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HMMT 十一月 2012 · 冲刺赛 · 第 16 题

HMMT November 2012 — Guts Round — Problem 16

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 10 ] Yuhang is making a bracelet for his one true love using beads. How many distinct bracelets can be made from 2 red beads, 2 green beads, and 2 blue beads, if two bracelets are distinct if and only ifone cannot be made into the other through rotations and reflections?
解析

英文解析

  1. [ 10 ]
    Answer: 11 We divide this problem into cases based on the relative position of the two red beads:
    Guts Round
    • They are adjacent. Then, there are 4 possible placements of the green and blue beads: GGBB,
    GBBG, GBGB, BGGB.
    • They are 1 bead apart. Then, there are two choices for the bead between then and 2 choices forthe other bead of that color, for a total of 4.
    • They are opposite. Then, there are three choices for the placement of the green beads.
    This gives a total of 11 arrangements.