返回题库

HMMT 二月 2005 · TEAM2 赛 · 第 1 题

HMMT February 2005 — TEAM2 Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [15] Let 0 < m ≤ n be integers. How many different (i.e., noncongruent) dominoes can be formed by choosing two squares of an m × n array?
解析
  1. [15] Let 0 < m ≤ n be integers. How many different (i.e., noncongruent) dominoes can be formed by choosing two squares of an m × n array? Solution: We must have 0 ≤ a < m , 0 ≤ b < n , a ≤ b , and a and b not both 0. The number of pairs ( a, b ) with b < a < m is m ( m − 1) / 2, so the answer is 2 m ( m − 1) m − m + 2 mn − − 1 = mn − . 2 2