benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let P be a point selected uniformly at random in the cube [0,1]³. The plane parallel to x+y+z=0 passing through P intersects the cube in a two-dimensional region R. Let t be the ex…

Problem

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

problem

Let PP be a point selected uniformly at random in the cube [0,1]3[0,1]^{3}. The plane parallel to x+y+z=0x+y+z=0 passing through PP intersects the cube in a two-dimensional region R\mathcal{R}. Let tt be the expected value of the perimeter of R\mathcal{R}. If t2t^{2} can be written as ab\frac{a}{b}, where aa and bb are relatively prime positive integers, compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
Let P be a point selected uniformly at random in the cube [0,1]³. The plane parallel to x+y+z=0 passing through P intersects the cube in a two-dimensional region R. Let t be the expected value of the perimeter of R. If t² can be written as (a)/(b), where a and b are relatively prime positive integers, compute 100a+b.
Original LaTeX notation
Let $P$ be a point selected uniformly at random in the cube $[0,1]^{3}$. The plane parallel to $x+y+z=0$ passing through $P$ intersects the cube in a two-dimensional region $\mathcal{R}$. Let $t$ be the expected value of the perimeter of $\mathcal{R}$. If $t^{2}$ can be written as $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers, compute $100 a+b$.

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
76a706a8-d357-596a-88aa-9bf5f0428724
task_key
test--76a706a8-d357-596a-88aa-9bf5f0428724
task_revision_id
1
config / split
/ test

Official source

initial import