Finding the Invalid Move

So, I'm going to start a new game.

I will give you a few set of moves playable in a random position and a move unplayable in that position. Your mission is to find that invalid move, without knowing the position. This may sound impossible, but there is a certain way of solving it.

Puzzle 1

White to play

e4, dxe4, d3

I will reveal the answer in 2-3 days if no one can solve it. :)

@notmtwain -- This isn't really what I meant. Imagine the starting position and the possible moves you could play there, you could play either e4, d4 or even Na3. But you surely cannot play Nxf7 from that position, so that would be the invalid move.

The question I'm giving now has no position provided (it's not the starting position!), so you have to imagine it and use logical thinking to solve it, while the moves provided are the moves that can be played on that very same move, all but one of them.

dxe4

what about these:

g4

Nh1

f3

If I understand the premise correctly then e4 and dxe4 can't both be possible for white to make; for the first the square must be empty and for the second there must be a black piece on e4.

d3 and dxe4 can't both be possible since the pawn is already on d3 or isn't. 

So, dxe4 is invalid.

The invalid moves are E3 d3  e3-e4  if i am not correct then what is the answer?

@Martin_Stahl -- Correct! This was what I meant.

Puzzle 2

Black to play

Bh1, g1=Q, Rhc1, Ng1

There is 1 invalid move only.

I think I know the answer to this one but I'll let somone else do it.

Though, I wan't to clarify one of the conditions. All the pieces are in positions/squares where they could move to the suggested square but one of them is prevented for some reason. Correct?

...Bh1 is invalid.

Bh1!

The pawn would be on g2 if it were to go to g1. The knight could be on h3 and rook could be on back rank anywhere. The bishop can't get to h1 with the pawn in its way.

Aghhhh 3 minutes late

+1

Bh1 is correct!

Puzzle 3

White to play

Bbc6, R1xb8, Qb6xb8, axb4

There is 1 invalid move only.

P.S. You can post your own puzzles if you want to. :D

R1xb8 is invalid as a bishop is already on the b file!

R1xb8 is correct!

Puzzle 4

At the same move, if White were to play, the possible moves are:

Kh1, Kxh2, Nh3

If Black were to play, the possible moves are:

Rhxe2, Bxg1, Qe3

In the following 6 moves, 3 of them are invalid.

I think it can be made more interesting if checks are thrown into the mix. Here's a few that should work... (one invalid move per set)

White moves: 0-0-0+, dxc5+, cxd5+, Ned7.

White moves: Ka1+, Kc1+, Kb2+, Ka3+

White moves: bxa6+, bxc6+, dxc6+, dxe6+, Nbc8+