benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let n>3 be a positive integer. Equilateral triangle ABC is divided into n² smaller congruent equilateral triangles (with sides parallel to its sides). Let m be the number of rhombu…

Problem

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

problem

Let n>3n>3 be a positive integer. Equilateral triangle ABC is divided into n2n^2 smaller congruent equilateral triangles (with sides parallel to its sides). Let mm be the number of rhombuses that contain two small equilateral triangles and dd the number of rhombuses that contain eight small equilateral triangles. Find the difference m−dm-d in terms of nn .
Plain-text mathematical notation (without MathML)
Let n>3 be a positive integer. Equilateral triangle ABC is divided into n² smaller congruent equilateral triangles (with sides parallel to its sides). Let m be the number of rhombuses that contain two small equilateral triangles and d the number of rhombuses that contain eight small equilateral triangles. Find the difference m−d in terms of n .
Original LaTeX notation
Let $n>3$ be a positive integer. Equilateral triangle ABC is divided into $n^2$ smaller congruent equilateral triangles (with sides parallel to its sides). Let $m$ be the number of rhombuses that contain two small equilateral triangles and $d$ the number of rhombuses that contain eight small equilateral triangles. Find the difference $m-d$ in terms of $n$ .

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
a86fd96e-e118-5df4-9502-8de8eed3e9bb
task_key
test--a86fd96e-e118-5df4-9502-8de8eed3e9bb
task_revision_id
1
config / split
/ test

Official source

initial import