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HMMT 二月 2001 · 冲刺赛 · 第 3 题

HMMT February 2001 — Guts Round — Problem 3

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  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
  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 1 Solution: Define the Catalan numbers by C ( n ) = . The current solution is the n +1 n C (number of triangles) = C (5) = 42 . ∞ ( ) ∏ 1