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HMMT 二月 2012 · 冲刺赛 · 第 4 题

HMMT February 2012 — Guts Round — Problem 4

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 2 ] Luna has an infinite supply of red, blue, orange, and green socks. She wants to arrange 2012 socksin a line such that no red sock is adjacent to a blue sock and no orange sock is adjacent to a greensock. How many ways can she do this?
    15 ANNUAL HARVARD-MIT MATHEMATICS TOURNAMENT, 11 FEBRUARY 2012 — GUTS ROUNDTH
解析

英文解析

  1. [ 2 ] Luna has an infinite supply of red, blue, orange, and green socks. She wants to arrange 2012 socksin a line such that no red sock is adjacent to a blue sock and no orange sock is adjacent to a greensock. How many ways can she do this?
    2011
    Answer: 4 · 3 Luna has 4 choices for the first sock. After that, she has 3 choices for each of
    2011
    2011 remaining socks for a total of 4 · 3 .