A strange tree in a town has a certain number of long branches and short branches.Each year,a quarte

题目

A strange tree in a town has a certain number of long branches and short branches.Each year,a quarter of the number of short branches are lost as they become long branches.However,this would lead to the tree growing too many long branches,so the people living in the Town decided to chop off 2 long branches at the end of each year.At the beginning of 2010,the tree had 4 long branches and 64 short branches.If the tree also double the number of short branches at the beginning of each year,how any more short branches than long branches would there be at the beginning of year 2012?( the answer is 104)

答案

我先把题目写一遍,后面看着方便：一棵树有一定数量的长树枝和短树枝.每年,1/4的短枝会变成长枝.然后,这导致树长得太快,所以人们决定每年底砍掉2个长枝.在2010年初,这棵树有4个长枝和64个短枝.如果每年初树的短枝数量会翻倍,那么在2012年初短枝比长枝多多少?
根据题意列出下表
长 短
2010初 4 64 题目告诉的初始量
2010末 4-2=2 64 年末,长枝砍掉2个,短枝不变
2011初 2+64/4=18 (64-64/4)*2=96 第二年,短枝的四分之一变为长枝.所以短枝就变为48个,再翻倍
2011末 18-2=16 96 第二年末,长枝砍2个,短枝不变
2012初 16+96/4=40 (96-96/4)*2=144 第三年,短枝的四分之一变为长枝.所以短枝就变为72个,再翻倍answer:144-40=104