Finding the Invalid Move

@Remellion

cxd5+ for the first one. Since castling queenside gives check, that means that the King is on the d-file; after dxc5+ the pawn attacks a square on the d-file, so it is logical; the Black King is confirmed to be on d6, so Ned7 does not do anything nor step on that square; cxd5+ however only attacks the c6 and e6 squares, not attacking the d-file, so there shouldn't be check.

The answer is cxd5+ :D

I'll leave the other three questions for the other users to answer.

@GuessWhoIAm: If you say you can play dxc5+, then your pawn was from d4, and 0-0-0 wouldn't be check, right?

Also, I found one of the four is cooked (post edited to remove it), but the other 3 should be sound.

I think I understand what you mean now. :P

So the position would be like White King on e1, rook on a1, pawn on c4, knight on e5 and rook/Queen on a4/b4 with Black King on d4 and pawn on d5. :P

Correct! Yep, dxc5+ is the illegal one, and the position must be exactly as you gave (well, black anything on d5.) The black king can't be on the first rank (why not?) and must be on d4 not d3 (because of Ned7).

Also, it can't be that the other moves are the illegal ones. (Each case leads to a contradiction; in particular the 2 pawn capture checks are mutually exclusive.)

There may be other interesting ideas out there to be found. I'll think about it.

For the third one:

Only one move is invalid, so there must be a pawn on b5 (bxa6 and bxc6 both need one). Black K is on d7 or b7 (bxc6 and dxc6 can't both discover). If Nbc8+ is legal, the knight is on b6. For it to be legal, the K must be on b7 (if on d7 then a N on b6 would already give check). But then the N can't give a direct check, nor a discovered check diagonally. If there is a pawn on b5, however, Nbc8 can't discover a check from an R or Q. So Nbc8 is illegal. (Two scenarios shown. In both, black just played c7-c5)

Hm. Nicely done. So the third one was broken too. The intention was that bxa6 was the illegal one. I'll think about how to better fix that later.

I had other ideas for Puzzle 3. Instead thosition would be White pawns on b5 and d5, and rook/Queen on a5 and e5, along with Black King on c5. Nbc8+ would be the invalid move.

this thread was kind of weird

Do you mean "in-VAL-id" or "in-vah-lid" ?

Maybe Kh1, Bxg1, and Qh3 are invalid

f4 fxe4+ fxg4+ Bh3 Nxc6+ h4+

I will not tell you how many moves are invalid

Rhg2#, Bh1#, Qh4+, h6, Ke4, g8=R#, a5

at least 2 are wrong

@chessniu:

First one, everything is valid.

For your second post again everything is valid. I see no problems with having all moves at once.

Of course the position is simply legal with the underpromotions.

@chessniu -- For your answer, according to your position, Rhxe2 would be invalid too, since there is nothing to take there. 

But here's a tip, White is already in check, but when Black is to play, he can play normally.

Well, 5 out of 6 valid is fine too right? (Rhxe2 invalid.)

i changed it 

h3+ h4+ Bh4+ Nh4+ gxh4+ Bxf4+ Qh6+

If Qh6 is valid what else is

a4 b4 c4 d4 e4 f4 g4 h4 Qh4 Rh4 Bh4 Nh4 Kh4

How many must be invalid

@NateTimms -- Yes, but there are certain times where two moves cannot be available in any possible position, you can refer to the first puzzle.

@chessniu:

1. If Qh6+ is valid, at most everything except h3+ (king can't be on g4 as queen nor h-pawn can discover check) and gxh4+ (h4 either has or doesn't have a black piece) is valid; i.e. at least 2 invalid.

2. At least 1 is invalid - but if only one is invalid, it's impossible to tell which one! (Except Nh4. Nh4 must be valid.)

By shifting the rook along the 4th rank, a4 through g4 can be made invalid.

Removing the rook means Rh4 is invalid.

Placing the rook on h1 and removing the h-pawn means h4 is invalid.

Placing the rook on h5 and placing the king elsewhere means Kh4 is invalid.

Placing the rook on h5 and king on g5, with queen or bishop on e1 means that either Bh4 or Qh4 is invalid.

Very interesting idea here.

@NateTimms: The problems here involve setting up a position such that the listed moves are all legal (simultaneously, as options for either player) in a given position. Not a series of moves. Although that in itself might be interesting.