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| nick89
| | Joined: 26 May 2005 | | Posts: 2 | | : | |
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 Posted: Sat May 28, 2005 8:01 am Post subject: I Don't Understand Nishio |
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In an attempt to solve a recent puzzle i started of by using basic rules of elimination, to get this far:
| Code: |
+-------+-------+-------+
| 6 1 . | . 4 . | . 9 . |
| . 2 . | . 9 . | . . 6 |
| . 5 . | 6 . . | . . 1 |
+-------+-------+-------+
| . 7 6 | . 5 . | . 4 . |
| . 9 5 | 4 . 8 | 6 . 7 |
| . 3 . | . 6 . | 2 5 . |
+-------+-------+-------+
| 5 6 . | . . 4 | . 7 . |
| 3 4 7 | . 1 . | . 6 . |
| . 8 . | 5 7 6 | . . 4 |
+-------+-------+-------+
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As far as i can gather, basic logic will take this puzzle no further.
From reading your topic on Nishio i have a vague feeling for it, but i don't really understand it or how to implement it.
I have a feeling using Nishio I can solve a key cell in column 8.
Also i need to understand this procedure for the sudoku solver that me and a friend are doing as a programming project. |
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| rubylips
| | Joined: 07 Apr 2005 | | Posts: 62 | | : | | Location: London |
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| Posted: Wed Jun 01, 2005 12:08 pm Post subject: |
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An algorithm to implement Nishio is suggested on this forum under the (My) Nishio definition topic.
The given puzzle has a Nishio in the 3s, though I believe its discovery isn't sufficient to allow a logical solution to the puzzle. Consider where the 3s might go in Row 9 - they are clearly restricted to Box 9 (i.e. the bottom right-hand box). It follows that any 3s in Box 9 will have to lie on Row 9. We are left with the following graph of possible locations for the value 3 on the grid:
| Code: | . . ? | ? . ? | ? . ?
. . ? | ? . ? | ? ? .
. . ? | . ? ? | ? ? .
----------+----------+---------
. . . | ? . ? | ? . ?
. . . | . ? . | . ? .
. 3 . | . . . | . . .
----------+----------+---------
. . . | ? ? . | . . .
3 . . | . . . | . . .
. . . | . . . | ? ? . |
Were you to place a 3 in r1c4, it would become impossible to place the remaining 3s, so we're able to eliminate the move from the list of candidates. Unfortunately, its elimination doesn't leave us with a single clear candidate for a logical move. |
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| djense
| | Joined: 26 May 2005 | | Posts: 3 | | : | |
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| Posted: Wed Jun 01, 2005 10:56 pm Post subject: |
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Hello,
Just run a program with this input and found that there are at least two solutions to this problem :
| Code: | 6 1 3 | 8 4 5 | 7 9 2
4 2 8 | 1 9 7 | 5 3 6
7 5 9 | 6 2 3 | 4 8 1
------+-------+------
8 7 6 | 2 5 1 | 9 4 3
2 9 5 | 4 3 8 | 6 1 7
1 3 4 | 7 6 9 | 2 5 8
------+-------+------
5 6 2 | 3 8 4 | 1 7 9
3 4 7 | 9 1 2 | 8 6 5
9 8 1 | 5 7 6 | 3 2 4 |
or :
| Code: | 6 1 8 | 7 4 2 | 3 9 5
7 2 3 | 1 9 5 | 4 8 6
4 5 9 | 6 8 3 | 7 2 1
------+-------+------
8 7 6 | 2 5 1 | 9 4 3
2 9 5 | 4 3 8 | 6 1 7
1 3 4 | 9 6 7 | 2 5 8
------+-------+------
5 6 1 | 3 2 4 | 8 7 9
3 4 7 | 8 1 9 | 5 6 2
9 8 2 | 5 7 6 | 1 3 4 |
There might be more... |
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| MadOverlord
| | Joined: 01 Jun 2005 | | Posts: 80 | | : | | Location: Wilmington, NC, USA |
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| Posted: Thu Jun 09, 2005 12:21 am Post subject: |
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| I checked, there are 19 possible solutions! |
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