I've been studying endgames through the book, Pandolfini's Endgame Course, as well as the computer program, Chessimo. Anyhow, the following position from the program has me stumped. I'll post the entire puzzle, but I'd appreciate an explanation of white's first three moves.

The first thing to know is that he can't take the back pawn of connected pawns where one supports the other without the front one promoting.  So Kc5 wont be drawing for him.

There are multiple ways to wins this, but Ke6 prepares to take opposition. If you play for example Kd5 he plays Kb7 taking diagonal opposition and you make no progress. So Ke6 in effect makes him choose a square, from which you can take direct or distant opposition.

After Ka7 Ke7 takes distant opposition (an odd number of squares on the same file). Now when he picks a direction you outflank him the other way. I'm not sure this problem is the most instructive example ever though.

On 4 white can take opposition with Kd7 and go in the opposite direction to the black king. Or if black replies with Ka7 take opposition again and black is forced to a8 after which you get b6, Kb8 and the black pawn is gone.

Yeah it's not the greatest endgame puzzle I've seen.

Thank you for the enlightening responses. Just to clear things up, the puzzle was from Chessimo, and has little to do with Pandolfini (whose book, I might add, has made long car/bus rides quite entertaining).

Anyhow, I learned quite a bit from reading the comments, so thanks again!

Actually 1. Kd5 Kb7? 2. Kc5+- looses as in the puzzle (see position after white's 4th move). Black better defends with 1... Kc7! when 2. Kc5 Kb7 3. b6?? doesn't work due to stalemate trick 3... Ka6!=.

Therefore 1. Kd5 doesn't lead to anywere (the same can be said of 1. Kd7 Kb7!) and 1. Ke6! seems to be the only move to make progress at the begining. This move can be thought as gaining the opposition, if you will, because the black king can't use c6. Later on white has alternative wins like 4. Kd7 with ideas 4... Kb6 5. Kc8+- or 4... Kb8 5. Kc6+- etc.

Ok, 1. Kd5 Kc7 2. Ke6! seems to actually win about as easily as 1. Ke6.

As Shadow said, Kd5, Ke6 and Ke7 all win in 19.

My point about black taking diagonal opposition was irrelevant though, since white doesn't actually need to break through. 1. Kd5 Kb7 2. Kc5 and if he takes opposition with Kc7 you can just push the pawn.

As I said, I don't think it's the most instructive example.

I think this position is very instructive in how the ideas of opposition, diagonal opp. etc can be misleading.

Here the idea is that if it was blacks turn, white wins. So how to swap turns?

Kd5, i.ex. could be met by Kc7 (not Kb7, misleading concept of diagonal opposition that would lead to stalemate, as pointed out). But black can't pass move and stay in Kc7, so Ke6! puts black in zugzwang, which is the right concept. Now, white is ready to step in the d file taking the lateral opposition and we reach the initial position but black to move.

Yes, one can certainly benefit from analysing this but it must be said that as a puzzle it's problematic due to multitude of valid solutions.