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 Post subject: Pinata Killer Sudoku 15
PostPosted: Sun Oct 28, 2012 6:53 pm 
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Pinata Killer Sudoku 14 Solution
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Pinata Killer Sudoku 15
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Sudoku Solver Score: 2.00

3x3::k:5383:5383:5383:5900:5900:5900:9473:2579:2579:7171:5383:2317:2317:5900:5900:9473:3860:3860:7171:7171:2318:2318:9473:9473:9473:2837:2837:4613:7171:7171:9473:9473:1296:3343:2837:2837:4613:4614:4614:4614:4614:1296:3343:2582:2582:4613:5892:5892:8194:8194:3345:3345:5911:5911:5892:5892:4106:4106:8194:8194:8194:5911:5911:5892:4616:1289:1289:6923:6923:8194:2840:2840:4616:4616:4616:6923:6923:6923:8194:2578:2578:

In this puzzle, the pink squares are an extra group, in which the numbers cannot repeat, it is a Girandola Group

It is better to solve in Jsudoku as you can see the extra group, which you can't see in Sudoku Solver, after copying the puzzle code into Jsudoku, Left click on Design, Extra Groups then Girandola


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PostPosted: Thu Nov 01, 2012 2:32 am 
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Pinata wrote:
It is better to solve in Jsudoku as you can see the extra group, which you can't see in Sudoku Solver, after copying the puzzle code into Jsudoku, Left click on Design, Extra Groups then Girandola
That's probably true, if one wants to solve within a software solver. But surely it's better to use an Excel worksheet like I do? Yes, that's a serious comment. I can't imagine how anyone can solve in a software solver with small 3x3 grids of numbers, although I know that some solvers do work that way. The numbers in my worksheet are about twice the size of those in SudokuSolver and are arranged in a nice row of 9 before I start making eliminations. Also when working with an Excel worksheet, the only help is the cursor and the Sum function. Of course I do have to make all eliminations manually; I suppose getting them done automatically is one of the few advantages of working in a software solver.

Here are my original diagram for this puzzle and my worksheet with the candidates after I'd done the Prelims. The Girandola group is marked by thick borders.

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PostPosted: Thu Nov 01, 2012 2:36 am 
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Thanks Pinata for this week’s killer. It starts easily, probably a good thing to get solvers drawn into a puzzle ;-), but then becomes a really tough one.

Those of us whose use of this site goes back to its predecessor, Ruud’s site, may remember Nasenbaer's fairly similar Centre Dot Killers (they are in Archive Part A, which can be most easily accessed through the Archive home page and then using the link in the “and the following puzzles” hidden list). They used the group R258C258.

Here is my walkthrough for Pinata Killer #15:
The nine cells with thick borders (see diagram in my previous post) form a Girandola group, in which numbers cannot be repeated.

Prelims

a) R1C89 = {19/28/37/46}, no 5
b) R2C34 = {18/27/36/45}, no 9
c) R2C89 = {69/78}
d) R3C34 = {18/27/36/45}, no 9
e) R45C6 = {14/23}
f) R45C7 = {49/58/67}, no 1,2,3
g) R5C89 = {19/28/37/46}, no 5
h) R6C67 = {49/58/67}, no 1,2,3
i) R7C34 = {79}
j) R8C34 = {14/23}
k) R8C89 = {29/38/47/56}, no 1
l) R9C89 = {19/28/37/46}, no 5
m) 11(4) cage at R3C7 = {1235}

1. Naked pair {79} in R7C34, locked for R7

2. 45 rule on R6789 1 innie R6C1 = 2, R45C1 = 16 = {79}, locked for C1 and N4

3. 28(5) cage at R2C1 = {14689/34678} (cannot be {13789/15679/23689/24589/24679/25678/34579} because 2,7,9 only in R3C2), no 2,5
3a. 7,9 only in R3C2 -> R3C2 = {79}

4. 23(5) cage at R6C2 = {13568/23468}
4a. 2 of {23468} must be in R7C2 -> no 4 in R7C2

5. 45 rule on R89 3(2+1) innies R8C1 + R89C7 = 19
5a. Max R8C1 = 8 -> min R89C7 = 11, no 1 in R89C7
5b. Max R89C7 = 17 -> no 1 in R8C1

6. 45 rule on R1234 3 innies R4C167 = 17 = {179/269/278/359/467} (cannot be{368/458} because R4C1 only contains 7,9)
6a. 4 of {467} must be in R4C6 -> no 4 in R4C7, clean-up: no 9 in R5C7
6b. 45 rule on R5 3 innies R5C167 = 17 = {179/269/278/359/467} (cannot be{368/458} because R5C1 only contains 7,9)
6c. 4 of {467} must be in R5C6 -> no 4 in R5C7, clean-up: no 9 in R4C7
6d. R4C167 = {179/278/359/467} (cannot be {269} = [926] because R5C167 cannot be [737])
6e. R5C167 = {179/278/359/467} (cannot be {269} = [926] because R4C167 cannot be [737])
6f. R5C89 = {19/28/46} (cannot be {37} which clashes with R5C167)

