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Omni-MATH / Let P be a regular 2006-gon. A diagonal is called [i]good[/i] if its endpoints divide the boundary of P into two parts, each composed of an odd number of sides of P. The sides of P…

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problem

Let PP be a regular 20062006-gon. A diagonal is called [i]good[/i] if its endpoints divide the boundary of PP into two parts, each composed of an odd number of sides of PP. The sides of PP are also called [i]good[/i]. Suppose PP has been dissected into triangles by 20032003 diagonals, no two of which have a common point in the interior of PP. Find the maximum number of isosceles triangles having two good sides that could appear in such a configuration.
Plain-text mathematical notation (without MathML)
Let P be a regular 2006-gon. A diagonal is called [i]good[/i] if its endpoints divide the boundary of P into two parts, each composed of an odd number of sides of P. The sides of P are also called [i]good[/i].
Suppose P has been dissected into triangles by 2003 diagonals, no two of which have a common point in the interior of P. Find the maximum number of isosceles triangles having two good sides that could appear in such a configuration.
Original LaTeX notation
Let $P$ be a regular $2006$-gon. A diagonal is called [i]good[/i] if its endpoints divide the boundary of $P$ into two parts, each composed of an odd number of sides of $P$. The sides of $P$ are also called [i]good[/i].
Suppose $P$ has been dissected into triangles by $2003$ diagonals, no two of which have a common point in the interior of $P$. Find the maximum number of isosceles triangles having two good sides that could appear in such a configuration.

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Source and history

task_id
e5ef13d8-001a-5854-93cf-1ba405003bfe
task_key
test--e5ef13d8-001a-5854-93cf-1ba405003bfe
task_revision_id
1
config / split
/ test

Official source

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