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Omni-MATH / Find a real number t such that for any set of 120 points P₁,…P₁₂₀ on the boundary of a unit square, there exists a point Q on this boundary with |P₁Q|+|P₂Q|+⋯+|P₁₂₀Q|=t.

Problem

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problem

Find a real number

t

such that for any set of 120 points

P_1, \ldots P_{120}

on the boundary of a unit square, there exists a point

Q

on this boundary with

|P_1Q| + |P_2Q| + \cdots + |P_{120}Q| = t

Plain-text mathematical notation (without MathML)

Find a real number t such that for any set of 120 points P₁,…P₁₂₀ on the boundary of a unit square, there exists a point Q on this boundary with |P₁Q|+|P₂Q|+⋯+|P₁₂₀Q|=t.

Original LaTeX notation

Find a real number $t$ such that for any set of 120 points $P_1, \ldots P_{120}$ on the boundary of a unit square, there exists a point $Q$ on this boundary with $|P_1Q| + |P_2Q| + \cdots + |P_{120}Q| = t$.

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Source and history

task_id: 36d5e112-ee69-5dd2-bdde-c1b2ed89146a
task_key: test--36d5e112-ee69-5dd2-bdde-c1b2ed89146a
task_revision_id: 2
config / split: / test

Official source

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