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.|

*-----------*