HMMT 2014 C9
- Combinatorics
- Answer
There is a heads up coin on every integer of the number line. Lucky is initially standing on the zero point of the number line facing in the positive direction. Lucky performs the following procedure: he looks at the coin (or lack thereof) underneath him, and then,
- If the coin is heads up, Lucky flips it to tails up, turns around, and steps forward a distance of one unit.
- If the coin is tails up, Lucky picks up the coin and steps forward a distance of one unit facing the same direction.
- If there is no coin, Lucky places a coin heads up underneath him and steps forward a distance of one unit facing the same direction.
He repeats this procedure until there are 20 coins anywhere that are tails up. How many times has Lucky performed the procedure when the process stops?
Dataset text NuminaMath olympiads. Quoted with source.
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6098
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