Is the half-filled magic square problem NP-complete?
Filling a partially-filled Latin square is NP-Complete. "The complexity of completing partial Latin squares" Charles J. Colbourn. Discrete Applied Mathematics, Volume 8, Issue 1, April 1984, Pages 25-30 http://dx.doi.org/10.1016/0166-218X(84)90075-1

Can a Latin square problem be turned into a magic square problem via modular arithmetic? My intuition says yes, but the rest of my brain says "Get back to grading!"