Astonishing win!

This is an amazing & funny game. This renewed my faith that miracles do happen in chess! :)

King Pawn Endings -1

White to play & win
Please try to find the solution yourself, and make a note of the time you take to solve it. Seems interesting!

Composition

Compose a position where White has only a bare king and Black has king and three pawns (no double or triple pawns). It is Black to play and the result is a draw.

Solution to the previous diagram

Solution: 1.Rd8+ Nc8 2.Rxc8+ Ka7 3.Rxc7+! [3.Kf7 a2 4.Rxc7+ Kb6 5.Rb7+ (5.Bxa2 Ra1–+) 5...Kxa6 6.Rb4 a1Q 7.Ra4+ Qxa4 8.Bxa4=] 3...Kxa6 [3...Kb6 4.a7 Rg1+ 5.Kf7 c1Q 6.a8Q Kxc7 7.Qa7+ Kc8 8.Qd7+ Kb8 9.Qe8+ Kb7 10.Qxe7+ Ka6 11.Qb4+–; 3...Kb8 4.Rxe7 Rg1+ 5.Kf7 c1Q 6.Rb7+ Ka8 7.e7+–] 4.Rxc6+ Kb5. [4...Kb7 5.Bd5; 4...Ka5 5.Kf7] This is where the engines get tricked. 5.Rxc2! Rxc2 6.Bxc2 a2 7.Bd1!! a1Q 8.Bh5 Qh1 [8...Qg1+ 9.Bg6+–] 9.Be8+ Kc5 10.h5+– and White wins.

Difficult for engine, can you solve it?

White to play and win.
Please give the complete analysis with variations,because the key move lies in between!
Happy Solving :)

Solution to the interesting position

The solution is 1.Ka1!! Not 1.Kc2? Bh7! 2.Rxh8 Bxg6+ 3.Kb3 Bxh5 and Black wins;
or 1.g4? Bxc4 2.Rxh8 Bd3+ 3.Ka1 Bd2 mates. 1...Ka4 2.g4. This is the only move and the right solution. 2...Ka5 3.g5 Ka4 4.Kb1 Ka5 5.Kc2 Ka4 6.Kc3 Ka5 7.Kd4! and the rest as easy 7...Ka6 8.Ke5 Ka5 9.Kf4 Ka4 10.Kg3 Ka5 11.Kf2 Ka4 12.Ke1 Ka5 13.Kd1 Ka4 14.Kc2 Ka5 15.Kc3 Ka4 16.Ra8 a5 17.Rb8 and White wins.

Answer to the previous position

There is a unique point to this study, one that has made it famous in problem circles – and one that you are most unlikely to encounter anywhere else. White draws by expoiting the 50-move-rule! This states that that a player can claim a draw if no capture has been made and no pawn has been moved in the last fifty consecutive moves (fifty moves by each side).

1.f6! Qb3 2.f7! White must be careful: If he plays 2.Kh6? the drawing idea of the main line fails by one move. 2...Qd1 3.f7 Qf3 4.Kg7 Qg4+ 5.Kh8 Qf5 6.Kg7 Qg5+ 7.Kh7 Qf6 8.Kg8 Qg6+ 9.Kf8 Ka4 10.Ke7 Qg7 11.Ke8 Qe5+ 12.Kd7 Qf6 13.Ke8 Qe6+ 14.Kf8 Kb3 15.Kg7 Qe7 16.Kg8 Qg5+ 17.Kh8 Qf6+ 18.Kg8 Qg6+ 19.Kf8 Kb2 20.Ke7 Qg7 21.Ke8 Qe5+ 22.Kd8 Qf6+ 23.Ke8 Qe6+ 24.Kf8 Kc1 25.Kg7 Qe7 26.Kg8 Qg5+ 27.Kh8 Qf6+ 28.Kg8 Qg6+ 29.Kf8 Kd1 30.Ke7 Qg7 31.Ke8 Qe5+ 32.Kd7 Qf6 33.Ke8 Qe6+ 34.Kf8 Ke2 35.Kg7 Qe7 36.Kg8 Qg5+ 37.Kh8 Qf6+ 38.Kg8 Qg6+ 39.Kf8 Kf3 40.Ke7 Qg7 41.Ke8 Qe5+ 42.Kd7 Qf6 43.Ke8 Qe6+ 44.Kf8 Kf4 45.Kg7 Qe7 46.Kg8 Qg5+ 47.Kh7 Qf6 48.Kg8 Qg6+ 49.Kf8 Ke5 50.Ke7 Qg7 51.Ke8 Ke6 52.Kd8 Qxf7 and Black has made a capture just in time to avoid a 50-move draw.

2...Qd1+ 3.Kh6! Qf3 4.Kg7 Qg4+ 5.Kh8 Qf5 6.Kg7 Qg5+ 7.Kh7 Qf6 8.Kg8 Qg6+ 9.Kf8 [9.Kh8? Qxf7 10.Nc2 dxc2] 9...Ka4! 10.Ke7! Qg7 11.Ke8 Qe5+ 12.Kd7 Qf6 13.Ke8 Qe6+ 14.Kf8 Kb3 15.Kg7 Qe7 16.Kg8 Qg5+ 17.Kh8 Qf6+ 18.Kg8 Qg6+ 19.Kf8 Kb2 20.Ke7 Qg7 21.Ke8 Qe5+ 22.Kd8 Qf6+ 23.Ke8 Qe6+ 24.Kf8 Kc1 25.Kg7 Qe7 26.Kg8 Qg5+ 27.Kh8 Qh6+ 28.Kg8 Qg6+ 29.Kf8 Kd1 30.Ke7 Qg7 31.Ke8 Qe5+ 32.Kd7 Qf6 33.Ke8 Qe6+ 34.Kf8 Ke2 35.Kg7 Qe7 36.Kg8 Qg5+ 37.Kh8 Qf6+ 38.Kg8 Qg6+ 39.Kf8 Kf3 40.Ke7 Qg7 41.Ke8 Qe5+ 42.Kd7 Qf6 43.Ke8 Qe6+ 44.Kf8 Kf4 45.Kg7 Qe7 [45...Qd7 46.Kf6!] 46.Kg8 Qg5+ 47.Kh7 Qf6 48.Kg8 Qg6+ 49.Kf8 Ke5 50.Ke7! Qg7 [50...Qe6+ 51.Kf8 Kf6 52.Kg8=; or 50...Qd6+ 51.Ke8 Ke6 52.Nc2!=] 51.Ke8 Ke6 52.Kd8! With this move, White can claim the draw by the fifty-move rule since move two no piece has been captured and no pawn moved. Incidentally 52.Nc2 is also a draw by the 50 move rule.

Now who of you got had thought so much :)