MathDB

Usamo 1998

Source:

January 14, 2005

AMCUSA(J)MOUSAMOfunctionfloor functionconicshyperbola

Problem Statement

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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