A particle on a decagon vertex moves each second on a die roll: 1 or 2 clockwise, 3 or 4 anticlockwise, otherwise it stays. What is the expected time to reach the opposite vertex?
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A particle sits on a vertex of a decagon. Each second a die is rolled: on a 1 or 2 the particle moves one vertex clockwise, on a 3 or 4 it moves one vertex anticlockwise, and on a 5 or 6 it stays where it is. What is the expected time for it to reach the vertex that was farthest away at the start?
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