[D]3Q3R/pp3pk1/6b1/4K3/8/8/PPq5/8 w - - 0 1
But try it by removing the Pf7:
[D]3Q3R/pp4k1/6b1/4K3/8/8/PPq5/8 w - - 0 1
You will get no analysis at all...
This is more interesting:
[D]2Q2R2/pp2k1p1/8/4KP2/8/8/PP5r/8 w - - 0 1
Houdini finds the two checkmating moves (1.Qd8#; 1.Qe8#)
If we try to remove one of them by defending d8 or e8 with a black Bishop we get the following:
[D]2Q2R2/pp2k1p1/8/b3KP2/8/8/PP5r/8 w - - 0 1
Houdini finds the 1.Qe8#! Bravo!
But try this:
[D]2Q2R2/pp2k1p1/8/4KP1b/8/8/PP5r/8 w - - 0 1
You will get nothing in the analysis window... It only shows Depth=1/15 but no moves.
[D]2Q2R2/pp2k1p1/8/4K2b/8/8/PP5r/8 w - - 0 1
Bingo! Now it shows the 1.Qd8#!
If you defend again the e6 square (e.g. with a Knight):
[D]2Q2R2/pp2k1p1/8/4K2b/3N4/8/PP5r/8 w - - 0 1
Guess what happens?

