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HMMT 二月 2000 · 代数 · 第 4 题

HMMT February 2000 — Algebra — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. What is the few est n um b er of m ultipli ations required to rea h x from x , using only 2 4 8 16 32 previously generated p o w ers of x ? F or example, x ! x ! x ! x ! x ! x ! 64 128 256 512 1024 1536 1792 1920 1984 2000 x ! x ! x ! x ! x ! x ! x ! x ! x ! x uses 15 m ultipli ations.
解析
  1. The pri e starts at $100. Clearly , the order of pri e hanges do es not matter. It is redu ed b y 10% three times ( 100!100 !90 ! 81!81 !72 : 90), and the new pri e is 72.90.Itisinreasedby1072.90. It is in reased b y 10% four times (72 : 90 ! 80:19!80 : 19 !88 : 209 ! $97 : 0299 ! 106:73289),andthenewprieis106 : 73289) , and the new pri e is106.73289. Rounded to the nearest en t, this is $106 : 73 . 1