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HMMT 二月 2008 · TEAM2 赛 · 第 5 题

HMMT February 2008 — TEAM2 Round — Problem 5

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 10 ] Prove that 572 is not a juggling sequence.
解析

英文解析

  1. [ 10 ] Prove that 572 is not a juggling sequence.
    Solution: We are given j (0) = 5, j (1) = 7 and j (2) = 2. So f (3) = 3 + j (0) = 8 andf (1) = 1 + j (1) = 8. Thus f (3) = f (1) and so f is not a permutation of Z , and hence 572 isnot a juggling pattern. (In other words, there is a “collision” at times t ≡ 2 (mod 3).) 3