}
27a. must have 4 -> 4 locked for r7 and n8
27b. no 2 in r8c3, no 6 in r9c3

28. 9 in n7 in one of 11(2) cages -> one cage must have 2: 2 locked for n7
28a. no 7 in 9(2)n7

29. "45" on n7: 2 remaining innies r89c3 = 6 = [51] only
29a. -> r89c4 = [19]

30. "45" on n6: 2 outies r3c7+r5c6 = 14 = [59/68](can't be [77] since both cells in same cage)
30a. r1c7 = 7 (hsingle n3)

31. r5c6 = (89) -> one of 8/9 for 34(6) cage is in r45c7 ->hidden killer pair 8,9 in n6 -> r6c7 = (89)
31a. 34(6) must have 3 = 389{167/257}(no 4)

much easier now.
Cheerio
Ed


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PostPosted: Sun Aug 19, 2012 1:25 am 
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Congratulations Ed on beating me to it! I was just about to start checking my walkthrough when I saw that you'd posted your one.

Pinata Killer #4 starts fairly easily. Then I found that it turned very difficult so I didn't enjoy it as much as Ed clearly did. His step 14a was a neat way to crack the puzzle, then step 23 was a nice step giving the first placement.

Here is my walkthrough for Pinata Killer #4:
Prelims

a) R23C5 = {49/58/67}, no 1,2,3
b) R2C67 = {59/68}
c) R34C2 = {19/28/37/46}, no 5
d) R34C6 = {18/27/36/45}, no 9
e) R7C12 = {29/38/47/56}, no 1
f) R89C1 = {18/27/36/45}, no 9
g) R89C2 = {29/38/47/56}, no 1
h) R8C34 = {15/24}
i) R9C34 = {19/28/37/46}, no 5
j) 10(4) cage at R7C7 = {1234}
k) 38(6) cage at R5C3 = {356789}, no 1,2,4

1a. Naked quad {1234} in 10(4) cage at R7C7, CPE no 1,2,3,4 in R9C89
1b. 45 rule on N78 2(1+1) innies R7C3 + R9C6 = 11 = [74/83/92]
1c. Naked quad {1234} in 10(4) cage at R7C7, 1 locked for C7 and N9
1d. Naked sext {356789} in 38(6) cage at R5C3, CPE no 3,5,6 in R5C12

2. 45 rule on N9 2(1+1) outies R6C9 + R9C6 = 9 = [54/63/72]

3. 45 rule on C9 2 innies R45C9 = 3 = {12}, locked for C9 and N6
3a. 15(3) cage at R1C9 = {348/357/456}, no 9
3b. 1 in N3 only in 12(3) cage at R1C8 = {129/138/156} (cannot be {147} which clashes with 15(3) cage), no 4,7
3c. 9 in C9 only in 27(4) cage at R6C9, locked for N9

4. 1,2 in R6 only in R6C456, locked for N5, clean-up: no 7,8 in R3C6
4a. 24(5) cage at R4C5 = {12489/12579/12678}, no 3
4b. One of 1,2 in {12579} must be in R6C5 (R456C5 cannot be {579} which clashes with R23C5) -> no 5 in R6C5

5. 45 rule on N6 2 outies R3C7 + R5C6 = 1 innies R6C9 + 8
5a. Min R6C9 = 5 -> min R3C7 + R5C6 = 13, no 2,3 in R3C7 + R5C6

6. 45 rule on N8 3 innies R8C4 + R9C46 = 13 must contain one of 6,7,8,9 -> R9C4 = {6789}, R9C3 = {1234}

7. 45 rule on R12 4 outies R3C1589 = 13 = {1237/1246/1345}, no 8,9, 1 locked for R3, clean-up: no 4,5 in R2C5, no 9 in R4C2, no 8 in R4C6
7a. 7 of {1237} must be in R3C5 -> no 7 in R3C19

8. Hidden killer quad 6,7,8,9 in R7C12, R7C3, R89C1 and R89C2 for N7, R7C12, R7C3 and R89C2 each contain one of 6,7,8,9 -> R89C1 must contain one of 6,7,8 -> R89C1 = {18/27/36}, no 4,5
[Alternatively 6 in N7 only in R7C12/R89C2 = {56} or in R89C1 = {36} -> R89C1 cannot be {45}, locking-out cages.]

