Because there is such a straightforward though intractable brute force solution, but several straightforward improvements that can be made on it, I think this i

Because there is such a straightforward though intractable brute force solution, but several straightforward improvements that can be made on it, I think this is actually a fairly reasonable interview question. If they can't get the naive brute force solution in a few minutes, that indicates something pretty bad. If they treat it as a permutation question and get the n! brute force answer, that is much better (and is still something that can be done in about the same amount of time. If you treat the problem as numbered permutations then checking for diagonals even becomes non-tedious, making it easier to write out on a whiteboard than the naive brute force solution). If they get a proper solution in only a few minutes, you know that they either have their act together, or that they have seen the problem before and remember the solution. That in itself is a good indicator, though if they get a proper solution right away there should be some follow-up questions to get a handle on how exactly they were able to solve it that quickly.