返回题库

HMMT 十一月 2019 · GEN 赛 · 第 1 题

HMMT November 2019 — GEN Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Dylan has a 100 × 100 square, and wants to cut it into pieces of area at least 1. Each cut must be a straight line (not a line segment) and must intersect the interior of the square. What is the largest number of cuts he can make?
解析
  1. Dylan has a 100 × 100 square, and wants to cut it into pieces of area at least 1. Each cut must be a straight line (not a line segment) and must intersect the interior of the square. What is the largest number of cuts he can make? Proposed by: Carl Schildkraut Answer: 9999 Since each piece has area at least 1 and the original square has area 10000, Dylan can end up with at most 10000 pieces. There is initially 1 piece, so the number of pieces can increase by at most 9999. Each cut increases the number of pieces by at least 1, so Dylan can make at most 9999 cuts. Notice that this 1 is achievable if Dylan makes 9999 vertical cuts spaced at increments of units. 100