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OlympiadBench / 1716 / Let x₁,…,x₁₀₀ be nonnegative real numbers such that…

Problem

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

answer type

Numerical

is multiple answer

false

language

English

question

Let

x_{1}, \ldots, x_{100}

be nonnegative real numbers such that

x_{i}+x_{i+1}+x_{i+2} \leq 1

for all

i=1, \ldots, 100

(we put

x_{101}=x_{1}, x_{102}=x_{2}

). Find the maximal possible value of the sum

S=\sum_{i=1}^{100} x_{i} x_{i+2}

Plain-text mathematical notation (without MathML)

Let x₁,…,x₁₀₀ be nonnegative real numbers such that x_(i)+x_(i+1)+x_(i+2)≤1 for all i=1,…,100 (we put x₁₀₁=x₁,x₁₀₂=x₂ ). Find the maximal possible value of the sum

S=∑_(i=1)¹⁰⁰x_(i)x_(i+2)

Original LaTeX notation

Let $x_{1}, \ldots, x_{100}$ be nonnegative real numbers such that $x_{i}+x_{i+1}+x_{i+2} \leq 1$ for all $i=1, \ldots, 100$ (we put $x_{101}=x_{1}, x_{102}=x_{2}$ ). Find the maximal possible value of the sum

$$
S=\sum_{i=1}^{100} x_{i} x_{i+2}
$$

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1716
task_id: 5bc37ee9-51af-50fb-b36a-5b5b8032bbdc
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1716
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

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