MathDB
2017 Guts #23

Source:

November 25, 2022
2017Guts Round

Problem Statement

Ben creates an 8×88\times8 grid of coins, where each coin faces heads with probability 12\tfrac{1}{2}, and tails with probability 12\tfrac{1}{2}. Ben then makes a series of moves; each move consists of selecting a coin in the grid and flipping over all coins in the same row and column as the selected coin. Suppose that in Ben’s current grid of coins, it is possible to make a series of moves so that all coins in the grid are heads, and that Ben will make the fewest number of moves to do so. What is the expected number of moves that Ben makes?
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