Solution
Nobody found a good continuation for white to attack after the best black defense, so let me post the solution:
Black has to try 1. ... Rfe8!. Then, after 2. Qh6?, black would win with 2. ... Qxf6!.
So what should white play instead?
Amazingly white wins after
1. ... Rfe8!
2. Kg1! (threatening 3. Qh6).
If black plays now 2. ... Qc5, then
3. Rh3 Qf8
4. Qg5 wins, because black hasn't any good defense against Qh4. For example
4. ... b5? (The best try is 4. ... Re6, but after 5. Bxe6 white will win as well.)
5. Qh4 h5
6. Bxh5! 1:0 :-)
RE: Chess problem 42 / Schachaufgabe 42