benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let Y be as in problem 14. Find the maximum Z such that three circles of radius √(Z) can simultaneously fit inside an equilateral triangle of area Y without overlapping each other.

Problem

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

problem

Let YY be as in problem 14. Find the maximum ZZ such that three circles of radius Z\sqrt{Z} can simultaneously fit inside an equilateral triangle of area YY without overlapping each other.
Plain-text mathematical notation (without MathML)
Let Y be as in problem 14. Find the maximum Z such that three circles of radius √(Z) can simultaneously fit inside an equilateral triangle of area Y without overlapping each other.
Original LaTeX notation
Let $Y$ be as in problem 14. Find the maximum $Z$ such that three circles of radius $\sqrt{Z}$ can simultaneously fit inside an equilateral triangle of area $Y$ without overlapping each other.

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
d788ce8c-b2c3-5270-a7f8-737dc56282c2
task_key
test--d788ce8c-b2c3-5270-a7f8-737dc56282c2
task_revision_id
1
config / split
/ test

Official source

initial import