Pawn ending exercise

I recently played a pawn ending in bullet thinking it was a dead draw. It actually was a drawn position, but I didn't think about my opponents only pawn break. When he makes that pawn break my king must be close enough and mindlessly I wasted some tempos by moving my king back and fourth on the other side of the board. After the game I thought it would be a good exercise to see how close my king needed to be to be able to draw. I think I solved the exercise and thought I should share it in a forum. So the exercise is to find out which of these positions is won for white and which are drawn (White to move in all positions). The only difference between the positions is the placement of the black king.

note: The diagrams below are static positions, not puzzles

Nice idea but you should edit the positions so that they don't look like solvable puzzles.   They are all just static positions.  I thought they were stuck. (While that would be cool, I realize how much work that would be.)

After figuring that out, I finally got back to your question about how far away the black king has to be for  white to break through successfully.

Yes that was the question and they are just diagrams without moves. I made them that way, so if someone wants to use an analyse board they can just click on the bottom left of the diagram. Puzzles look slightly different.

I added a note in the first post.

Well, my guess from playing with it for a while is that with the king on the e file it's a draw and with the king on any of the other files, white wins. 

Is that what you found?

Nope, that is incorrect.

Nope. It's a draw with the king on the c-file.

Yeah, this is a good little exercise. It is a draw if black's king starts (when it's white's move) on any legal square of the c, d, e, f, g or h files (on his side of the pawn wall). a or b, white wins.

It is a little interesting that the defense black uses on the c or d-file is different than if he starts on the e, f, g or h-files.

When black starts on an e-h file he plays the opposition game around the g-5, f-7 pawn tension. Neither king can allow the other to cross lines.

When black starts on the c or d-files, he allows either the white capture on g-6 which let's black recapture with a wall, or if white pushes to h6, black's king covers the h-file promotion in time and white can never pawn push to h-7.

Correct! With the king on the a- or b-file white wins, but the others are drawn. It's quite easy once you realize you just need to make sure your king can get into the square of the h-pawn (the rule of the square) after g4 hxg4 Kxg4.  I hope you like ice cream, cause I just sent you an ice cream trophy. 

Mmm, ice cream.

There is a very easy way to deal with pure pawn endgames. No need to remember maxims about opposition or the square or whatnot, since they're often wrong in a particular situation. No, in the words of the great (physicist) Richard Feynman, "Shut up and calculate".

I guess the strategy you mention with the king on the d-file is the same that Remellion showed works on the c-file. It also works when the king is on the e-, f-, g- or h-file. If the black king start on the f-file black can draw, even by allowing gxh5. I just want to show why it doesn't work with the king on the d-file.

I think the square of the pawn and key squares really makes calculation in pawn endings much easier. In this case there's nothing wrong with raw calculation, so I'm not going to argue.

In the game both players had about 10 seconds (with one second increment) and even though my king was close enough I blundered by not playing hxg4. My opponent did not find the win and later blundered by moving his king to the wrong square (with 2 seconds left I think).