HMMT 十一月 2012 · 冲刺赛 · 第 16 题

HMMT November 2012 — Guts Round — Problem 16

[ 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 if one cannot be made into the other through rotations and reflections?

解析

[ 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 for the 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.