Is this position legal?

Huh.  For White pieces, I considered the knight, a rook wouldn't help, a bishop is already there, a pawn is impossible, the king would violate castling, and the queen is the entire problem.  For Black pieces, you run into the problem of not enough available material no matter which piece it is.  I just can't see it.

Look over the two cases in your previous post, the promoted white bishop and the white knight. There was something you didn't explore.

I can't get any far than this o.O.

White cannot castle because black needs to capture white's bishop on c1 by using the knight via b3. Black has the dark-squared bishop so he/she cannot use that to capture on c1 as it will be captured by white's promoted dark-squared bishop.

If white promotes dark squared bishop using the g-pawn, there will need to be a capture on a dark square because of the g3 pawn. This will need to be a capture of black's rook. The e-pawn will then need to be doubled and no black piece can do that. At least one other capture will be needed to get the g-pawn to promote a dark-squared bishop. Therefore, promoting the g-pawn will not work.

If white promotes the h-pawn by capturing a light-squared bishop on g6 and then a rook on h8, there will be no black piece that can double the pawns on the e-file.

Is this legal?

Looks legal.. Too lazy to prepare a proof game...

Still wrong. In mine, still everyone's missing something. White can castle - how? Black does not need to capture the bishop on c1 with the knight.

And @shdu02, legal without any problems.

I've tried with the DSB too. Doesn't work.

Would it help if I said that nothing was captured on c1?

You guys I have solved it, hint the King captures the rook on a1 and later white places a Knight on b2, the h pawn captures on g6 then goes g7 and then gxh8=B then moves to a1 after the king has gone to b1 and the original bishop returns to c1 from a3 journey. The whitesquared bishop goes to a4 when the b5 pawn captures and then a3.

Sample game
1.b3 e6 2.Bb2 Ke7 3.Bf6+ Kd6 4.Nc3 Kc5 5.g3 Kb4 6Bg2 Ka3 7.Bc6 Kb2 8.Bg5 a5 9.Nb1 Kxa1 10.Ba4 b5 11. Be7 bxa4 12.Ba3 Bb7 13.Bc1 Be4 14.h4 g5 15.h5 Bg6 16.hxg6 Ra6 17.Nc3 Ra8 18.Nd5 Kb1 19.g7 Ra6 20.gxh8=B a3 21.Ba1 e5 22.Nf3 Rg6 23.Nd4 Nf6 24.Nf3 Rg8 25.Nd4 Rh8 26.Nb5 Na6 27.Nd6 Nb8 28.Nc4 Na6 29.Nb2 Nb8 30.Nf4 axb2 31.Nd5 bxa1=R 32.Nb4 c6 33.Nd5 Na6 34.Nf4 Nb8 35.Nh5 Ng4 36.Nf4 Ne3 37.fxe3 Rg8 38.Ng6 c5 39.Nh8 Rxh8
 I don't know how to post game in forum. 

Just worked it out now, but thanks anyway.

I can't post a game. Not that I don't know how to. Just the mobile...

Well done RubiksRevenge! It's precisely that idea that works - an extra capture by the black pawn, and white must promote to a bishop anyway; also disguised by the plausible trap of considering only bNb3xBc1. Very well done, that was not an easy one if you haven't seen retros before.

Judging from the response, perhaps an even easier one. It even tells you the answer. :P
Is it OK for white to castle?

Thanks for posting these, I am quite new this this puzzle aspect of chess and only stumbled upon this thread recently. I imagine that it requires a greater skill to create problems in the first place. This last puzzle seems quite hard to solve for White being able to castle but I know that these puzzles tend to have a "Yes" answer so will keep looking. From first impresions it is obvious that every black pawn that is missing has been promoted to 5 Knights and a Rook, but I have problems with running out of white material for the black pawns to capture to make the journeys to the g file and the a/b/c files and so can't end up with the 2 white Knights. To get the setup observed with the Black K,R,N white R and a3 b3 c2 pawns seems to me to require the "a" pawn to make 4 captures which then later leaves the black d,e,f to capture more material. Any way I like solving a little bit by little bit so will keep trying when I have free time.