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There is feedback mechanism going on all the time the fingers are moving. Friction between the fingers and the wooden stick is proportional to the weight of the stick at the point above the fingers. If the right hand finger moves towards the centre it reduces the weight directly above the left finger because there is now more wood to the right of the right finger. The decrease in friction above the left finger causes it to slip and move towards the centre. The process is now reversed and the right finger now starts to move. The two fingers end up at the centre of mass of the stick by an unseen oscillation of moments.

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Q: Why do the two fingers get to the middle of the meter stick at the same time?
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