Why stockfish cant find the solution?

Reading over that post after getting some sleep, I should point out that it should be Kf5, not Ke5 in that sequence of non-forcing, non-checking moves I mentioned. I just shouldn't post that late :)

As a side note, Komodo recommends 1.Nf6+ with a +1.3 assessment at depth 17 (a few seconds of activity). And it stays there for a very long time because it doesn't find a win after 4.d8:Q Kg4. After putting the position on the board and a search at depth 23, it assesses 5.Bd1+ as +2 (actually 5.Qf6 is mate in 25 moves, as is found quickly by other engines).

Once again we see the trade-off between more brute force (which misses the solution in the initial position but finds 5.Qf6 #25) or a more complex evaluation function (which plays the initial position convincingly but for "a wrong reason" in some line).

Vlastimil Hort once showed it in a pre-simul program. He called it „Tal‘s favourite study“.

@a_pleasant_illusion thank you :)

@Shaquille-O-Neal No problem!

Just to give a concrete example of what I mentioned towards the end of my post, there's a fun modification of Stockfish called McBrain that lets you manipulate a lot of Stockfish's behavior.

You can enable a setting called "BruteForce" that turns off all reductions, and with that setting on it finds Nf6+ with the right winning line after about 100 seconds on my slow laptop.

It's several hundred points weaker than regular Stockfish, but it does a lot better on this position. Life is full of trade-offs :)