HMMT 2023 C9
- Combinatorics
- Answer
There are 100 people standing in a line from left to right. Half of them are randomly chosen to face right (with all possible choices being equally likely), and the others face left. Then, while there is a pair of people who are facing each other and have no one between them, the leftmost such pair leaves the line. Compute the expected number of people remaining once this process terminates.
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{2^{100}}{\binom{100}{50}}-1
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