king-and-pawn-endgame-triangulation-1 flawed

https://www.chess.com/drills/practice/king-and-pawn-endgame-triangulation-1, this endgame seems impossible to win, but the computer shows it as white is going to mate soon. And it makes a blunder at move 3 when you do this sequence:

White king e4 - Black king e8

White king f4 - Black king f8

White king e 5 - Black king f7 (BLUNDER; It can just go back to e8 and draw).

Is there a way that is FORCED so that the black king can do nothing to stop white kings advance. It seems like it can go just go back and forth on e8 and f8 for ever and drop down to f7 to block any advances, thanks. 

Ke8 and the mate is faster.

White goes Ke6 taking the opposition.

Let's say Kf8 afterwards. f7 and he has to go Kg7. White goes Ke7 and he will promote the pawn and win (of course he has to be careful because of stalemate tricks, but the win is straightforward).

If instead of Kf8 he goes Kd8, still f7 and it is even easier to win because there are no stalemate tricks.

I've been working this drill and I agree. I have only won the drill a few times on account of the engine's blunder. If the opponent's king is able to triangulate in tempo with my king, then there is no zugzwang which allows promotion

I'll show an image to help. The rule is, when white steps on a color, black MUST step on the same color, otherwise black will lose.

If white's last move put him on green black also moved to green, so he's safe for now, (but notice if it were black to move, he would have to move off the green square, so he would lose, that will be important for later)

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Now let's analyze how white wins.

1.Ke4 touches both red and green, so the black king is forced to be ready to move to red or green. Let's say he goes to g8
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But now white will move 2.Kf4, and black has no way to be ready to move to red and green. Whatever color black lands on, white will land on the corresponding color to win.

For example

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@llama47, nice to see a pattern; I came a "long" way from months ago after getting my rating up into better territory. I saw I could make a win with a lil triangle with the king but did not learn the color complex stuff.

Some books call it "mined squares" or "corresponding squares" I use colors to make it easier.

And it's usually not brought up in simple situations like this, but it nicely illustrates the logic of why the win works.

Yea I have not read any chess books so far... the diagrams weird me out, I am used to the moving screens like in chess.com. Seems like a online book with animated boards is more for me.

Corresponding squares are a difficult topic.  Sometimes you can use the simpler concept of opposition, including distant & virtual opposition.  The technique is to maintain the opposition, and prevent your opponent from seizing the opposition, until you can make the winning move.

Using this method, another solution to the above is :

    1. Kf4  { distant opposition }  Ke8

    2. Ke4  { virtual opposition }  Kf8

    3. Ke5  { Black cannot seize the opposition by moving to e7 or g7 } Kf7

    4. Kf5  { White seizes the opposition }  Kf8

    5. Kg6  Kg8  6. Kxh6  { now the win is easy }