Manuals/calci/NQUEENS

NQUEENS (GridSize)

• $GridSize$ is any positive integer.

Description

• This functions creates the N-queens puzzle.
• In $NQUEENS(GridSize)$, $Gridsize$ is the size of the row and columns.
• Generally eight queens puzzle is the problem of placing eight chess queens on an 8x8 chessboard so that no two queens attack each other.
• Thus, a solution requires that no two queens share the same row, column or diagonal.
• The eight queens puzzle is a great example of the more general N Queens problem of placing N non attacking queens on an nxn chessboard where solutions exist for all natural numbers n with the exception of n=2 and n=3.
• This function will return the result as "0" when the value of the Grid size is 2 or 3.
• Also this will return as Error when the parameter value is non positive integer.

Examples

1. NQUEENS(4)

1

_|Q|_|_|

_|_|_|Q|

Q|_|_|_|

_|_|Q|_|

2

_|Q|_|_|

_|_|_|Q|

Q|_|_|_|

_|_|Q|_|

2 Solutions

• 2. NQUEENS(6)

1

_|Q|_|_|_|_|

_|_|_|Q|_|_|

_|_|_|_|_|Q|

Q|_|_|_|_|_|

_|_|Q|_|_|_|

_|_|_|_|Q|_|

2

_|_|Q|_|_|_|

_|_|_|_|_|Q|

_|Q|_|_|_|_|

_|_|_|_|Q|_|

Q|_|_|_|_|_|

_|_|_|Q|_|_|

3

_|_|_|Q|_|_|

Q|_|_|_|_|_|

_|_|_|_|Q|_|

_|Q|_|_|_|_|

_|_|_|_|_|Q|

_|_|Q|_|_|_|

4

_|_|_|_|Q|_|

_|_|Q|_|_|_|

Q|_|_|_|_|_|

_|_|_|_|_|Q|

_|_|_|Q|_|_|

_|Q|_|_|_|_|

4 Solutions

See Also

• GENERATESUDOKU
• MAGICSQUARE
• BIRTHDAYPROBABILITY

References

• N Queens

• List of Main Z Functions

• Z3 home