Consider the problem of placing $\backslash ($ k $\backslash )$ knights on an $\backslash ($ n $\backslash$times n $\backslash )$ chessboard such that no two knights are attacking each other, where $\backslash ($ k $\backslash )$ is given and $\backslash ($ k $\backslash$leq n $\backslash )$ :

$($a$)$ Choose a CSP formulation. In your formulation, what are the variables?

$($b$)$ What are the possible values of each variable?

$($c$)$ What sets of variables are constrained, and how?

$($d$)$ Now consider the problem of putting as many knights as possible on the board without any attacks. Explain how to solve this with local search by defining a sensible objective function.