Solving this puzzle is all about asking the right question!

The BK only has f1 available. So the square he's on, e2, and f1 must be covered for mate in 2. The only piece that can cover both is c2B. If some other piece moves first, then 2. Bd3 could mate, however, g2 would have to be all ready covered by then.

Therefore, we have a definitive question, "What piece moving in what way can safely cover g2?"

How about Nh4? That does cover g2, but it UNcovers e1 & g1, leaving e1, e2, f1, g1 & g2 uncovered! Now we see that it's g1 & g2 that require cover, which the Kt can't do. So we can <<modify our Question>> by asking, "What one move can safely cover g1 & g2?" Ans: Only Rg4.

Therefore, ask: what happens if 1. Rg4? 1...K×f3 is likely. Then 2. Bd1# settles that. B guards R by x-ray or skewer. How about if capture is declined? 1...Kf1 is answered with 2. Bd3#, since our safe-distant R covers both g1 & g2.

You can be 100% certain the 9 (60%) fails did NOT ask this modified question.