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Omni-MATH / Find the largest real number c such that ∑_(i=1)¹⁰¹x_(i)²≥cM² whenever x₁,…,x₁₀₁ are real numbers such that x₁+⋯+x₁₀₁=0 and M is the median of x₁,…,x₁₀₁.

Problem

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problem

Find the largest real number cc such that ∑i=1101xi2≥cM2\sum_{i=1}^{101} x_{i}^{2} \geq c M^{2} whenever x1,…,x101x_{1}, \ldots, x_{101} are real numbers such that x1+⋯+x101=0x_{1}+\cdots+x_{101}=0 and MM is the median of x1,…,x101x_{1}, \ldots, x_{101}.
Plain-text mathematical notation (without MathML)
Find the largest real number c such that ∑_(i=1)¹⁰¹x_(i)²≥cM² whenever x₁,…,x₁₀₁ are real numbers such that x₁+⋯+x₁₀₁=0 and M is the median of x₁,…,x₁₀₁.
Original LaTeX notation
Find the largest real number $c$ such that $$\sum_{i=1}^{101} x_{i}^{2} \geq c M^{2}$$ whenever $x_{1}, \ldots, x_{101}$ are real numbers such that $x_{1}+\cdots+x_{101}=0$ and $M$ is the median of $x_{1}, \ldots, x_{101}$.

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Source and history

task_id
b649c569-fd3f-5567-93d4-83e6512fee5f
task_key
test--b649c569-fd3f-5567-93d4-83e6512fee5f
task_revision_id
1
config / split
/ test

Official source

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