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HMMT 二月 2001 · 团队赛 · 第 6 题

HMMT February 2001 — Team 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. What is the radius of the smallest sphere in which 4 spheres of radius 1 will fit?
解析

英文解析

  1. What is the radius of the smallest sphere in which 4 spheres of radius 1 will fit?
    Solution: The centers of the smaller spheres lie on a tetrahedron. Let the points of thetetrahedron be (1 , 1 , 1), ( − 1 , − 1 , 1), ( − 1 , 1 , − 1), and (1 , − 1 , − 1). These points have distance
    √ √