Impossible puzzle

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Impossible puzzle

Postby arvindcr » Tue May 23, 2006 9:32 pm

Some games are easy, others hard. The question is, are there any impossible games?

The constraint is that all values preset in the sudoku problem itself must be legal – that is integers from 1 through 9, and no repeats in rows, columns, or in the 3X3 boxes.

If you think that impossible puzzle, could you give me an example?
arvindcr
 
Posts: 1
Joined: 23 May 2006

Re: Impossible puzzle

Postby Sped » Tue May 23, 2006 10:08 pm

arvindcr wrote:Some games are easy, others hard. The question is, are there any impossible games?

The constraint is that all values preset in the sudoku problem itself must be legal – that is integers from 1 through 9, and no repeats in rows, columns, or in the 3X3 boxes.

If you think that impossible puzzle, could you give me an example?

Sure. Here's one with no solutions:

Code: Select all
 *-----------*
 |.3.|18.|.9.|
 |..6|..9|..1|
 |21.|...|...|
 |---+---+---|
 |...|..6|.7.|
 |9.7|.2.|6.8|
 |.8.|7..|...|
 |---+---+---|
 |...|...|.29|
 |1..|2..|4..|
 |.7.|.45|.3.|
 *-----------*


Here's an invalid puzzle with multilple solutions:

Code: Select all
 *-----------*
 |.3.|1..|...|
 |..6|...|..1|
 |21.|...|...|
 |---+---+---|
 |...|..6|.7.|
 |9.7|.2.|6.8|
 |.8.|7..|...|
 |---+---+---|
 |...|...|.29|
 |1..|2..|4..|
 |.7.|.45|.3.|
 *-----------*


Here's a valid puzzle with a unique solution:

Code: Select all
 *-----------*
 |.3.|18.|.6.|
 |..6|..9|..1|
 |21.|...|...|
 |---+---+---|
 |...|..6|.7.|
 |9.7|.2.|6.8|
 |.8.|7..|...|
 |---+---+---|
 |...|...|.29|
 |1..|2..|4..|
 |.7.|.45|.3.|
 *-----------*
Sped
 
Posts: 126
Joined: 26 March 2006

Postby tso » Tue May 23, 2006 10:19 pm

No-solution puzzles are easy to construct:


This puzzle is impossible to complete, as there is nowhere in box one to place a 1.

Code: Select all
. . . | 1 . . | . . .
. . . | . . . | 1 . .
. . 2 | . . . | . . .
------+-------+------
1 . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
------+-------+------
. 1 . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
tso
 
Posts: 798
Joined: 22 June 2005


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