## Is there a fish in here?

Advanced methods and approaches for solving Sudoku puzzles

### Is there a fish in here?

The following 6’s candidate grid came up in a recent puzzle after running through the basics. I count five strong links, but see no loops or obvious chains. Is there a fish in this bowl? Sure seems hard to spot the patterns. Other single-digit methods?

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`. . 6 | . . . | 6 6 .. 6 6 | . . . | . 6 6. . . | . . . | . . .------+-------+------. . . | . . 6 | . 6 66 . 6 | . . . | . 6 .6 . 6 | . . 6 | . . 6------+-------+------6 . . | . . . | 6 . .6 6 6 | . . . | . . 6. . . | . . . | . . .`
Sudtyro

Posts: 68
Joined: 21 December 2006

I did a pattern check on your grid, but there is no fish nor any other single-digit technique available.

Ruud
Ruud

Posts: 664
Joined: 28 October 2005

### Pattern check for FISH

Is the "pattern check" a machine algorithm, or is it something that can be done manually?
Sudtyro

Posts: 68
Joined: 21 December 2006

### Re: Pattern check for FISH

Sudtyro wrote:Is the "pattern check" a machine algorithm, or is it something that can be done manually?
Doing it manually is cumbersome. One way is to find valid templates and "exclude" those digits, e.g. you can start following:
if one of A or B is true, there is always a valid pattern for the digits marked with +
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` . . 6 | . . . |+6 6 . .+6 6 | . . . | . 6 6 . . . | . . . | . . . ------+-------+------ . . . | . . B | . A 6 6 . A | . . . | . B . 6 . B | . . A | . . 6 ------+-------+------ 6 . . | . . . | 6 . .+6 6 6 | . . . | . .+6 . . . | . . . | . . . `
Now i write 9 for digits, that cannot be eliminated. Assume that A or B and C or D is true.
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` . . C | . . . | 9 D . . 9 D | . . . | . C 6 . . . | . . . | . . . ------+-------+------ . . . | . . A | . 9 B+6 . 9 | . . . | . 9 . 6 . 9 | . . B | . . A ------+-------+------ 6 . . | . . . |+6 . . 9+6 6 | . . . | . . 9 . . . | . . . | . . . `
now six 6's are left to check
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` . .+9 | . . . | 9 9 . . 6 9 | . . . | . 9+6 . . . | . . . | . . . ------+-------+------ . . . | . .+9 | . 9 9 9 . 9 | . . . | .+9 .+6 . 9 | . . 6 | . . 9 ------+-------+------ 6 . . | . . . |+9 . . 9+9 6 | . . . | . . 9 . . . | . . . | . . . `
now four
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` . . 9 | . . . |+9 9 . .+6 9 | . . . | . 9 9 . . . | . . . | . . . ------+-------+------ . . . | . . 9 | .+9 9 9 .+9 | . . . | . 9 . 9 . 9 | . .+6 | . . 9 ------+-------+------+6 . . | . . . | 9 . . 9 9 6 | . . . | . .+9 . . . | . . . | . . . `
and a last one
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` . . 9 | . . . | 9+9 . .+9 9 | . . . | . 9 9 . . . | . . . | . . . ------+-------+------ . . . | . . A | . 9 B+9 . 9 | . . . | . 9 . 9 . 9 | . . B | . . A ------+-------+------ 9 . . | . . . |+9 . . 9 9+6 | . . . | . . 9 . . . | . . . | . . . `

Of course this is not an optimal way, better methods ?
ravel

Posts: 998
Joined: 21 February 2006

I think a pattern check means you just trial and error each digit in the pattern and see if the placement of any digit will prevent other digits to be placed validly (each row/column/box should have exactly one of that digit placed)...

For this particular pattern, only a total of 23 digits to test, so shouldn't be too hard manually (particularly if you use a solver program such as Simple Sudoku to help)... I'd say it takes less than 0.5ms with Ruud's program...
udosuk

Posts: 2698
Joined: 17 July 2005

Not exactly. A template ceck means to generate all possible complete solutions for a single digit (46656 for an empty grid). Then you combine them to find any candidate that isn't part of at least one solution.

In your case there are 12 different complete solutions for digit 6 and every candidate is part of at least one of them. So there is no exclusion possible.

Obi-Wahn

Posts: 61
Joined: 05 January 2007