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HMMT 十一月 2008 · GEN1 赛 · 第 3 题

HMMT November 2008 — GEN1 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. [ 3 ] How many diagonals does a regular undecagon (11-sided polygon) have?
解析

英文解析

  1. [ 3 ] How many diagonals does a regular undecagon (11-sided polygon) have?
    Answer: 44 There are 8 diagonals coming from the first vertex, 8 more from the next, 7 from thenext, 6 from the next, 5 from the next, etc., and 1 from the last, for 8 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 44
    total.
    Third method: Each vertex has 8 diagonals touching it. There are 11 vertices. Since each diagonal
    8 · 11
    touches two vertices, this counts every diagonal twice, so there are = 44 diagonals. 2