HMMT 2004 C10
- Combinatorics
- Answer
In a game similar to three card monte, the dealer places three cards on the table: the queen of spades and two red cards. The cards are placed in a row, and the queen starts in the center; the card configuration is thus RQR. The dealer proceeds to move. With each move, the dealer randomly switches the center card with one of the two edge cards (so the configuration after the first move is either RRQ or QRR). What is the probability that, after 2004 moves, the center card is the queen?
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{1}{3}+\frac{1}{3 \cdot 2^{2003}}
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