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1.e7 wins
1… Kf7
2.e8=Q+ KxQ
3.Ke6 and Rh8 mate follows!
1.e7 Kf7
2.e8=Q+ Kxe8
3.Ke6
… is off to a flying start, but it’s not quite a win for White. Black intercepts the back-rank mate with:
3…Rf1
1.Rh8+ Kxh8
2.e7 Rd1+
3 Ke6 c8(Q)
4 e8(Q)+ Kh7
5 Qh5 + with perpetual
I wish the blog managers would post the answer after a few days.
1.Rh8+ Kxh8
2.e7 Rd1+
3 Ke6 c8(Q)
4 e8(Q)+ Kh7
5 Qh5 + with perpetual
Not quite perpetual enough, alas:
1.Rh8+? Kxh8
2.e7 Rd1+
3.Ke6
(3.Ke4 doesn’t bail White out either)
3…c1=Q
4.e8=Q+ Kh7
5.Qh5+ Qh6+
… forces the trade of queens and wins.
It’s quite an amusing end position after:
1.e7 Kf7
2.e8=Q+ Kxe8
3.Ke6 Rf1
4.Ra4 Rd1
5 Rh4 etc
With the black pawns on the second rank corralling the king so the only way to stop the mates on a8 and h8 is by shuffling the rook between d1 and f1.
A nitpicky footnote:
4.Rb4?
… doesn’t work because of:
4…Rb1!
Clever!
erick posted the correct solution, BTW.