benchmarks.wiki / Public workspace
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Omni-MATH / There is a grid of height 2 stretching infinitely in one direction. Between any…
Problem
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problem
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.
Plain-text mathematical notation (without MathML)
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 (1)/(2) 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.
Original LaTeX notation
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 $\frac{1}{2}$ 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.Discussion
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Source and history
- task_id
fa3fa7ab-7cc1-53d2-97a1-87a9ddc40f64- task_key
test--fa3fa7ab-7cc1-53d2-97a1-87a9ddc40f64- task_revision_id
- 1
- config / split
- / test
initial import