possible or impossible?

this one isn't really hard

you're right again!

I hope this is harder...

You're right s0030135!

I see that no one could solve cobra's puzzle from post #217.

It is indeed very difficult, so here's the solution:

Here's another beautiful puzzle by cobra91. Possible or impossible?

First one:

I can't find another way to get to this position so the Bishop on h6 had to be promoted by the b-pawn, the pawn had to take and white is missing 2 bishops so that's possible. But then I saw that white has 2 doubled pawns and black is missing two pieces (which only one could have been captured by a pawn) did I believe it's impossible, but I could have missed something.

second:

I can't find a last move by black...

Edit: Maybe it was 1.Ba2 Kxa2

The second one's last move was: 1.O-O

Not sure but I think so 

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Maybe you're right... The Bishop can be used for something else...

The first one is the samething so the Bishop could have gone to h6

Nice to see some action around here!

Of course, remember that before claiming a position legal, you must provide a proof game.

For the first diagram, black's last move indeed could not have been e6, since then black only has 1 piece for white to capture, and white needs at least 2 captures to get those two doubled pawns.

So that only leaves either Nxg4, or Ka2/Kxa2. Can you prove either is possible or impossible?

Regarding the option of castling, take a closer look

The second position is of course similar, but different still. Also note that, in this case black's last move must have been with his king. There is no other option.

Looking forward to more analysis! Fear not, if you give in I will post solutions/hints..

Immposible. A dark square pawn promotins isn't possible.

This is with black to move...

possible because of pawn reaching last rank and turning to bishop

all possible

Alright, I see that there isn't much new relevant or deeper analysis which is required. So, I will give half of the solutions.

The first position is possible. How? you must provide a proof game!

The second position is impossible. Why? you must provide some deeper analysis

If you still can't get through I will post the full solutions.

In the first one I didn't know how to put the pawns in the centre in that formation...

The key, of course, is, if it's White to move, what was Black's last move?

Everything on the 8th rank is trapped.  (And that actually IS the 8th rank, that's listed, so the board isn't flipped or anything.)

fxe6 is impossible since the h5 pawn has no way to get there unless it's the F pawn.  Similarily, h6-h5 is impossible.

So that leaves king moves.  Since the king is trapped, the last move by White must have been getting Black into check.  But the White rook is very limited by the king and rook next to it.  O-O is impossible, as someone stated, because it implies the White king never moved, and then Black has no way to get its king to that part of the board.

Which leaves Kxa2.  I frankly see no reason why the following is impossible:

OK, that was rather silly of me.  in THAT diagram, Black STILL has no valid previous move.

If the thing discovering the check is a knight instead of a bishop, it could be done.  But White has both Knights.  It cannot be a promoted Knight because there is nowhere for White to promote - White's missing pawns have to be the G and H pawns, which do not have any path to promotion.

EDIT:  Wait, I think I found it: