benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Barry picks infinitely many points inside a unit circle, each independently and…

Problem

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

problem

Barry picks infinitely many points inside a unit circle, each independently and uniformly at random, P1,P2,…P_{1}, P_{2}, \ldots Compute the expected value of NN, where NN is the smallest integer such that PN+1P_{N+1} is inside the convex hull formed by the points P1,P2,…,PNP_{1}, P_{2}, \ldots, P_{N}. Submit a positive real number EE. If the correct answer is AA, you will receive ⌊100⋅max(0.2099−|E−A|,0)⌋\lfloor 100 \cdot \max (0.2099-|E-A|, 0)\rfloor points.
Plain-text mathematical notation (without MathML)
Barry picks infinitely many points inside a unit circle, each independently and uniformly at random, P₁,P₂,… Compute the expected value of N, where N is the smallest integer such that P_(N+1) is inside the convex hull formed by the points P₁,P₂,…,P_(N). Submit a positive real number E. If the correct answer is A, you will receive ⌊100⋅max(0.2099−|E−A|,0)⌋ points.
Original LaTeX notation
Barry picks infinitely many points inside a unit circle, each independently and uniformly at random, $P_{1}, P_{2}, \ldots$ Compute the expected value of $N$, where $N$ is the smallest integer such that $P_{N+1}$ is inside the convex hull formed by the points $P_{1}, P_{2}, \ldots, P_{N}$. Submit a positive real number $E$. If the correct answer is $A$, you will receive $\lfloor 100 \cdot \max (0.2099-|E-A|, 0)\rfloor$ points.

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
46fb21d5-2278-5f56-a20f-ca3ef5267662
task_key
test--46fb21d5-2278-5f56-a20f-ca3ef5267662
task_revision_id
1
config / split
/ test

Official source

initial import