Another chess puzzle

A game ended with 6.BxRc4# (mate). What were the previous moves?

Assuming it is White that mates, Black must have made 5 moves.

Play might go
1. e4 a6
2. Bxa6 Other move
3. B move Ra4
4. Some move Rc4
But I can't see what Black can do with just 2 moves.

Otherwise he requires 4 moves to move his rook to c4, 1 move to move his king onto the a2-g8 diagonal, and at least 1 pawn move in which case it is impossible.

Therefore the Black king must be mated by discovered check (possibly using the White queen), but this seems equally problematic.

Originally posted by THUDandBLUNDER
Therefore the Black king must be mated by discovered check (possibly using the White queen), but this seems equally problematic.

You're on the right track...