HMMT 二月 2008 · TEAM1 赛 · 第 6 题
HMMT February 2008 — TEAM1 Round — Problem 6
题目详情
- [ 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
- [ 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. d Solution: The simplest example is the set of 2 points of the form ( a , a , . . . , a ), where 1 2 d a ∈ { 0 , 1 } for each k . This is the set of vertices of a d -dimensional cube. k