Three-fold repetition and en-passant

I believe the OP's question, though failed in its original intent, has shed some light on a rather obscure tactic, or strategy, involving en passant.

I mean it's just a pin, really, but an unusual one. Beautifully so, if I may add. Perhaps because it not only involves, but also bends a rule that it itself is also rather unusual. If you take a look at tactics-solving you'll most likely find that people lose a lot of en passant tactics, statistically speaking, anyway.

Not too long ago, chess.com published an article that sort of highlighted how unaccustomed some players were to the rule of en passant. It was written by the boss himself, I believe. The OP must've been simply dazzled by this under-explored play and for a moment thought he'd discovered something. A momentary lapse in judgement brought on by high levels of excitement. It can happen to anyone.

https://www.chess.com/article/view/his-pawn-cheated-and-killed-my-pawn

En Passant was actually introduced in the year 1490, a few centuries after the double pawn move was introduced in Italy - 1275.

In either case, though, I am undoubtedly sure that an illegal move is no move at all. This I assure you all. You may rest your minds now, and perhaps expand yourselves over an actual match.

I wanna see an en passant checkmate now....offa e4 !

Is it fun because it is actually a mate in 3? 

No luv. Checkmate in (2) moves.

....Think !

Okay. Here's a big giant hint. The rook on e4 doesn't move !

(wow....feels like I just gave it away)

Not according to stockfish.js 

Is that with tablebase? 

Maybe that's because the computer doesn't know if the king or rook have already moved.

These types of problems rely on tricking people with incomplete information. If people were fully informed of castling rights, they would get the solution immediately. In another similar "trick problem" the viewer isn't informed of the right-to-en-passant, which is the solution to the problem. In another famous problem the solution is to promote a pawn to a piece of the opposite color, which isn't even legal, but in the context of the problem it's made legal... without saying it. This last one is just outright cheating.

Also, another example is where the board is flipped where your pawn is really just 1-step to promotion...  Yes, I agree that these aren't very good chess puzzles.

It should have been covered in a tablebase.

"if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same."

I believe the rule is actually pretty clear.

1) Does the same person have the move? Easy to determine

2) pieces of the same kind and colour occupy the same squares? Easy to determine

3) the possible moves of all the pieces of both players are the same?

List all possible moves by both sides - are the identical each time.

It doesn't matter here if the player could castle if it wasn't though check, etc. What matters are what moves are actually playable in the position and do they exactly match. So you could have a position where en-passant might normally be playable the first time but it would place their king in check. Because of the fact it doesn't place the king in check, the move is NOT on the list. And that means it WOULD be 3-fold repetition if the position occurs twice more, same person on the move, with the exact same moves actually playable.

At least that it how I would rule as an arbiter, and I think you would have a very hard case overruling that decision as wrong based on the rule as written.