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HMMT 二月 2001 · 冲刺赛 · 第 3 题

HMMT February 2001 — Guts Round — Problem 3

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [7] Find the number of triangulations of a general convex 7-gon into 5 triangles by 4
    diagonals that do not intersect in their interiors.
    ∞
    ( )
    ∏ 1
解析

英文解析

  1. [7] Find the number of triangulations of a general convex 7-gon into 5 triangles by 4
    diagonals that do not intersect in their interiors.
    ( )
    2 n
    Solution: Define the Catalan numbers by C ( n ) = . The current solution is the 1
    n +1 n
    C (number of triangles) = C (5) = 42 .
    ∞
    ( )
    ∏ 1