The author of this problem should be noted, he or she did put effort into composing it.
1. Qa4! is a nice decoy sacrifice, the decoy hiding the immediate battery formation.
Hendrik, in a good chess problem, it is expected that "none of the logical moves work." In fact, knowing it is a composition would make you look at 1. Qa4! first or early on, as David Levy once noted, in any chess problem, look first for the sacrifice of a queen, if that doesn't work, a rook, and so on.
i saw that Qe5 leads to mate...
it threatens f4# and the only way to stop it is by Bg3m which resolves in Rxg3#
am i right?