[Only just spotted …]
9. 17(3) cage at R7C8 must contain one of 2,3,4
9a. Killer triple 2,3,4 in 10(4) cage at R7C7 and 17(3) cage, locked for N9

10. 27(4) cage at R6C9 = {5679} (only remaining combination), locked for C9
10a. Naked triple {348} in 15(3) cage at R1C9, locked for N3, clean-up: no 6 in R2C6
10b. 7 in N3 only in R13C7, locked for C7
10c. 8 in N9 only in 17(3) cage at R7C8, locked for C8

11. 45 rule on C89 2 innies R4C89 = 1 outie R6C7
11a. Min R4C89 = 4 -> min R6C7 = 4
11b. Max R4C89 = 9, no 9 in R4C8

12. 45 rule on N3 3 innies R123C7 = 18 = {279/567}
12a. 9 of {279} must be in R2C7 -> no 9 in R13C7
12b. Min R3C7 + R5C6 = 13 (step 5a), max R3C7 = 7 -> min R5C6 = 6

13. R4C9 = {12} -> 34(6) cage at R3C7 = {136789/145789/235789/245689}, CPE no 9 in R5C8

14. R3C1589 (step 7) = {1237/1246/1345}
14a. 4,6 of {1246} must be in R3C59 -> no 6 in R3C18

15. Hidden killer pair 1,2 in R5C12 and R5C9, R5C9 = {12} -> R5C12 must contain one of 1,2
15a. 13(3) cage at R4C1 contains one of 1,2 = {139/148/157/238/247} (cannot be {256} because 5,6 only in R4C1), no 6
15b. R5C12 contains one of 1,2 -> no 1,2 in R4C1
15c. 3 of {139} must be in R4C1 -> no 9 in R4C1

16. 45 rule on N1 3 innies R1C3 + R3C23 = 1 outie R2C4 + 17
16a. Max R1C3 + R3C23 = 24 -> max R2C4 = 7

17. 45 rule on R7 4 innies R7C3789 = 19 = {1279/1369/1378/1459/1468/1567/2359/2368/2458/2467/3457}
[Unfortunately the only way I can see to make use of this is to use a contradiction move :( , although it does prove to be useful in opening up more steps.]
17a. R7C3789 cannot be {1567} = [71]{56} because 15(3) cage at R7C4 contains 4 (only remaining place for 4 in R7 because R7C12 cannot be {47}) clashes with R7C3 + R9C6 = [74] (step 1b), combo blocker
-> R7C3789 = {1279/1369/1378/1459/1468/2359/2368/2458/2467/3457}
17b. R7C3789 contains two of 1,2,3,4 -> R7C8 = {234}
17c. Naked quad {1234} in R789C7 + R7C8, locked for N9
17d. Naked quad {1234} in 10(4) cage at R7C7 and R789C7 + R7C8 -> R7C8 = R9C6
17e. R7C3 + R9C6 = 11 (step 1b) -> R7C38 = 11 -> R7C79 = 8, no 4 in R7C7, no 9 in R7C9
17f. R7C3789 = {1279/1378/2359/2368/2467/3457} (cannot be {1369/1459/1468/2458} which don’t contain pairs totalling 8 and 11)

18. 15(3) cage at R7C4 = {159/168/249/348/456} (cannot be {258/267/357} which clash with R7C3789), no 7
18a. R8C4 + R9C46 = 13 (step 6) = {139/238/247/256/346} (cannot be {148} which clashes with 15(3) cage at R7C4, cannot be {157} because 1,5 only in R8C4)
18b. 15(3) cage = {159/168/348/456} (cannot be {249} which clashes with R8C4 + R9C46), no 2

19. 45 rule on R789 1 innie R7C3 = 1 outie R6C9 + 2
19a. R7C3789 (step 17f) = {1378/2359/2467} (cannot be {1279/2368/3457} which clash with R7C3 + R6C9 = [97/86/75], combo blockers)
19b. 15(3) cage at R7C4 (step 18b) = {159/168/456} (cannot be {348} which clashes with R7C3789), no 3
19c. R8C4 + R9C46 = 13 (step 18a) = {139/238/247/346} (cannot be {256} which clashes with 15(3) cage), no 5, clean-up: no 1 in R8C3
19d. 17(3) cage at R8C5 = {179/278/359/368/467} (cannot be {269/458} which clashes with 15(3) cage at R7C4)
19e. R7C12 = {29/38/47} (cannot be {56} which clashes with 15(3) cage), no 5,6 in R7C12

