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Omni-MATH / James is standing at the point (0,1) on the coordinate plane and wants to eat a hamburger. For each integer n≥0, the point (n,0) has a hamburger with n patties. There is also a wal…

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problem

James is standing at the point (0,1)(0,1) on the coordinate plane and wants to eat a hamburger. For each integer n≥0n \geq 0, the point (n,0)(n, 0) has a hamburger with nn patties. There is also a wall at y=2.1y=2.1 which James cannot cross. In each move, James can go either up, right, or down 1 unit as long as he does not cross the wall or visit a point he has already visited. Every second, James chooses a valid move uniformly at random, until he reaches a point with a hamburger. Then he eats the hamburger and stops moving. Find the expected number of patties that James eats on his burger.
Plain-text mathematical notation (without MathML)
James is standing at the point (0,1) on the coordinate plane and wants to eat a hamburger. For each integer n≥0, the point (n,0) has a hamburger with n patties. There is also a wall at y=2.1 which James cannot cross. In each move, James can go either up, right, or down 1 unit as long as he does not cross the wall or visit a point he has already visited. Every second, James chooses a valid move uniformly at random, until he reaches a point with a hamburger. Then he eats the hamburger and stops moving. Find the expected number of patties that James eats on his burger.
Original LaTeX notation
James is standing at the point $(0,1)$ on the coordinate plane and wants to eat a hamburger. For each integer $n \geq 0$, the point $(n, 0)$ has a hamburger with $n$ patties. There is also a wall at $y=2.1$ which James cannot cross. In each move, James can go either up, right, or down 1 unit as long as he does not cross the wall or visit a point he has already visited. Every second, James chooses a valid move uniformly at random, until he reaches a point with a hamburger. Then he eats the hamburger and stops moving. Find the expected number of patties that James eats on his burger.

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Source and history

task_id
98c2cb27-9783-5ba1-88aa-3b7f2a787ba1
task_key
test--98c2cb27-9783-5ba1-88aa-3b7f2a787ba1
task_revision_id
1
config / split
/ test

Official source

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