benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Pyramid EARLY is placed in (x,y,z) coordinates so that E=(10,10,0),A=(10,−10,0),R=(−10,−10,0),L=(−10,10,0), and Y=(0,0,10). Tunnels are drilled through the pyramid in such a way th…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Pyramid EARLYE A R L Y is placed in (x,y,z)(x, y, z) coordinates so that E=(10,10,0),A=(10,−10,0),R=(−10,−10,0),L=(−10,10,0)E=(10,10,0), A=(10,-10,0), R=(-10,-10,0), L=(-10,10,0), and Y=(0,0,10)Y=(0,0,10). Tunnels are drilled through the pyramid in such a way that one can move from (x,y,z)(x, y, z) to any of the 9 points (x,y,z−1),(x±1,y,z−1)(x, y, z-1),(x \pm 1, y, z-1), (x,y±1,z−1),(x±1,y±1,z−1)(x, y \pm 1, z-1),(x \pm 1, y \pm 1, z-1). Sean starts at YY and moves randomly down to the base of the pyramid, choosing each of the possible paths with probability 19\frac{1}{9} each time. What is the probability that he ends up at the point (8,9,0)(8,9,0)?
Plain-text mathematical notation (without MathML)
Pyramid EARLY is placed in (x,y,z) coordinates so that E=(10,10,0),A=(10,−10,0),R=(−10,−10,0),L=(−10,10,0), and Y=(0,0,10). Tunnels are drilled through the pyramid in such a way that one can move from (x,y,z) to any of the 9 points (x,y,z−1),(x±1,y,z−1), (x,y±1,z−1),(x±1,y±1,z−1). Sean starts at Y and moves randomly down to the base of the pyramid, choosing each of the possible paths with probability (1)/(9) each time. What is the probability that he ends up at the point (8,9,0)?
Original LaTeX notation
Pyramid $E A R L Y$ is placed in $(x, y, z)$ coordinates so that $E=(10,10,0), A=(10,-10,0), R=(-10,-10,0), L=(-10,10,0)$, and $Y=(0,0,10)$. Tunnels are drilled through the pyramid in such a way that one can move from $(x, y, z)$ to any of the 9 points $(x, y, z-1),(x \pm 1, y, z-1)$, $(x, y \pm 1, z-1),(x \pm 1, y \pm 1, z-1)$. Sean starts at $Y$ and moves randomly down to the base of the pyramid, choosing each of the possible paths with probability $\frac{1}{9}$ each time. What is the probability that he ends up at the point $(8,9,0)$?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
81e473f7-1b03-5345-9bd6-2fc4ada13f4b
task_key
test--81e473f7-1b03-5345-9bd6-2fc4ada13f4b
task_revision_id
1
config / split
/ test

Official source

initial import