20. 45 rule on N7 3 innies R789C3 = 14 = {149/158/239/257/347} (cannot be {248} which clashes with R7C12)
20a. R7C3 + R9C6 (step 1b) = [74/83/92], R8C4 + R9C46 (step 19c) = {139/238/247/346}
20b. R789C3 = {158/239/347} (cannot be {149} because R8C4 + R9C46 cannot be [292], cannot be {257} because R8C4 + R9C46 doesn’t contain {148})
20c. R8C4 + R9C46 = {139/247} (cannot be {238/346} because R789C3 doesn’t contain {248}), no 6,8, clean-up: no 2,4 in R9C3
20d. R7C12 (step 19e) = {29/47} (cannot be {38} which clashes with R789C3), no 3,8 in R7C12
20e. R89C2 = {29/47/56} (cannot be {38} which clashes with R789C3), no 3,8 in R89C2
20f. R89C1 (step 8) = {18/36} (cannot be {27} which clashes with R7C12), no 2,7 in R89C1
20g. 8 in N7 only in R7C3 + R89C1, CPE no 8 in R6C1
[The rest is fairly straightforward.]

21. 3 in R7 only in R7C78, locked for N9
21a. R7C3789 (step 19a) = {1378/2359}, no 4,6
21b. R7C9 = {57} -> no 7 in R7C3, clean-up: no 4 in R9C6 (step 1b), no 5 in R6C9 (step 2)
21c. 4 in N9 only in R89C7, locked for C7
21d. 5 in C9 only in R789C9, locked for N9

22. 6 in R7 only in 15(3) cage at R7C4, locked for N8
22a. 15(3) cage at R7C4 (step 19b) = {168/456}, no 9
22b. 9 in R7 only in R7C123, locked for N7, clean-up: no 2 in R89C2
22c. R34C2 = {28/37}/[91] (cannot be {46} which clashes with R89C2), no 4,6 in R34C2

23. 13(3) cage at R1C1 = {148/157/247/256/346} (cannot be {139/238} which clash with R89C1), no 9

24. R789C3 (step 20b) = {158/239}, no 4, clean-up: no 2 in R8C4
24a. Killer pair 1,4 in 15(3) cage at R7C4 and R8C4, locked for N8

25. Naked sext {356789} in 38(6) cage at R5C3, CPE no 7 in R5C12
25a. 13(3) cage at R4C1 (step 15a) = {139/148/238/247} (cannot be {157} because 5,7 only in R4C1), no 5 in R4C1

26. R3C7 + R5C6 = R6C9 + 8 (step 5)
26a. Min R6C9 = 6 -> min R3C7 + R5C6 = 14, no 6,7 in R5C6

27. 24(5) cage at R4C5 (step 4a) = {12579/12678} (cannot be {12489} which clashes with R5C6), no 4, 7 locked for N5, clean-up: no 2 in R3C6
27a. Killer pair 8,9 in 24(5) cage and R5C6, locked for N5

28. 4 in N5 only in R4C46, locked for R4
28a. 4 in N4 only in 13(3) cage at R4C1 (step 25a) = {148/247}, no 3,9, 8 locked for N4, clean-up: no 2 in R3C2

29. 34(6) cage at R3C7 (step 13) = {136789/235789}, 3 locked for N6

30. 45 rule on C8 3 innies R456C8 = 16 = {349/457} (cannot be {367} which clashes with R6C9), no 6

31. 38(6) cage at R5C3 = {356789} -> R7C3 = 8, R9C6 = 3 (step 1b), R6C9 = 6 (step 2), R9C3 = 1, R9C4 = 9, R89C3 = [36], R8C3 = 5 (step 24), R8C4 = 1

32. Naked pair {24} in R89C7, locked for C7 and N9 -> R7C78 = [13]
32a. Naked triple {456} in 15(3) cage at R7C4, locked for R7 and N8 -> R7C9 = 7, R89C9 = [95], R89C8 = [68]
32b. 2 in N3 only in 12(3) cage at R1C8 = {129} (only remaining combination), locked for C8 and N3, clean-up: no 5 in R2C6
32c. Naked triple {567} in R123C7, locked for C7
32d. Naked pair {89} in R25C6, locked for C6