[I was a bit slow spotting this; I’ve put it here because it simplifies the next steps.]
7. 32(7) cage at R6C4 = {1234589/1234679/1235678}, CPE no 2 in R7C89

8. Double hidden killer quad 6,7,8,9 for C89, the five 2-cell cages in C89 contain six of 6,7,8,9 -> 23(4) cage at R6C8 must contain two of 6,7,8,9 = {1589/3479/3569/3578/4568} (cannot be {1679} which contains three of 6,7,8,9)
[Alternatively, with hindsight, 23(4) cage cannot be {1679} because this would make both R45C7 and R6C67 = {58}, which is impossible because R45C7 “sees” R6C7. I’m glad I saw the double hidden killer quad first; it’s a technically “cleaner” way to do this step, although use of the combined cage as in steps 8a and 8b is technically “clean”.]
8a. Combined cage R45C7 + R6C67 = {58}{49}/{58}{67}/{67}{49}/{67}{58} (R45C7 and R6C67 must have different combinations because R45C7 “sees” R6C7, allowing the use of a combined cage)
8b. 23(4) cage = {1589/3569/3578/4568} (cannot be {3479} which clashes with combined cage R45C7 + R6C67)
8c. 23(4) cage = {1589} can only be {19}{58} (because R6C89 = {59/89} clash with combined cage)
Similarly
23(4) cage = {3569} can only be {39}/{56}
23(4) cage = {3578} can only be {37}/{58}
23(4) cage = {4568} can only be {58}/{46}
-> R6C89 = {19/37/39/58}, no 4,6
and R7C89 = {46/56/58}, no 1,3
8d. R8C89 = {29/38/47} (cannot be {56} which clash with R7C89), no 5,6

[Now to go a bit further with this analysis, looking at the effect of R6C89 on adjacent cages …]
9. Consider combinations for R6C89 (step 8c) = {19/37/39/49/58}
R6C89 = {19} => R6C67 = {58/67}, 4 in N6 only in R5C89 = {46} => R45C7 = {58}, R6C67 = [67], R4C89 = {23}
or R6C89 = {37} => R45C7 = {58}, R6C67 = {49}, 6 in N6 only in R5C89 = {46} => R4C89 = {12}, R6C67 = [49]
or R6C89 = {39} => R6C67 = {58/67}, 4 in N6 only in R5C89 = {46} => R45C7 = {58}, R6C67 = [67], R4C89 = {12}
or R6C89 = {58} => R45C7 = {67}, R5C89 = {19}, R6C67 = [94], R4C89 = {23}
-> R5C89 = {19/46}, no 2,8, R6C67 = [49/67/94], R6C6 = [469], R6C7 = [479]

10. R4C89 = {12/23} (from analysis in step 9), no 5, 2 locked for R4 and 11(4) cage at R3C8, no 2 in R3C89, clean-up: no 3 in R5C6
10a. 11(4) cage at R3C8 = {1235}, 5 locked for R3 and N3, clean-up: no 4 in R3C45

11. R4C167 (step 6d) = {179/359/467}, no 8
11a. R5C167 (step 6e) = {179/278/467}, no 5, 7 locked for R5

[Now to look at the effect of R7C89 on adjacent cages …]
12. Consider the combinations for R7C89 (step 8c) = {46/56/58}
R7C89 = {46} = 10 => 45 rule on N9 3 innies R789C7 = 14 = {158} (only remaining combination, cannot be {239} which clashes with R8C89 = {29/38} when R7C89 = {46}, cannot be {257} which clashes with R45C7) => no 5 in R7C7
or R7C89 = {56} = 11 => 45 rule on N9 3 innies R789C7 = 13 = {139/148/238/247}
or R7C89 = {58} = 13 => 45 rule on N9 3 innies R789C7 = 11 = {137/146/236}
-> no 5 in R7C7
12a. 5 in C7 only in R45C7 = {58} or R789C7 = {158}, no 8 in R123C7 (locking cages)

13. R8C1 + R89C7 = 19 (step 5)
13a. Max R789C7 = 14 (step 12) -> max R89C7 = 13 -> min R8C1 = 6
13b. R8C1 = {68} -> R89C7 = 11,13 -> R789C7 (step 12) = {158/238/247} (only combinations which can have a total of 11 or 13 for R89C7), no 6,9
13c. Killer pair 7,8 in R45C7 and R789C7, locked for C7, clean-up: no 6 in R6C6

14. Naked pair {49} in R6C67, locked for R6
14a. 32(7) cage at R6C4 = {1235678} (only remaining combination), no 4
14b. R789C7 (step 13b) = {158/238}, no 7, 8 locked for C7 and N9, clean-up: no 5 in R4C7, no 3 in R8C89, no 2 in R9C89
[And the rest is straightforward …]

15. Naked pair {67} in R45C7, locked for C7 and N6, clean-up: no 4 in R5C89
15a. Naked pair {19} in R5C89, locked for R5 and N6 -> R45C1 = [97], R45C7 = [76], R4C6 = 1 (step 11), R5C6 = 4, R6C67 = [94]

