HMMT 二月 2000 · 代数 · 第 4 题
HMMT February 2000 — Algebra — Problem 4
题目详情
英文原题
- What is the few est number 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
英文解析
- The pri e starts at $100. Clearly , the order of pri e hanges do es not matter. It isredu ed b y 10% three times ( $100 ! $90 ! $81 ! $72 : 90), and the new pri e is
$72.90. It is in reased b y 10% four times ($72 : 90 ! $80 : 19 ! $88 : 209 ! $97 : 0299 !
$106 : 73289) , and the new pri e is $106.73289. Rounded to the nearest en t, this is
$106 : 73 . 1