Can someone expand upon Artificial Intelligence strategies for solving this? Are there "easy" mathematical strategies? Is there a solution for an arbitrary lar

Can someone expand upon Artificial Intelligence strategies for solving this? Are there "easy" mathematical strategies? Is there a solution for an arbitrary large grid? Complexity? From a first glance this reminds me of "constraint satisfaction" classes of problems. I remember studying the famous one where you are asked to colour a map such that no two adjacent cities share the same colour. Does this fall into that group or is there a better way? Edit: just saw chaoxu's comment. cool.