benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / We are given 2n natural numbers

Problem

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

problem

We are given 2n2n natural numbers 1,1,2,2,3,3,…,n−1,n−1,n,n.1, 1, 2, 2, 3, 3, \ldots, n - 1, n - 1, n, n. Find all nn for which these numbers can be arranged in a row such that for each k≤nk \leq n, there are exactly kk numbers between the two numbers kk.
Plain-text mathematical notation (without MathML)
We are given 2n natural numbers
1,1,2,2,3,3,…,n−1,n−1,n,n.
Find all n for which these numbers can be arranged in a row such that for each k≤n, there are exactly k numbers between the two numbers k.
Original LaTeX notation
We are given $2n$ natural numbers
\[1, 1, 2, 2, 3, 3, \ldots, n - 1, n - 1, n, n.\]
Find all $n$ for which these numbers can be arranged in a row such that for each $k \leq n$, there are exactly $k$ numbers between the two numbers $k$.

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
4333141a-ab1b-5187-94ad-b5fd349af9cf
task_key
test--4333141a-ab1b-5187-94ad-b5fd349af9cf
task_revision_id
1
config / split
/ test

Official source

initial import