There's a cheapo with Ne5 followed by Nf7 and if d3-d2 followed by d1=Q??, the cute g3#. Though Black can easily just stop that via Bf2.
Then there's the forcing g3+ followed by f4+ and while Kg5?? leads to the saving Ne5+ fork to grab the passer, don't see an issue with Kf5
Don't see anything else so far.
What about Ne5, d2, f4, Bf2, Nf3+ ?
That's a nice idea with Nf7, Shivsky. Good analysis!
The key to saving white's game lies in the possiblity of constructing the following fortress.
In this position, it does not matter where the Black Queen is.
White is threatening g3 mate, while the black King is trapped, hence the black Queen can do nothing more in the position except prevent mate.
Even though black is +5 on material, Black would have no win.
Can White achieve this from the 2nd diagram ?
What about Ne5, d2, f4, Bf2, Nf3+ ?
That was close Cheryl!
Black has the nasty alternative Bg1+, instead of Bf2.
It takes 4 knight moves to get to the position. Wonder which 4?
Wait a second, is the first move Nc6 part of the solution?
Yes, but that bishop does have to bite the dust or white will have no fortress.
Well, my friend always said, "If you can't find something in 15 minutes, stop looking for it. It'll turn up somewhere." My 15 minutes are up! Good luck to the next solver.
I think I solved it.
Looking again, I'm not sure what happens after 3...Bg1+
It was close! unfortunately Bg1+ drives the white King from h2 and leads to mate in a few moves for black after d1=Q next move.
ok, this time around I think I have solved it.
That's it. No way can the Black Queen boss that knight!
Martin, that looks nearly forced but what happens if black decides to move queen instead to e6? Or b4? I like the latter because it would deny the e4 square and the queen could mozy on down to the first rank. Also, knight must move or get captured.
Great thought, though!
Very beautiful study. It appears far more intuitive to look for clever forks, mates or stalemate ideas ... but the fortress idea is something else! :)
Very instructive!
This must be it:
@chessarx, you must be missing something. No matter where black puts his queen the fortress will hold (like bouncing_check showed in more detail). Black can't deny the e4 square since it is protected by a white pawn.
Thanks, Martin! I didn't have my coffee yet, when I initially looked at it. 
Well, I just came back and found what I was looking for. My friend was right!
Missed the key move Nc3. Good job everyone, and nice fortress puzzle, Senator. Thanks everyone!
Here's an instructive endgame composition by that genius Troitsky.
White to play and save the day.
First off, in the starting position, we can see that black has the wrong colour h-pawn for the black-squared bishop.
A strategy for white to save the game then is .. "seek and destroy the black d-pawn".
Secondly, the white King cannot try stopping the d-pawn without losing the knight and the game.
It turns out that the knight cannot stop this d-pawn!!
Should white just resign then ?
Does white have a swindle ? Let's see!
After 1.Nc6 d3, can white save the game ?