The Reti Composition(s)

You may be familiar with the following endgame composition by Richard Reti, but you may not have been aware of the four other compositions that follow it. All are White to move and draw and, if you have not seen them before, you are in for a treat. How is it possible that White can save any of these positions?

Reti,R
1921

1.Kg7! h4 [1...Kb6 2.Kf6 h4 3.Ke5 h3 4.Kd6 h2 5.c7 Kb7 6.Kd7=] 2.Kf6! Kb6 [2...h3 3.Ke7 h2 4.c7 Kb7 5.Kd7=] 3.Ke5! Kxc6 [3...h3 4.Kd6 h2 5.c7 Kb7 6.Kd7=] 4.Kf4 h3 5.Kg3 h2 6.Kxh2= *

Reti,R
1921

Kb4 first also works1.c6 h5 [1...Kb6 2.Kb4 h5 3.Kc4 Kxc6 4.Kd4 h4 5.Ke4 h3 6.Kf3 h2 7.Kg2 h1Q+ 8.Kxh1=] 2.Kb4 Kb6 [2...h4 3.Kc5 h3 4.Kd6 h2 5.c7 Kb7 6.Kd7=] 3.Kc4 h4 4.Kd5 Kc7 5.Ke4 Kxc6 [5...h3 6.Kf3 h2 7.Kg2 h1Q+ 8.Kxh1 Kxc6=] *

Here's a third composition of Reti's. This is not quite as pretty as his classic K+P compositions just above, but it may still surprise a few of you. The key is gaining time to catch the passed pawn.

Reti Composition

Diagram

It looks hopeless for white... like so many of Reti's compositions, how can the white king catch the advanced black g-pawn?1.e7 Bb5 Required to prevent e8(Q) 2.Kc5 And here's the key. White attacks the Bb5, gaining the time needed to catch the g-pawn 2...Be8 [2...g3 3.Kxb5 g2 4.e8Q+] 3.Kd4 g3 4.Ke3 Bc6 5.e8Q+ Bxe8 6.Kf3= White has succeeded in catching black's passed pawn. *

Feiter,K
1939

1.Kb7 a5 2.Kc7 Kc5 [2...a4 3.f5 a3 4.f6 a2 5.f7 a1Q 6.f8Q=] 3.Kd7 Kd5 4.Ke7 Ke4 [4...a4 5.f5 a3 6.f6 a2 7.f7 a1Q 8.f8Q=] 5.Ke6! a4 [5...Kxf4 6.Kd5 a4 7.Kc4 a3 8.Kb3 a2 9.Kxa2] 6.f5 a3 7.f6 a2 8.f7 a1Q 9.f8Q= *

The final problem may have the most surprising solution of all. To capture the black pawn, the white king must begin its journey in the wrong direction!

Prokesch
1947

1.Kc8! Kc6 2.Kb8! Kb5 [2...h5 3.a6+-] 3.Kb7 Kxa5 [3...h5 4.a6+- h4 5.a7 h3 6.a8Q h2 7.Qh8] 4.Kc6 h5 5.Kd5 h4 6.Ke4 h3 7.Kf3 h2 8.Kg2 h1Q+ 9.Kxh1= *