Possible or Impossible?

Is this position possible?

no

I think yes, but it's a close one, because you need material to move to other line so pawns come from a,b,c,d,e,f.

Now, whoose turn is here, because if that's white to move that is impossible, because where from that king come?

If it's black's turn I think it's possible, because last white's move was Bxa7, black king could have gone from b8.

Yes, although some of the black pawns on the kingside have to promote so they can get to the queenside and be captured by the white pawns.

It´s impossible for the following reason:

White´s pawns need 15 diagonal takes to reach the position. That means that all of Black´s pieces and pawns would have to be taken by White´s a-f pawns.

For this to be possible, Black´s f-g pawns must be made to take diagonally towards the centre until they can be taken at least by the e and f pawns. For this, White must sacrifice his pieces; he cannot use the a-f pawns, and the g and h pawns would force taking in the wrong direction (remember that every single black piece must be taken by a pawn moving diagonally leftwards, otherwise White has less than the necessary 15 pawn moves needed to achieve the position).

Since he must use his 7 major and minor pieces to lure Black´s f-h pawns across, it becomes obvious that 7 is too few:

The g and h pawns both need 3 diagonal takes before they come within range; the f pawn 2. That would require 8 piece sacrifices by White, which is not possible.

Edit: aha, brilliant, Evgeniy! I take it back!

Actually horsesforcourses gave a better solution which results in a position shown in the first post and mine has lots of white pieces on the board

sac all white's material!

For everyone who has been wondering, it can be both White or Black to move.

well that's still quite easy. How about this?

amazing... lol Pretty crazy what position you can achieve if both sides are working toward it.

FYI it can be done in 40 moves but so far nobody except me has found it.

Can you show it then TheMushroomDealer?

sure 

It might be possible to find even a quicker way but I'm a bit sceptical about it.

The following position can be reached in 34 moves. Also there's two solutions to a mate in 8: