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Omni-MATH / Anastasia is taking a walk in the plane, starting from (1,0). Each second, if she is at (x,y), she moves to one of the points (x−1,y),(x+1,y),(x,y−1), and (x,y+1), each with …

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problem

Anastasia is taking a walk in the plane, starting from (1,0)(1,0). Each second, if she is at (x,y)(x, y), she moves to one of the points (x−1,y),(x+1,y),(x,y−1)(x-1, y),(x+1, y),(x, y-1), and (x,y+1)(x, y+1), each with 14\frac{1}{4} probability. She stops as soon as she hits a point of the form (k,k)(k, k). What is the probability that kk is divisible by 3 when she stops?
Plain-text mathematical notation (without MathML)
Anastasia is taking a walk in the plane, starting from (1,0). Each second, if she is at (x,y), she moves to one of the points (x−1,y),(x+1,y),(x,y−1), and (x,y+1), each with (1)/(4) probability. She stops as soon as she hits a point of the form (k,k). What is the probability that k is divisible by 3 when she stops?
Original LaTeX notation
Anastasia is taking a walk in the plane, starting from $(1,0)$. Each second, if she is at $(x, y)$, she moves to one of the points $(x-1, y),(x+1, y),(x, y-1)$, and $(x, y+1)$, each with $\frac{1}{4}$ probability. She stops as soon as she hits a point of the form $(k, k)$. What is the probability that $k$ is divisible by 3 when she stops?

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Source and history

task_id
7ccc7354-3452-5f1b-8227-39819f9e7c99
task_key
test--7ccc7354-3452-5f1b-8227-39819f9e7c99
task_revision_id
1
config / split
/ test

Official source

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