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N-queens puzzles can be viewed as constraint satisfaction problems.

In a \(n\times n\) chessboard, the goal is to place n queens such that no two queens can attack each other.

Variable \(\{X_{i}\}\). Let \(X=\{x_{1},x_{2},...,x_{n}\}\) where \(X_{i}\) represents the there is a queen on the chessboard \((X_{i},i)\).

Domain \(D=\{1,2,....,n\}\)

Constraints \(\{C_{1},C_{2}\}\):

\(C_{1}:\forall i\forall j\) \(X_{i}\neq X_{j}\) , it represents that no two queens are in the same row.

\(C_{2}:\forall i\forall j\) \(|X_{i}-X_{j}|\neq|i-j|\) , it represents that no two queens are in the same diagonal.

\chessboard

[style=4x4,setwhite=Qd4, pgfstyle=straightmove,arrow=to,linewidth=0.2ex, color=red,pgfstyle=straightmove,markmoves=d4-h8,d4-a7,d4-a1,d4-g1,d4-d8,d4-d1,d4-a4,d4-h4,shortenstart=1ex,showmover=false]

References

  1. CMS/CERN. A New Boson with a Mass of 125 GeV Observed with the CMS Experiment at the Large Hadron Collider. Science 338, 1569-1575 (2012). Link

  2. Barry R Holstein. The mysterious disappearance of Ettore Majorana. J. Phys.: Conf. Ser. 173, 012019 IOP Publishing, 2009. Link

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