HMMT 2018 U27
- Guts
- Answer
There are 2018 frogs in a pool and there is 1 frog on the shore. In each time-step thereafter, one random frog moves position. If it was in the pool, it jumps to the shore, and vice versa. Find the expected number of time-steps before all frogs are in the pool for the first time.
Dataset text NuminaMath olympiads. Quoted with source.
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2^{2018}-1
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