PWC: When a capture is made, the captured unit (except a King) is replaced on the square the capturing unit just leaves. A Pawn is immovable on its 1st rank.

Non-stop Equihopper(NE): Moves along any line over another unit of either colour to a square situated such that the hurdle stands at the mid-point between the Equihopper’s departure and arrival squares. The English (standard) Equihopper cannot pass over an obstruction other than the hurdle when playing along Queen-lines. The non-stop/French Equihopper does not have this restriction. 

Chess4E71:

Bobby Fischer’s Chess960 has recently been added to the Laws, yet in time even this will become tired and stale, and we will turn instead to a fresh challenge: perhaps Chess4E71!
So what is this future format? For each square select a random number from 1 to 13 and either assign a random unit to that square (2×6 possibilities) or possibly keep the square empty (1 possibility). Finally flip a coin to decide which side has the move. Now just somehow play chess from this random starting position. Exciting! The number of possible starting positions is exactly 2*13^64, approximately 4*10^71, which written in scientific E notation is 4E71, hence the name.

Interpretations of the existing rules & conventions
– If a player has no king, they can’t be checkmated. If neither player has a king, then no checkmate is possible. So in a “retro composition” the game ends in dead position, otherwise the game continues until it ends some other way (e.g. stalemate).
– If in the starting position, the player to move is apparently checking or even checkmating the opponent’s king, then he simply moves as normal, bearing in mind that the king can never be captured. A waiting move here is sufficient to maintain the check or checkmate.
– A pawn starting the game on the first to sixth rank can make a double move as its first move. Any pawn making a double move is potentially liable to en passant capture. In a composition, the en passant convention may apply after any double move whatever the rank.
– A pawning starting the game on the first to fourth rank, promotes in the usual way if it reaches the eighth rank. But a pawn starting on the fifth to eighth rank remains a pawn when it reaches the eighth rank, and cannot move further.

New conventions for 4E71
– Pawn double move: A pawn on any rank is permitted to make a double move only if it can be proved that the pawn has not moved previously in the game.
– Pawn promotion: A pawn moving to the eighth rank is permitted to promote to another piece only if it can be proved that it started on the first to fourth rank. If there is no such proof, the pawn remains a pawn.

Interpretations & conventions for zero-rex, apparent check & pawns are now believed to be complete, and are sufficient for existing compositions. Interpretations & conventions to cover multi-rex & castling (which must extend Chess960) will be developed later.

Proposed new convention (applies more broadly than 4E71)
– For a problem to be considered a “retro composition” (for purposes of 50 move rule or dead position), there must be some non-trivial reasoning about the history of the game. It is not sufficient simply to observe that one player is in check. Nor is it sufficient to simply apply a convention, existing or new.
– If a composition comprises twins (with or without a zero position), then the retro status of each twin is considered separately. If the keyword “conjoined twins” is used however, then retro content in one twin is sufficient to render the entire composition a retro.

Annan Chess: If two pieces of the same colour are standing close to each other in N-S-direction, the front piece moves only like the rear piece as long as the contact is existing. The front piece is that piece that is closer to the own promotion line. White/Black Pawns on the 1st/8th rank cannot move, but can give their kind of moving to a front piece. Officers moving with the power of a Pawn to the promotion line do not promote; if they make a double-step with the power of a Pawn, they cannot be captured en-passant; but officers with the power of a Pawn can capture a Pawn en-passant.

Messigny Chess: Instead of an ordinary move, any unit (Ks included) may be swapped with another of the same type and opposite colour, provided neither of the units involved was swapped on the previous move.

Grasshopper(G): Moves along Q-lines over another unit of either color to the square immediately beyond that unit. A capture may be made on arrival, but the hurdle is not affected.

Chess4E71 (see revised definition in later problem No.1135): 
Bobby Fischer’s Chess960 has recently been added to the Laws, yet in time even this will become tired and stale, and we will turn instead to a fresh challenge: perhaps Chess4E71!
So what is this future format? For each square select a random number from 1 to 13 and either assign a random unit (2×6 possibilities to that square) or possibly keep the square empty (1 possibility). Finally flip a coin to decide which side has the move. Now just somehow play chess from this random starting position. Exciting! The number of possible starting positions is exactly 2*13^64, approximately 4*10^71, which can be written as 4E71, hence the name.
To be honest, I am not sure how *all* the rules will work out, but for the purposes of this problem, Articles 1.2 & 3.7 of the Laws of Chess should see you through.