Mysterious Moves of Chesstempo

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ClavierCavalier

I just completed this puzzle on chesstempo.com.  The puzzle itself is pretty straight forward.  I looked at the continuation (Starting with 3... e4) and have some questions about the moves.  Why 4. Bg1 instead of 4. Be3?  What's the point of 13. Kd5 instead of playing 13. f7?

 

 

1d3_1-0

It could have been taken from a game so the solution is the moves played in the game 

PerpetuallyPinned

1- White can just keep the bishop on the diagonal. Your 4.Be3 seems to be the quickest way. Bg1 may not be the 2nd quickest either.

2- f7 is obviously the no nonsense approach