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Found problems: 1

2005 National Olympiad First Round, 20
Tags: permutation statistics , inversions in permutations
We are swapping two different digits of a number in each step. If we start with the number $12345$, which of the following cannot be got after an even number of steps? $ \textbf{(A)}\ 13425 \qquad\textbf{(B)}\ 21435 \qquad\textbf{(C)}\ 35142 \qquad\textbf{(D)}\ 43125 \qquad\textbf{(E)}\ 53124 $