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HMMT 二月 2008 · TEAM2 赛 · 第 7 题

HMMT February 2008 — TEAM2 Round — Problem 7

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 30 ] Determine the number of juggling sequences of length n with exactly 1 ball.
解析

英文解析

  1. [ 30 ] Determine the number of juggling sequences of length n with exactly 1 ball.
    Answer: 2 − 1. Solution: With 1 ball, we simply need to decide at times should thenball land in our hand. That is, we need to choose a non-empty subset of { 0 , 1 , 2 , . . . , n − 1 }
    where the ball lands. It follows that the answer is 2 − 1.n