2006 IMO 第 2 题

Let $P$ be a regular 2006-gon. A diagonal is called good 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 good. 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.

令 $P$ 为常规的 2006 年边形。如果一条对角线的端点将 $P$ 的边界分为两部分，每部分由 $P$ 的奇数条边组成，则该对角线被称为好的对角线。 $P$ 的边也称为好的。假设 $P$ 已被 2003 个对角线分割成三角形，其中没有两个三角形在 $P$ 内部有公共点。求在这种配置中可能出现的具有两个好边的等腰三角形的最大数量。