Look at the position below.
Who's move is it (assuming this position originated from the original starting position)?
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Suppose it is white to move. Then black must have made the previous move, resulting in the shown position. So one of black's pieces must have moved from some other square to the square it is now in. But what could that move possibly have been?! If you look at each of black's pieces in turn there is no square from which it could have moved to its current position.
Since assuming it is white's turn to move results in a contradiction, it must be black's turn.