Cool idea! The post left me wondering what the complexity of finding a solution is. After some detective work, I have found this:

Bell, J., & Stevens, B. (2009). A survey of known results and research areas for n-queens. Discrete mathematics, 309(1), 1-31.

Check out Theorem 3 - would be sweet to implement one of these, and have it as a WFR!

Apparently, the n-queens completion puzzle is NP-hard, see:

Gent, I. P., Jefferson, C., & Nightingale, P. (2017). Complexity of n-queens completion. Journal of Artificial Intelligence Research, 59, 815-848.

Would it be difficult to allow for pre-set placements, per the completion puzzle?

Hi Brad! Yes! I actually got the inspiration from your post "Analyzing a Competitive New Method for GenerateTiling," so thank you for the idea!

I agree with you that the compile advantage could be 10× or more by optimizing the code. It would be really cool to know how many nodes the search tree has. I can totally ask about it and check if it's possible to compare the search trees directly or at least output statistics about vertex count per level based on the algorithm to see if there is an interesting result for the chapter in your upcoming book about game theory. I will definitely get back to you, hopefully with some helpful results!

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