A friend and I yesterday asked ourselves what the highest number of possible mates in a (legal) position is. We were able to come up with the following position which has a total of 76 unique mates in 1, but we then failed to improve upon this one.
Q3Q3/4K2Q/6R1/3R4/QB2k3/5R1N/2R5/QQ1Q1N1B w - - 0 1
Do you know if this problem ever has been solved and what the highest possible number is? It was hard for us to come up with a reasonably low upper bound so that I have no idea whether this solution is close to the maximum.