2005 IMO Shortlist Problems/C5

There are $n$ markers, each with one side white and the other side black. In the beginning, these $n$ markers are aligned in a row so that their white sides are all up. In each step, if possible, we choose a marker whose white side is up (but not one of the outermost markers), remove it, and reverse the closest marker to the left of it and also reverse the closest marker to the right of it. Prove that if $n\equiv{1}\pmod{3}$, it’s impossible to reach a state with only two markers remaining.

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