Originally posted by Nowakowski
Hint: 6. Qxg7+
[fen]2r2nk1/p3q1pp/1prnNp1B/4pP1Q/PP1p3N/1B2P2P/P2P3P/6RK w - - 0 1 [/fen]
I suspect this 'problem' was 'composed' by computer - just place a lot of white pieces in striking distance of the black King, then ask Fritz if there's a forced mate. The end result of such 'compositions' is ugly solutions full of duals [i.e. multiple ways to mate the black King at the end].
As such, I recommend that solvers not waste time on this. Here is one of the cleaner lines:
1. Bxg7 Nxe6 2. Bxe6+ Qxe6 3. Bxf6+ Kf8 4. Qh6+ Ke8 5. fxe6 Rc1 6. Qh5+ Kf8 [or 6...Nf7 7.Qxf7#]
Here is one of the ugly lines:
1. Bxg7 Nxe6 2. Bxe6+ Qxe6 3. Bxf6+ Kf8 4. Qh6+ Kf7 5. Qg7+ Ke8 6. fxe6 and white threatens mate by Qe7, Qg8 or Qh8 - duals, since black can't stop all the threats.
This problem was solved by computer. [quid pro quo]
Notice how the "hint" 6.Qxg7+ never showed up. That's because there are multiple variations that run 7 moves. In view of this, the 'hint' never should have been given.