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OlympiadBench / 1939 / Let n be a fixed positive integer. Find the maximum possible value of

Problem

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

answer type

Expression

is multiple answer

false

language

English

question

Let

n

be a fixed positive integer. Find the maximum possible value of

\sum_{1 \leqslant r<s \leqslant 2 n}(s-r-n) x_{r} x_{s}

where

-1 \leqslant x_{i} \leqslant 1

for all

i=1,2, \ldots, 2 n

Plain-text mathematical notation (without MathML)

Let n be a fixed positive integer. Find the maximum possible value of

∑_(1≤r<s≤2n)(s−r−n)x_(r)x_(s)

where −1≤x_(i)≤1 for all i=1,2,…,2n.

Original LaTeX notation

Let $n$ be a fixed positive integer. Find the maximum possible value of

$$
\sum_{1 \leqslant r<s \leqslant 2 n}(s-r-n) x_{r} x_{s}
$$

where $-1 \leqslant x_{i} \leqslant 1$ for all $i=1,2, \ldots, 2 n$.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1939
task_id: 81d4229a-0224-5e1a-a146-f33678723ed7
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1939
task_revision_id: 2
config / split: OE_TO_maths_en_COMP / train

Official source

initial import