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HMMT 二月 2008 · TEAM1 赛 · 第 6 题

HMMT February 2008 — TEAM1 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. [ 10 ] Construct a set of 2 d -dimensional lattice points so that for any two chosen points A, B ,
    the line segment AB does not pass through any other lattice point.
解析

英文解析

  1. [ 10 ] Construct a set of 2 d -dimensional lattice points so that for any two chosen points A, B ,
    the line segment AB does not pass through any other lattice point.
    Solution: The simplest example is the set of 2 points of the form ( a , a , . . . , a ), whered
    1 2
    a ∈ { 0 , 1 } for each k . This is the set of vertices of a d -dimensional cube.dk