Of course most everyone can argue successfully that no such problem exists, but GM John Nunn, in his book Solving in Style describes the following mate-in-three as such:

Authors Jonathan Levitt and David Friedgood in Secrets of Spectacular Chess suggest to really understand such a problem, at least a half-hour is needed, and that it is well worth the investment.

that is a tough one & thanks!  the 1st move comes out of left field, but then it fits like clockwork