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HMMT 十一月 2014 · THM 赛 · 第 6 题

HMMT November 2014 — THM Round — Problem 6

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. Let P , P , P be pairwise distinct parabolas in the plane. Find the maximum possible number of
    1 2 3
    intersections between two or more of the P . In other words, find the maximum number of points thatican lie on two or more of the parabolas P , P , P .
    1 2 3
解析

英文解析

  1. Let P , P , P be pairwise distinct parabolas in the plane. Find the maximum possible number of
    1 2 3
    intersections between two or more of the P . In other words, find the maximum number of points thatican lie on two or more of the parabolas P , P , P .
    1 2 3
    Answer: 12 Note that two distinct parabolas intersect in at most 4 points, which is not difficultto see by drawing examples. Given three parabolas, each pair intersects in at most 4 points, for at 1
    most 4 · 3 = 12 points of intersection in total. It is easy to draw an example achieving this maximum,
    for example, by slanting the parabolas at different angles.