Change the signs on the cups to their opposite.Spoiler for solution
Gee, bonanova, usually you are good at impressing me with your mathematical prowess. However, this time it seems that you decided to travel south to get to the north pole.
If only one statement is true, then only one of the signs has the correct answer. The only number to appear once is "three". That seems like a much more direct way to solve it to me.