[Just noticed that I missed clean-up: no 6 in R34C6 from step 31 …]
33. Naked pair {45} in R34C6, locked for C6 -> R7C6 = 6

34. R8C5 = 8 (hidden single in N8), clean-up: no 5 in R3C5

35. Naked pair {47} in R89C2, locked for C2, clean-up: no 3 in R34C2
35a. Naked pair {12} in R4C29, locked for R4

36. 38(6) cage at R5C3 = {356789}, 7 locked for N4 -> R4C1 = 8, R5C12 = 5 = [41], R4C2 = 2, R3C2 = 8, R7C12 = [29]

37. Naked triple {157} in 13(3) cage at R1C1, locked for C1 and N1 -> R6C1 = 9, R6C7 = 8

38. Naked pair {36} in R12C2, locked for C2, N1 and 15(4) cage at R1C2 -> R6C2 = 5
38a. R12C2 = {36} = 9 -> R2C34 = 6 = {24}, locked for R2

39. Naked triple {127} in R6C456, locked for R6 and N5 -> R6C3 = 3, R6C8 = 4

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for Pinata Killer #4 at 1.75 because of my analysis in steps 17, 19 and 20. I used a contradiction move as part of step 17, followed by combo blockers and further combination analysis involving interactions between hidden cages in N7 and N8.


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PostPosted: Sun Aug 19, 2012 2:49 pm 
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Joined: Sat Jul 28, 2012 11:05 pm
Posts: 92
Ed wrote:
Another top-notch killer. Thanks a lot Pinata! How do you work out the difficulty level for these?

Saw step 5 quickly but no way did that crack it. Perhaps I missed something. Took a long time to find 14a. which was the key. This optimised walk-through makes it look easier than it felt.

Start to 13th August 2012
24 steps:
Please let me know if anything is not correct or could be clearer.

1. "45" on c9: 2 innies r45c9 = 3 = {12} only: both locked for c9 & n6

2. 10(4)r7c7 = {1234} only

3. "45" on n9: 2 outies r6c9+r9c6 = 9 (no 9)
3a. r9c6 = (1234) -> r6c9 = (5678)

4. 27(4)r6c9 = {3789/4689/5679}
4a. must have 9 -> 9 locked for n9 and c9

5. r6c9 cannot repeat in n9 in r789c7 (no common digits); r9c6 cannot clone in n9 in r789c9 since implied 9(2) with r6c9 (step 3): but remaining two cells (in r789c9) can't sum to 18
5a. -> implied 9(2) in r789c8 in 17(3) -> remaining cell = 8
5a. ->17(3)n9 must have 8 = {278/368/458}(no 1)
5b. 8 locked for c8 and n9

6. 1 in n9 only in c7, 1 locked for c7 and no 1 in r9c6 (same cage)
6a. no 8 in r6c9 (outies n9 = 9)

7. 27(4)r6c8 = {5679} only: all locked for c9

8. 15(3)n3 = {348} only: all locked for n3
8a. 14(2)r2c6 = {59}[86]
8b. r2c6 = (589), r2c7 = (569)

9. 12(3)n3 = {129/156}(no 7)

10. "45" on n3: 3 innies r123c7 = 18 and must have 7 for n3 and 7 also locked for c7
10a. = {279/567}
10b. 9 in {279} must be in r2c7 -> no 9 in r13c7

11. "45" on n69: 3 outies r3c7+r49c6 = 17
11a. max. r3c7+r9c6 = 11 -> min. r5c6 = 6
11b. max. r59c6 = 13 -> min. r3c7 = 4 (no 2)

12. "45" on c8: 2 outies r5c9+r6c7 = 1 innie r4c8 + 3
12a. max. 2 outies = 11 -> no 9 in r4c8

13. 34(6)r3c7 must have 1/2 for r4c9 = {136789/145789/235789/245689} -> it must have both 8&9 in c67 (important in a sec)

14. "45" on c789: 3 outies r259c6 = 1 innie r1c7+13
14a. the only way for r25c6 to sum to 13 (which would then mean r9c6=r1c7) is [58]: but this forces 9 into c7 in both r2c7+one of r45c7 -> r25c6 <>13 ->r1c7<>r9c6
14b. 2 in c7 only in r1789c7 -> if r9c6 = 2 -> r1c7 = 2: but this means r9c6=r1c7 which is not possible -> no 2 in r9c6
14c. no 7 in r6c9 (outies n9 = 9)

15. 2 in 10(4)r7c7 only in r789c7: 2 locked for c7 and n9
15a. h18(3)r123c7 = {567} only: 5&6 locked for c7 & n3
15b. no 5 in r2c6
15c. 12(3)n3 = {129}: 9 locked for c8

16. "45" on n78: 2 innies r7c3+r9c6 = 11 = [83/74] = [3/7..]

