HMMT 2024 C7
- Combinatorics
- Answer
There is a grid of height 2 stretching infinitely in one direction. Between any two edge-adjacent cells of the grid, there is a door that is locked with probability independent of all other doors. Philip starts in a corner of the grid (in the starred cell). Compute the expected number of cells that Philip can reach, assuming he can only travel between cells if the door between them is unlocked.
Dataset text NuminaMath olympiads. Quoted with source.
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\frac{32}{7}
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