HMMT 二月 2000 · GEN 赛 · 第 25 题
HMMT February 2000 — GEN Round — Problem 25
题目详情
- Ho w man y p oin ts do es one ha v e to pla e on a unit square to guaran tee that t w o of them are stri tly less than 1/2 unit apart? p p
解析
- W e an pla e 9 p oin ts as sho wn, all at least unit apart, but the next p oin t m ust b e 2 1 less than , so 10 p oin ts m ust b e pla ed. There is no arrangemen t of 10 p oin ts with 2 1 distan e at least . The pro of of this is a simple appli ation of the Pigeonhole Prin iple. 2 p