17. 6(2)r8c3 = {15/24}(no 3,6,7,8,9)

18. "45" on n8: 3 innies r8c4+r9c46 = 13 and must have 3/4 for r9c6
18a. = {139/148/238/247/346}(no 5)
18b. no 1 in r2c3

19. two 11(2) cages in n7 = {29/38/47/56}(no 1)
19a. 9(2)n7: no 9

20. "45" on n7: 3 innies r789c3 = 14 and must have 7/8 for r7c3
20a. {167} blocked since r8c3 = (245)
20b. {257} blocked since it forces both 11(2) cages in n7 = {38}
20c. = {158/248/347}(no 9) = [3/8..]
20d. no 1 in r9c4

21. two 11(2) cages in n7: {38} blocked by r789c3
21a. = {29/47/56}(no 3,8)

22. 15(3)n8: {348} blocked by r9c6
22b. {357} blocked by innies n78 = [3/7..] (step 16)
22c. = {159/168/249/258/267/456}(no 3)

23. "45" on r89: 4 outies r6c9+r7c789 = 17
23a. min. r67c9 = 11 -> max. r7c78 = 6 -> no 3,4 in r7c7

24. r7c8 = 3 (hidden single r7)

much easier now.
Cheerio
Ed


Yes, your walkthrough is correct, how did you solve it after step 24 as this was quite a hard puzzle and could you explain to me Steps 12 and 12a as I found the walkthrough quite hard to understand the walkthrough.

I checked this puzzle with Sudoku Solver and it gave me a rating of 3.20

To work out the difficulty

1) I first create the solution

2) Use Jsudoku or Sudoku to create the cages

3) Check for validity and consistency

4) Use Jsudoku or Sudoku Solver to solve the puzzles

5) If they contain advanced enough techniques, I will keep the puzzle and if they don't contain advanced enough techniques the puzzle is discarded.


Last edited by Pinata on Sun Aug 19, 2012 3:06 pm, edited 1 time in total.

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PostPosted: Sun Aug 19, 2012 2:55 pm 
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Andrew wrote:
Congratulations Ed on beating me to it! I was just about to start checking my walkthrough when I saw that you'd posted your one.

Pinata Killer #4 starts fairly easily. Then I found that it turned very difficult so I didn't enjoy it as much as Ed clearly did. His step 14a was a neat way to crack the puzzle, then step 23 was a nice step giving the first placement.

Here is my walkthrough for Pinata Killer #4:
Prelims

a) R23C5 = {49/58/67}, no 1,2,3
b) R2C67 = {59/68}
c) R34C2 = {19/28/37/46}, no 5
d) R34C6 = {18/27/36/45}, no 9
e) R7C12 = {29/38/47/56}, no 1
f) R89C1 = {18/27/36/45}, no 9
g) R89C2 = {29/38/47/56}, no 1
h) R8C34 = {15/24}
i) R9C34 = {19/28/37/46}, no 5
j) 10(4) cage at R7C7 = {1234}
k) 38(6) cage at R5C3 = {356789}, no 1,2,4

1a. Naked quad {1234} in 10(4) cage at R7C7, CPE no 1,2,3,4 in R9C89
1b. 45 rule on N78 2(1+1) innies R7C3 + R9C6 = 11 = [74/83/92]
1c. Naked quad {1234} in 10(4) cage at R7C7, 1 locked for C7 and N9
1d. Naked sext {356789} in 38(6) cage at R5C3, CPE no 3,5,6 in R5C12

2. 45 rule on N9 2(1+1) outies R6C9 + R9C6 = 9 = [54/63/72]

3. 45 rule on C9 2 innies R45C9 = 3 = {12}, locked for C9 and N6
3a. 15(3) cage at R1C9 = {348/357/456}, no 9
3b. 1 in N3 only in 12(3) cage at R1C8 = {129/138/156} (cannot be {147} which clashes with 15(3) cage), no 4,7
3c. 9 in C9 only in 27(4) cage at R6C9, locked for N9

