Is this position legal?

1 and 2 trivially legal. 3 and 4 illegal because of the a4- and a8-queens both checking the black king. 5 and 6 trivially legal. 7 illegal because of the bishops.
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I finally managed to uncook an older puzzle. This is a triple bill: Is the position legal 1) as is; 2) with the g2-pawn on g3; 3) with the g2-pawn on h3?
1. illegal. The bishop on a6 had to be promoted on b1 and capture a rook. The pawn on c6 wouldve also had to cature a rook. The h1 rook couldn't get to c6 with these pawns.
2. legal. g3 bh3 kf1 kg2 and the rook can get to c6
3. illegal. i think. The only thing that white could've captured on h3 is the c8 bishop. This bishop could not have gotten there. If the a1 rook got to c6 then there would be a pawn on c4 and the bishop couldn't get back to a6.

@Justified08: All 5 trivially legal. No issues with doubled pawns, trapped pieces, lack of last moves, underpromotions or anything with those 5.
@Eeyores: Almost correct, but some part is wrong. But there is one oversight you made, which accounts for getting it half-correct overall. There are actually 3 ways to resolve the bB-wR queenside situation which must be accounted for, and you looked at just 1.

In #199 as far as I can see they're all easily legal, although some may need a few repeated moves at the end to get to the positions

I think it is, as you can take the pawns with queen, bishop or knight and then move them back to starting positions, hence it is legal.

I wonder why there isn't a chess book with such problems...
I would bet there are some. See for instance http://www.janko.at/Retros/

1st illegal because of the pawn structure on the kingside. 5 pawns in the region (f2-h2-h5 triangle) where only 4 could've got there. 2nd legal regardless of board orientation (except sideways :-P), just spend a while untangling the mess but it's easy.
For books, Raymond Smullyan's The Chess Mysteries of Sherlock Holmes is a good start. Very many easy puzzles and a few tough nuts. It guides one through the basic features of retro compositions in a comfortable fashion.
And the very first simple retro I encountered: Can white castle kingside (after clearing the knight and bishop out)?

That's correct, with something important left unstated. Now suppose we change the position slightly? Can white castle kingside (after moving the bishop)?

That's correct, with something important left unstated. Now suppose we change the position slightly? Can white castle kingside (after moving the bishop)?
Nice one, just got it.
(hint : the "rook" might need the g6 square to get out)

@remellion no it's not.Rh1 was a cute pawn on h2 because the original Rh1 was sacrificed to g6
how was the rook the h2 pawn? Diagram please??????