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Omni-MATH / Let n≥5 be an integer. Find the largest integer k (as a function of n ) such that there exists a convex n -gon A₁A₂…A_(n) for which exactly k of the quadrilaterals …

Problem

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problem

Let

n \geq 5

be an integer. Find the largest integer

k

(as a function of

n

) such that there exists a convex

n

-gon

A_{1}A_{2}\dots A_{n}

for which exactly

k

of the quadrilaterals

A_{i}A_{i+1}A_{i+2}A_{i+3}

have an inscribed circle. (Here

A_{n+j} = A_{j}

Plain-text mathematical notation (without MathML)

Let n≥5 be an integer. Find the largest integer k (as a function of n ) such that there exists a convex n -gon A₁A₂…A_(n) for which exactly k of the quadrilaterals A_(i)A_(i+1)A_(i+2)A_(i+3) have an inscribed circle. (Here A_(n+j)=A_(j) .)

Original LaTeX notation

Let $n \geq 5$ be an integer. Find the largest integer $k$ (as a function of $n$ ) such that there exists a convex $n$ -gon $A_{1}A_{2}\dots A_{n}$ for which exactly $k$ of the quadrilaterals $A_{i}A_{i+1}A_{i+2}A_{i+3}$ have an inscribed circle. (Here $A_{n+j} = A_{j}$ .)

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task_id: 935ed613-2578-5460-97be-025caa0bfd93
task_key: test--935ed613-2578-5460-97be-025caa0bfd93
task_revision_id: 4
config / split: / test

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