4. 1,2 in R6 only in R6C456, locked for N5, clean-up: no 7,8 in R3C6
4a. 24(5) cage at R4C5 = {12489/12579/12678}, no 3
4b. One of 1,2 in {12579} must be in R6C5 (R456C5 cannot be {579} which clashes with R23C5) -> no 5 in R6C5

5. 45 rule on N6 2 outies R3C7 + R5C6 = 1 innies R6C9 + 8
5a. Min R6C9 = 5 -> min R3C7 + R5C6 = 13, no 2,3 in R3C7 + R5C6

6. 45 rule on N8 3 innies R8C4 + R9C46 = 13 must contain one of 6,7,8,9 -> R9C4 = {6789}, R9C3 = {1234}

7. 45 rule on R12 4 outies R3C1589 = 13 = {1237/1246/1345}, no 8,9, 1 locked for R3, clean-up: no 4,5 in R2C5, no 9 in R4C2, no 8 in R4C6
7a. 7 of {1237} must be in R3C5 -> no 7 in R3C19

8. Hidden killer quad 6,7,8,9 in R7C12, R7C3, R89C1 and R89C2 for N7, R7C12, R7C3 and R89C2 each contain one of 6,7,8,9 -> R89C1 must contain one of 6,7,8 -> R89C1 = {18/27/36}, no 4,5
[Alternatively 6 in N7 only in R7C12/R89C2 = {56} or in R89C1 = {36} -> R89C1 cannot be {45}, locking-out cages.]

[Only just spotted …]
9. 17(3) cage at R7C8 must contain one of 2,3,4
9a. Killer triple 2,3,4 in 10(4) cage at R7C7 and 17(3) cage, locked for N9

10. 27(4) cage at R6C9 = {5679} (only remaining combination), locked for C9
10a. Naked triple {348} in 15(3) cage at R1C9, locked for N3, clean-up: no 6 in R2C6
10b. 7 in N3 only in R13C7, locked for C7
10c. 8 in N9 only in 17(3) cage at R7C8, locked for C8

11. 45 rule on C89 2 innies R4C89 = 1 outie R6C7
11a. Min R4C89 = 4 -> min R6C7 = 4
11b. Max R4C89 = 9, no 9 in R4C8

12. 45 rule on N3 3 innies R123C7 = 18 = {279/567}
12a. 9 of {279} must be in R2C7 -> no 9 in R13C7
12b. Min R3C7 + R5C6 = 13 (step 5a), max R3C7 = 7 -> min R5C6 = 6

13. R4C9 = {12} -> 34(6) cage at R3C7 = {136789/145789/235789/245689}, CPE no 9 in R5C8

14. R3C1589 (step 7) = {1237/1246/1345}
14a. 4,6 of {1246} must be in R3C59 -> no 6 in R3C18

15. Hidden killer pair 1,2 in R5C12 and R5C9, R5C9 = {12} -> R5C12 must contain one of 1,2
15a. 13(3) cage at R4C1 contains one of 1,2 = {139/148/157/238/247} (cannot be {256} because 5,6 only in R4C1), no 6
15b. R5C12 contains one of 1,2 -> no 1,2 in R4C1
15c. 3 of {139} must be in R4C1 -> no 9 in R4C1

16. 45 rule on N1 3 innies R1C3 + R3C23 = 1 outie R2C4 + 17
16a. Max R1C3 + R3C23 = 24 -> max R2C4 = 7

17. 45 rule on R7 4 innies R7C3789 = 19 = {1279/1369/1378/1459/1468/1567/2359/2368/2458/2467/3457}
[Unfortunately the only way I can see to make use of this is to use a contradiction move :( , although it does prove to be useful in opening up more steps.]
17a. R7C3789 cannot be {1567} = [71]{56} because 15(3) cage at R7C4 contains 4 (only remaining place for 4 in R7 because R7C12 cannot be {47}) clashes with R7C3 + R9C6 = [74] (step 1b), combo blocker
-> R7C3789 = {1279/1369/1378/1459/1468/2359/2368/2458/2467/3457}
17b. R7C3789 contains two of 1,2,3,4 -> R7C8 = {234}
17c. Naked quad {1234} in R789C7 + R7C8, locked for N9
17d. Naked quad {1234} in 10(4) cage at R7C7 and R789C7 + R7C8 -> R7C8 = R9C6
17e. R7C3 + R9C6 = 11 (step 1b) -> R7C38 = 11 -> R7C79 = 8, no 4 in R7C7, no 9 in R7C9
17f. R7C3789 = {1279/1378/2359/2368/2467/3457} (cannot be {1369/1459/1468/2458} which don’t contain pairs totalling 8 and 11)