16. Naked pair {23} in R4C89, locked for R4, N6 and 11(4) cage at R3C8, no 2 in R3C89
16a. Naked pair {15} in R3C89, locked for R3 and N3, clean-up: no 9 in R1C89, no 8 in R3C34
16b. Naked pair {58} in R6C89, locked for R6 and 23(4) cage at R6C8 no 5 in R7C89
16c. Naked pair {46} in R7C89, locked for R7 and N9, clean-up: no 7 in R8C89
16d. Naked pair {29} in R8C89, locked for R8 and N9, clean-up: no 3 in R8C34, no 1 in R9C89
16e. Naked pair {37} in R9C89, locked for R9 and N9

17. Naked pair {58} in R89C7, locked for 32(7) cage at R6C4 -> R7C7 = 1, no 5,8 in R7C56
17a. Naked pair {23} in R7C56, locked for R7, N8 and 32(7) cage at R6C4, no 3 in R6C45
17b. Naked pair {67} in R6C56, locked for R6 and N5

18. R8C1 + R89C7 = 19 (step 5)
18a. R89C7 = {58} = 13 -> R8C1 = 6

19. R8C2 = 3 (hidden single in R8), R6C23 = [13], clean-up: no 6 in R2C4, no 6 in R3C4
19a. Naked pair {14} in R8C34, locked for R8

20. 7 in R8 only in R8C56, locked for N8 -> R7C34 = [79], clean-up: no 2 in R2C4, no 2 in R3C4

21. Naked pair {58} in R4C45, locked for R4, N5 and 37(7) cage at R1C7, no 8 in R3C56

22. Naked pair {46} in R4C23, locked for 28(5) cage at R2C1, no 4 in R23C1
22a. 28(5) cage at R2C1 (step 3) = {14689/34678}, 8 locked for C1 and N1 -> R7C12 = [58], clean-up: no 1 in R2C4

23. 45 rule on N8 1 remaining innie R8C4 = 4, R8C3 = 1, R9C1 = 4, clean-up: no 5 in R2C3, no 8 in R2C4

24. R4C23 = 10 -> R2C1 + R3C12 = 18
24a. 45 rule on N1 2 remaining innies R23C3 = 6 = [42], R2C4 = 5, R3C4 = 7, R3C2 = 9, R23C1 = 9 = [18]

25. R3C567 = [463], clean-up: no 7 in R1C89
25a. Naked pair {29} in R12C7, locked for N3, clean-up: no 8 in R1C89, no 6 in R2C89
25b. Naked pair {46} in R1C89, locked for R1 -> R1C23 = [75], R2C2 = 6
25c. Naked pair {78} in R2C89, locked for R2
25d. Naked pair {23} in R27C6, locked for C6 -> R1C6 = 8

and the rest is naked singles, including use of the Girandola group to get a unique solution.

My solving path only used the Girandola group when I got down to naked singles, with the group being used to obtain a unique solution; otherwise each 2-cell row in C89 could have its remaining candidates either way round. It’s possible that earlier use of the Girandola group might have given a slightly shorter solving path; Sudoku Solver v3.6.1 makes some placements in C89 before it has finished making placements in the rest of the grid.

Rating Comment:
I’ll rate my walkthrough for Pinata #15 at least 1.75. I did heavy combination analysis on the 23(4) cage at R6C8 and then, having split it into combinations for its upper and lower halves, I used forcing chains for further analysis.


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PostPosted: Thu Nov 01, 2012 11:35 am 
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Who remembers who came up with the Girandola group and what it means?


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PostPosted: Thu Nov 01, 2012 1:30 pm 
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HATMAN wrote:
Who remembers who came up with the Girandola group and what it means?


I am not sure of either, I just wanted to create a puzzle with that group.


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PostPosted: Thu Nov 01, 2012 4:03 pm 
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I have checked your walkthough for Pinata Killer Sudoku 15 and it is spot on.


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PostPosted: Mon Jan 07, 2013 7:25 pm 
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HATMAN wrote:
Who remembers who came up with the Girandola group and what it means?

As I understand it, the puzzle form was introduced (invented?) by Uwe Wiedemann, and the name refers to a type of revolving firework.


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PostPosted: Sun Mar 23, 2014 4:21 pm 
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enxio27 wrote:
HATMAN wrote:
Who remembers who came up with the Girandola group and what it means?

As I understand it, the puzzle form was introduced (invented?) by Uwe Wiedemann, and the name refers to a type of revolving firework.

No No No ...

http://forum.enjoysudoku.com/girandola-t5839.html has the answer. I think it caught on because JC added it to JSudoku as an Extra Group.

tarek


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PostPosted: Thu Nov 06, 2014 10:18 pm 
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Wait. . . So YOU invented it, tarek? I found it first on Uwe Wiedemann's site, and as I recall, he didn't seem to know where it came from. Very cool!


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PostPosted: Mon Nov 17, 2014 7:21 am 
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I'll vouch for that, it was the meaning that I did not remember. We were playing about with extra groups at the time.


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