If the CSP has a solution, then after enforcing arc consistency, you can directly read off the solution from resulting domains. $7.$ In general, to determine whether the CSP has a solution, enforcing arc consistency alone is not sufficient; backtracking may be required. $8.$ If after a run of arc consistency during the backtracking search we end up with the filtered domains of $*$all$*$ of the not yet assigned variables being empty, this means the CSP has no solution. $9.$ If after a run of arc consistency during the backtracking search we end up with the filtered domains of $**$all$**$ of the not yet assigned variables being empty, this means the search should backtrack because this particular branch in the search tree has no solution. $10.$ If after a run of arc consistency during the backtracking search we end up with the filtered domain of $*$one$*$ of the not yet assigned variables being empty, this means the CSP ha