Push the h-pawn. After black is forced to guard it with the N or white grabs the pawn and queens the a-pawn. While black is guarding, white can queen the a-pawn, etc.
Can’t capture on g5 with the queen otherwise it’s stalemate. Can’t get any other checks in time. Can’t capture on g5 with the QUEEN. a8=R and the rest is simple
Black’s threat is only hard to deal with because of the secondary threat of stalemate:
1. a8Q Nh7 2. Qg8 Ng5!
And white can’t take at g5 without giving black draw by stalemate. Of course, if white underpromotes on move 1 to a rook, he doesn’t stalemate black at move 3 when he captures at g5.
Under promoting to R is correct but not without pitfalls. 1a8=R Nh7 2Rg8 Nf6 Now 2h6 as pointed out by many is correct,but if white tries to save his R by 2 Rg7 there is a surprise. 2 Rg7 Nxd5 3h6 Nc3 4bxc3 Else 4… Ne2# 4… b2 and white is in soup.
Push the h-pawn. After black is forced to guard it with the N or white grabs the pawn and queens the a-pawn. While black is guarding, white can queen the a-pawn, etc.
Can’t capture on g5 with the queen otherwise it’s stalemate. Can’t get any other checks in time. Can’t capture on g5 with the QUEEN. a8=R and the rest is simple
1. a8Q Nh7 2. Qg8 Ng5 3. Q:g5 is a stalemate, so white had better find a better idea. 3. Qf8 isn’t much better; 3… Nf6+ 4. Q:f3 ef is mate next.
Underpromotion seems to work, though – 1. a8R Nh7 2. Rg8 and now:
A) 2…Ng5 3. R:g5 Kh4 4. h6 and wins
B) 2…Nf6 3. h6! and there is no way to stop the pawn, whether or not black takes the R.
Black’s threat is only hard to deal with because of the secondary threat of stalemate:
1. a8Q Nh7
2. Qg8 Ng5!
And white can’t take at g5 without giving black draw by stalemate. Of course, if white underpromotes on move 1 to a rook, he doesn’t stalemate black at move 3 when he captures at g5.
1. a8/R Nh7
2. Rg8 Ng5
3. Rxg5 and there is not the stalemate that would have occurred if white had gotten a Queen.
The only problem White facing is a stalemate if a Queen capture the Knight on g5…so 1.a8=R! Nh7 2.Rg8 Ng5 Rxg5! wins
Going for the rook at the first move seems to be enough and prevents the stalemate of Black
1.a8=R Nh7 (the Knight is not safe otherwise)
2.Rg8 Nf6
(2…Ng5 3.Rxg5 Kh4 4.Rxg3 Kxg3 5.h6)
(2…Kh4 3.Kxg2 Kxh5 4.Kxg3)
3.h6 Kh4 4.Kxg2 Nxg8 5.h7 Nf6 6.h8=Q+
A draw, because white shall have to take that knight on g5:
1. a8=Q Nh7
2. Qg8 Ng5
3. Qxg5 stalemate
To take that knight on f3 instead was no option, since exf3 and f2#.
I found no time to sack something to prevent the stalemate, and no time to give black a check.
I’m afraid this try looses:
1. a1=Q Nh7
2. Qf8? (only move to threat Qf5+) Nxf8
3. h6 Nh7!
Pawn blocked, loosing desicive tempo. To start with 1. h6? didn’t help either.
Under promoting to R is correct but not without pitfalls.
1a8=R Nh7
2Rg8 Nf6
Now 2h6 as pointed out by many is correct,but if white tries to save his R by 2 Rg7 there is a surprise.
2 Rg7 Nxd5
3h6 Nc3
4bxc3 Else 4… Ne2#
4… b2 and white is in soup.