18. 15(3) cage at R7C4 = {159/168/249/348/456} (cannot be {258/267/357} which clash with R7C3789), no 7
18a. R8C4 + R9C46 = 13 (step 6) = {139/238/247/256/346} (cannot be {148} which clashes with 15(3) cage at R7C4, cannot be {157} because 1,5 only in R8C4)
18b. 15(3) cage = {159/168/348/456} (cannot be {249} which clashes with R8C4 + R9C46), no 2

19. 45 rule on R789 1 innie R7C3 = 1 outie R6C9 + 2
19a. R7C3789 (step 17f) = {1378/2359/2467} (cannot be {1279/2368/3457} which clash with R7C3 + R6C9 = [97/86/75], combo blockers)
19b. 15(3) cage at R7C4 (step 18b) = {159/168/456} (cannot be {348} which clashes with R7C3789), no 3
19c. R8C4 + R9C46 = 13 (step 18a) = {139/238/247/346} (cannot be {256} which clashes with 15(3) cage), no 5, clean-up: no 1 in R8C3
19d. 17(3) cage at R8C5 = {179/278/359/368/467} (cannot be {269/458} which clashes with 15(3) cage at R7C4)
19e. R7C12 = {29/38/47} (cannot be {56} which clashes with 15(3) cage), no 5,6 in R7C12

20. 45 rule on N7 3 innies R789C3 = 14 = {149/158/239/257/347} (cannot be {248} which clashes with R7C12)
20a. R7C3 + R9C6 (step 1b) = [74/83/92], R8C4 + R9C46 (step 19c) = {139/238/247/346}
20b. R789C3 = {158/239/347} (cannot be {149} because R8C4 + R9C46 cannot be [292], cannot be {257} because R8C4 + R9C46 doesn’t contain {148})
20c. R8C4 + R9C46 = {139/247} (cannot be {238/346} because R789C3 doesn’t contain {248}), no 6,8, clean-up: no 2,4 in R9C3
20d. R7C12 (step 19e) = {29/47} (cannot be {38} which clashes with R789C3), no 3,8 in R7C12
20e. R89C2 = {29/47/56} (cannot be {38} which clashes with R789C3), no 3,8 in R89C2
20f. R89C1 (step 8) = {18/36} (cannot be {27} which clashes with R7C12), no 2,7 in R89C1
20g. 8 in N7 only in R7C3 + R89C1, CPE no 8 in R6C1
[The rest is fairly straightforward.]

21. 3 in R7 only in R7C78, locked for N9
21a. R7C3789 (step 19a) = {1378/2359}, no 4,6
21b. R7C9 = {57} -> no 7 in R7C3, clean-up: no 4 in R9C6 (step 1b), no 5 in R6C9 (step 2)
21c. 4 in N9 only in R89C7, locked for C7
21d. 5 in C9 only in R789C9, locked for N9

22. 6 in R7 only in 15(3) cage at R7C4, locked for N8
22a. 15(3) cage at R7C4 (step 19b) = {168/456}, no 9
22b. 9 in R7 only in R7C123, locked for N7, clean-up: no 2 in R89C2
22c. R34C2 = {28/37}/[91] (cannot be {46} which clashes with R89C2), no 4,6 in R34C2

23. 13(3) cage at R1C1 = {148/157/247/256/346} (cannot be {139/238} which clash with R89C1), no 9

24. R789C3 (step 20b) = {158/239}, no 4, clean-up: no 2 in R8C4
24a. Killer pair 1,4 in 15(3) cage at R7C4 and R8C4, locked for N8

25. Naked sext {356789} in 38(6) cage at R5C3, CPE no 7 in R5C12
25a. 13(3) cage at R4C1 (step 15a) = {139/148/238/247} (cannot be {157} because 5,7 only in R4C1), no 5 in R4C1

