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A simple win is a4 bxa4 Kc2
1. a4 bxa4
2. Kc2 Ka3
3. h5 Kb4
4. h6 a3
5. h7 a2
6 h8(Q) 1-0
h4 and White will Queen first.
draw?
A win.
a4, ba (b4,Kxb4 is hopeless)
Kc2, a3 (Ka3 and Kb4 is way too slow)
h5, Ka1
h6, a2
h7, c3
Kb3,
Now if Kb1,
h8(Q), a1(Q)
Qh1 mate
or if c2,
h8(Q) mate
its a draw
Black gains a tempo during the pawn race
1 h5 Kxa3
2 h6 b4+
3 Kxc4 b3
4 h7 b2
5 h8/Q b1/Q
The other alternative for black (stalemate attempt) also fails (by a hair):
1. a4 bxa4
2. Kc2 Ka1
3. h5 a3
4. h6 a2
5. h7 c3
6. Kc1 c2
7. h8(Q)#
1.h4 is impossible. 1.h5?? leads to a draw after 1… Kxa3 2.h6 b5+
1.a4! is the winning move. Variants are easy to see.
a4 bxa
Kc2 comes immediately to mind
By my count, h5 is not fast enough.
a4 bxa Kc2 a3 h5 Ka1 h6 a2 h7 c3 Kc1 c2 h8(Q)#
a4 wins
1. a4 bxa4 (forced)
2. Kc2 Ka3
3. h5 Kb4
4. h6 a3
5. h7 etc.
The white pawn promotes, but the black pawns are hold
It is more of a 2 move that does the trick.