Puzzle of the week #168

Level: 
4-Rook
Chess Diagram: 

--------
--pp--pp
--------
--PP-P--
-p-----k
--------
PP----p-
------K-

Regardless how complicated a position looks like, you can break it down into simple elements to understand it, look for a plan based on experience and then execute it. If you try to jump head into it, most of the time you will be overwhelmed by how big and tough the task is and will not be able to solve it. This week's puzzle is from the same category: we have lots of pawns everywhere on the board and not surprisingly each one has a purpose. It is up to you to do your best and solve the following:
a) White to move and win. Explain your solution!

Total available points for this puzzle is 30. The answers will be published next week together with puzzle #169.

Puzzle #167 solution:
Polgar chess endgames - Puzzle 2071. A few good answers and a couple of so-so ones made the total of messages I received. I hoped you guys could remember the first thing you need to verify in Kings and pawns endgames with passed pawns: the square rule. My hope was more of you would see this in the position immediately and could try to solve the puzzle. In the end Alex had a very nice response:
"a) When I first saw it, the board looked very strange. It was then that I noticed the White a-pawn is closer to promoting than Black's h-pawn. The second thing I noticed was that Black was in White's a-pawn square and White was not in Black's h-pawn sqare. Black could simply win with: 1.a6 Kc6 2.Ke7 h5 White will not be able to catch the Black pawn.
b) My next thought was of stalemating. But whatever I tried to do, Black would just take White's a-pawn. Still I thought maybe I can get a head start!
1.Kc8 Kc6 (1... h5 2.a6 ... Black cannot stop White's pawn supported by the King) 2.Kb8 Kb5 (same reason as above) 3.Kb7 Kxa5 (if 3... h5, then 4.a6... and White promotes his pawn first) 4.Kc6 h5 5.Kd5 ... The Black King is out of the way and White has entered in Black's h-pawn square."

Correct solutions:
James, Daniel, Alex, Ziyao, Harmony - 20 points
Leroy - 18 points
Philip, Derrick, Kevin - 10 points

STANDINGS:

Ziyao - 399 points
Harmony - 395 points
James - 351 points
Philip - 342 points
Alex - 290 points
Leo - 255 points
Derrick - 222 points
Leroy, Daniel - 207 points
Jeffrey - 168 points
Frank - 136 points
Kevin - 102 points
Eric - 29 points
Danny - 19 points
Karl - 13 points

Comment: 

Rule of the square (3)