benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / A ±1-[i]sequence[/i] is a sequence of 2022 numbers a₁,…,a₂₀₂₂, each equal to either +1 or −1. Determine the largest C so that, for any ±1-sequence, there exists an integer k and in…

Problem

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

problem

A ±1\pm 1-[i]sequence[/i] is a sequence of 20222022 numbers a1,…,a2022,a_1, \ldots, a_{2022}, each equal to either +1+1 or −1-1. Determine the largest CC so that, for any ±1\pm 1-sequence, there exists an integer kk and indices 1≤t1<…<tk≤20221 \le t_1 < \ldots < t_k \le 2022 so that ti+1−ti≤2t_{i+1} - t_i \le 2 for all ii, and |∑i=1kati|≥C.\left| \sum_{i = 1}^{k} a_{t_i} \right| \ge C.
Plain-text mathematical notation (without MathML)
A ±1-[i]sequence[/i] is a sequence of 2022 numbers a₁,…,a₂₀₂₂, each equal to either +1 or −1. Determine the largest C so that, for any ±1-sequence, there exists an integer k and indices 1≤t₁<…<t_(k)≤2022 so that t_(i+1)−t_(i)≤2 for all i, and |∑_(i=1)^(k)a_(t_(i))|≥C.
Original LaTeX notation
A $\pm 1$-[i]sequence[/i] is a sequence of $2022$ numbers $a_1, \ldots, a_{2022},$ each equal to either $+1$ or $-1$. Determine the largest $C$ so that, for any $\pm 1$-sequence, there exists an integer $k$ and indices $1 \le t_1 < \ldots < t_k \le 2022$ so that $t_{i+1} - t_i \le 2$ for all $i$, and $$\left| \sum_{i = 1}^{k} a_{t_i} \right| \ge C.$$

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
7212e5da-2acf-58c9-b682-73a41b4898b7
task_key
test--7212e5da-2acf-58c9-b682-73a41b4898b7
task_revision_id
1
config / split
/ test

Official source

initial import