Puzzle of the week #181

Chess Diagram: 

[Event "Puzzle #181"][Date "2012.01.24"][Result "0-1"][SetUp "1"][FEN "8/8/2p5/1p1p4/p2Pk3/P1P5/4K3/8 w - - 0 49"]49.Kd2 Kf4 50.Kd3 Kf3 51.Kd2 Kf2 52.Kd3 Ke1 53.Kc2 Ke2 54.Kc1 Kd3 55.Kb2 Kd2 {White resigned}

Learning from your own games is one of the best methods of improving at chess. The reason is very simple: you know very well (or could easily remember) what you had in mind when you played those moves. All good players are analysing their games at home and keep the information private; others are more than happy to share it publicly in order to help others. Today's position comes from an endgame shared by an American player. He was playing Black in the given position and his last move had been 48... Ke4. White responded as shown.
Your tasks:
a) How could have White saved the game after 49.Kd2!? Kf4?
b) How should have Black played after 49.Kd2!? ... to win it anyway?

Total available points for this puzzle is 20. The answers will be published next week together with puzzle #182.

Puzzle #180 solution:
Fahrni study, 600 endgames by Portisch and Balazs. Most of you have understood the idea of the L-shape pawn formation; in the end the difference was between those who looked more careful at what the best defensive line might have been for Black, while others have been too quick to make it look too simple. Philip's answer was pretty good; see solution.
Congratulations to Leroy for finally solving the puzzle correctly on the first try!

[Event "Puzzle #180"][Date "2012.01.14"][Result "1-0"][SetUp "1"][FEN "8/8/p7/8/K4k2/5P1P/8/8 w - - 0 1"]1.h4 Kf5 2.Ka5 Kg6 3.f4 Kf5 (3...Kh5 4.f5 Kh6 5.Kxa6 Kh5 6.Kb6 {White wins}) 4.h5 Kf6 5.Kxa6 Kf5 6.Kb6 {White wins}

Correct solutions:
Leroy, Jeffrey, Daniel - 10 points
James, Harmony, Ziyao, Philip - 9 points
Leo - 8 points
Derrick - 6 points
Leo, Coco - 2 points
Alex - 1 points

Coco - 6 points for puzzle #179

Philip - 49 points
Jeffrey - 46 points
James - 41 points
Alex - 32 points
Ziyao, Harmony, Daniel - 29 points
Leo, Coco - 18 points
Derrick - 14 points
Leroy - 12 points


Pawn breakthrough