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Omni-MATH / Consider n disks C₁,C₂,…,C_(n) in a plane such that for each 1≤i<n, the center of C_(i) is on the circumference of C_(i+1), and the center of C_(n) is on the circumference of C₁. D…

Problem

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problem

Consider nn disks C1,C2,…,CnC_{1}, C_{2}, \ldots, C_{n} in a plane such that for each 1≤i<n1 \leq i<n, the center of CiC_{i} is on the circumference of Ci+1C_{i+1}, and the center of CnC_{n} is on the circumference of C1C_{1}. Define the score of such an arrangement of nn disks to be the number of pairs (i,j)(i, j) for which CiC_{i} properly contains CjC_{j}. Determine the maximum possible score.
Plain-text mathematical notation (without MathML)
Consider n disks C₁,C₂,…,C_(n) in a plane such that for each 1≤i<n, the center of C_(i) is on the circumference of C_(i+1), and the center of C_(n) is on the circumference of C₁. Define the score of such an arrangement of n disks to be the number of pairs (i,j) for which C_(i) properly contains C_(j). Determine the maximum possible score.
Original LaTeX notation
Consider $n$ disks $C_{1}, C_{2}, \ldots, C_{n}$ in a plane such that for each $1 \leq i<n$, the center of $C_{i}$ is on the circumference of $C_{i+1}$, and the center of $C_{n}$ is on the circumference of $C_{1}$. Define the score of such an arrangement of $n$ disks to be the number of pairs $(i, j)$ for which $C_{i}$ properly contains $C_{j}$. Determine the maximum possible score.

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Source and history

task_id
3b947214-4f8a-5f05-adf4-a813ea587ad4
task_key
test--3b947214-4f8a-5f05-adf4-a813ea587ad4
task_revision_id
1
config / split
/ test

Official source

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