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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