SPOILER, solution below (took about 2 minutes)
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1. e3 d6 2. Qh5 Bg4 3. e4 Bd1 4. Qxd1
Black only makes 3 moves. The c8 bishop has to be captured. Either a white piece captures it on it's starting square or black has to move a piece after the bishop is captured. So if white doesn't capture it with a piece on a starting square, some other black piece would have to be moving back to it's starting square. But black doesn't have enough moves to play d6, move the bishop out, and move another piece twice. So white has to capture the bishop on d1 or f1. The bishop can't get to f1 in 2 moves, so it has to be on d1.
The position below is after white's 4th move.
What's the only set of moves that could have gone before?
It took me about 5 minutes - so I guess that's the time to beat at the moment
(by Henrik Juel)