26. R3C7 + R5C6 = R6C9 + 8 (step 5)
26a. Min R6C9 = 6 -> min R3C7 + R5C6 = 14, no 6,7 in R5C6

27. 24(5) cage at R4C5 (step 4a) = {12579/12678} (cannot be {12489} which clashes with R5C6), no 4, 7 locked for N5, clean-up: no 2 in R3C6
27a. Killer pair 8,9 in 24(5) cage and R5C6, locked for N5

28. 4 in N5 only in R4C46, locked for R4
28a. 4 in N4 only in 13(3) cage at R4C1 (step 25a) = {148/247}, no 3,9, 8 locked for N4, clean-up: no 2 in R3C2

29. 34(6) cage at R3C7 (step 13) = {136789/235789}, 3 locked for N6

30. 45 rule on C8 3 innies R456C8 = 16 = {349/457} (cannot be {367} which clashes with R6C9), no 6

31. 38(6) cage at R5C3 = {356789} -> R7C3 = 8, R9C6 = 3 (step 1b), R6C9 = 6 (step 2), R9C3 = 1, R9C4 = 9, R89C3 = [36], R8C3 = 5 (step 24), R8C4 = 1

32. Naked pair {24} in R89C7, locked for C7 and N9 -> R7C78 = [13]
32a. Naked triple {456} in 15(3) cage at R7C4, locked for R7 and N8 -> R7C9 = 7, R89C9 = [95], R89C8 = [68]
32b. 2 in N3 only in 12(3) cage at R1C8 = {129} (only remaining combination), locked for C8 and N3, clean-up: no 5 in R2C6
32c. Naked triple {567} in R123C7, locked for C7
32d. Naked pair {89} in R25C6, locked for C6

[Just noticed that I missed clean-up: no 6 in R34C6 from step 31 …]
33. Naked pair {45} in R34C6, locked for C6 -> R7C6 = 6

34. R8C5 = 8 (hidden single in N8), clean-up: no 5 in R3C5

35. Naked pair {47} in R89C2, locked for C2, clean-up: no 3 in R34C2
35a. Naked pair {12} in R4C29, locked for R4

36. 38(6) cage at R5C3 = {356789}, 7 locked for N4 -> R4C1 = 8, R5C12 = 5 = [41], R4C2 = 2, R3C2 = 8, R7C12 = [29]

37. Naked triple {157} in 13(3) cage at R1C1, locked for C1 and N1 -> R6C1 = 9, R6C7 = 8

38. Naked pair {36} in R12C2, locked for C2, N1 and 15(4) cage at R1C2 -> R6C2 = 5
38a. R12C2 = {36} = 9 -> R2C34 = 6 = {24}, locked for R2

39. Naked triple {127} in R6C456, locked for R6 and N5 -> R6C3 = 3, R6C8 = 4

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for Pinata Killer #4 at 1.75 because of my analysis in steps 17, 19 and 20. I used a contradiction move as part of step 17, followed by combo blockers and further combination analysis involving interactions between hidden cages in N7 and N8.


I would have tried your walkthrough but for the contradictions, but I have no doubt that you. Ed and Hatman better than me at killer sudokus.


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PostPosted: Tue Aug 21, 2012 11:08 am 
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Posts: 1044
Location: Sydney, Australia
Pinata wrote:
how did you solve it after step 24 as this was quite a hard puzzle
I've added a few more steps. Hope it's enough. Send me a PM if you're stuck.
Pinata wrote:
could you explain to me Steps 12 and 12a as I found the walkthrough quite hard to understand
I try and write my walkthrough's with a new-to-killers person in mind. If you have any suggestions for how to improve them please let me know. I'm sure Andrew will feel the same.

Here's a picture of the "45" in step 12. As you can see, SudokuSolver does the adding up for me so I just have to interpret it correctly.

Image
Quote:
12. "45" on c8: 2 outies r5c9+r6c7 = 1 innie r4c8 + 3
12a. max. 2 outies = 11 -> no 9 in r4c8


Pinata wrote:

To work out the difficulty

4) Use Jsudoku or Sudoku Solver to solve the puzzles

5) If they contain advanced enough techniques, I will keep the puzzle and if they don't contain advanced enough techniques the puzzle is discarded.
This is nearly the same as what I do. I have attached the JSudoku solvers order that I use if you are interested. Right click on the solvers window in Jsudoku and import the order from your computer.

Cheers
Ed


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