Helpmate in 3:

Another simple Helpmate I composed. Black moves first, White mates on his 3rd move:

Solution in white - After 0...O-O  1. Bd3 Kh8  2. Rf1, the incredible zugzwang situation had me completely baffled for quite some time (and even caused me to experiment a bit with some other possible mating nets). Black needs to lose a tempo, and (surprisingly) it wasn't easy for me to see how that could be done. As it turns out, the answer is rather strange:

0...O-O  1. Bd3 Rf1+! (the only possible tempo loss for Black!) 2. Rxf1 Kh8  3. Rf8#

Good job! 

That solution (in cobra's comment) doesn't work if black takes the white rook on f1...

"Helpmate" is indeed accurate, it's very difficult (almost impossible) for black to get mated. Any of the three pieces moving will prevent it. (2...Kg8 protects f8, 2...N to anywhere opens up the g7 square for the king's escape, 2...R to anywhere still protects that square [not even mentioning Rxf1 completely eliminating the white Rf8# threat]) Also it's worth noting that on black's 2nd move 1...Kf7 just destroys any chances of mating in the corner.

Even a foolish player would literally have to help by moving perfectly to get himself into your checkmate. The black rook would have to move out of the way of the f8 square (using two moves) while white would stall on move three to keep the bishop and rook in the right places.

Any move by a piece other than the black rook results in no mate. Also, if the rook moves anywhere on the f-file even allowing white to take it, the next move has to be from the knight(opening up g7) or the Kg8 (his only open square consequently protecting against Rf8#).

I mean sure if black blunders the rook the king will escape and white will likely win, but I'm concluding here pointing out that 3 move Helpmate is impossible.

I wish people wouldn't try making open ended puzzles...especially when completely forgetting move order. I suggest OP edits title to "Helpmate in 3 moves if you allow white to move twice in a row"

This is a very nice helpmate and cobra91's solution is correct. For those not familiar with helpmates - an unconventional but very popular chess problem type - check out  https://en.wikipedia.org/wiki/Helpmate

Here's the solution again in spoiler white text. The convention in helpmate notation is that the first move given after a move number is Black's (which makes sense because Black normally moves first in helpmates: >1.0-0 Bd3 2.Rf1+! Rxf1 3.Kh8 Rf8 mate.< 

Black's 2.Rf1+! is a terrific tempo move. If Black had played 2.Kh8? instead, then after White's 2...Rf1, any legal move by Black would prevent the planned 3...Rxf8 mate. The solution is the ONLY sequence of moves that enables White to mate by the 3rd move.

Ok...
Rocky your solution makes sense, but I'm not sure why you're saying cobra's is correct. His notation has black moving as the second move given after the move number. If he's switching it up in move two so that black is now magically the first move given, that is what confused me. Also you both have the order of your king moves switched, where cobra has the sequence you explain right at the end of your post that prevents mate.

I thought the point was to get white to his checkmate position in three moves, which cobra either didn't do, or failed to explain with confusing notation.

its a helpmate, black helps you

The solutions to Helpmates are typically given with Black's first move as move number 1. It is only confusing to those who don't know the convention.

OMG you're missing the point. I didn't say the "convention" was confusing. I said switching back and forth between conventions in the same solution is confusing. Read cobra's comment.

There is no drama. You can't correctly play moves out from incorrect notation. Rf1 in cobra's solution moves the white rook. "It's not hard to do" is coming from someone who already has the solution from Rocky readily available. You are continually speaking to me from a perspective of hindsight not understanding of my experience.

This is what Cobra wrote for a final solution: "0...O-O  1. Bd3 Rf1+! (the only possible tempo loss for Black!) 2. Rxf1 Kh8  3. Rf8#"

It starts with black castling(0...O-O) white playing Bd3 and then black playing Rf1+!

At no point is there any switching he does between the players in his notation and the notation is correct otherwise. I fail to see how you think his notation means white played Rf1.

If you weird talking about the first attempt he provided(which was 0...O-O  1. Bd3 Kh8  2. Rf1, to remind you) that's indeed white that plays Rf1 because white is trying to get the rook to the f1 square, but moves it too early.

Either way, it seems you need to read cobra's comment again yourself, since it's perfectly annotated.