[求助]请教GWD21-7/21-17/11-3

shirleywang

gwd 21  9题

The function f is defined for each positive three digit integer n by  f(n)=2^x3^y5^z ( 2 的x次方乘以 3 的y 次方乘以5的z次方，where x,y and z are the hundreds, tens, and unit digit of n, respectively. If m and v are three-digit positive integer such that f(m)=9f(v), then m-v=?

key 20

完全没有思路。。。

gwd 21 7题

In the rectangular coordinate system, point (4,0) and (-4,0 ) both lie on circle c, what is the maximum possible value of the radius of c.

长方形和 circle 有什么关系么？

gwd 21 17题

  There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 cars red, 1 is blue, and 1 is yellow. If the cars are identical except for color （意思是相同颜色的车不能放一块?), how many different display arrangements of the 5 cars all possible?

key :20

gwd 11  3题

The sides of a square region, measured to the nearest centimeters, are 6 centimeters long. The least possible value of the actual area of the square region is ?

6cm难道不是就在说边长么？

。。。。。

hitlzc

MM下次问题目，在题目上就标明题号好了，以便后来人搜索，谢谢！

gwd 21  9题
The function f is defined for each positive three digit integer n by  f(n)=2^x3^y5^z ( 2 的x次方乘以 3 的y 次方乘以5的z次方，where x,y and z are the hundreds, tens, and unit digit of n, respectively. If m and v are three-digit positive integer such that f(m)=9f(v), then m-v=?
key 20

这道题题号好像不对吧？

因为f(m)=9f(v) ，设m的百十个位分别为X1,Y1,Z1;v的百十个位分别为X1,Y1,Z1。

则f(m)=2^(x1)3^(y1)5^(z1)=9* 2^(x2)3^(y2)5^(z2)=2^(x2)3^(y2+2)5^(z2)

所以X1=X2,Y1-Y2=2,Z1=Z2,因此M-V=20

gwd 21 7题

In the rectangular coordinate system, point (4,0) and (-4,0 ) both lie on circle c, what is the maximum possible value of the radius of c.

这道题题号好像也不对？rectangular coordinate 就是直角坐标系的意思。

应该是求最小的半径吧，最大的半径不确定啊。

open to discuss

gwd 21 17题

  There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 cars red, 1 is blue, and 1 is yellow. If the cars are identical except for color （意思是相同颜色的车不能放一块?), how many different display arrangements of the 5 cars all possible?

key :20

这道题题号也跟我所看到的21-17不同啊。

If the cars are identical except for color 的意思是除了颜色不同其他都一样，也就是说同样颜色的车不作区分。

我采用穷举法：一种是三辆红的都挨在一起，与蓝、黄排，有P(3,3)=6种排法

再一种是两辆红的在一起，另一辆不与这两辆挨着，有P(4,4)-C(2,1)P(3,3)＝12种排法

最后是三辆红的互相都不挨着，只有“红黄红蓝红”和“红蓝红黄红”两种方法。

所以共计20种。

gwd 11  3题

The sides of a square region, measured to the nearest centimeters, are 6 centimeters long. The least possible value of the actual area of the square region is ?

对，说的就是边长，但是measured to the nearest centimeters，所以这个边长范围在5.5－6.5之间。所以The least possible value of the actual area of the square region 应该是5.5^2

[此贴子已经被作者于2006-2-8 16:35:03编辑过]

hitlzc

备注：此处题号与本坛下载的题的题号有所区别，请大家注意。

shirleywang

感激版主！gwd 21 7 我再想想。

jennysxjing

gwd 21 17题

  There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 cars red, 1 is blue, and 1 is yellow. If the cars are identical except for color （意思是相同颜色的车不能放一块?), how many different display arrangements of the 5 cars all possible?

key :20

先给蓝车找个位C51，再给黄车找个位C41，余下的都是红车的，就是C51*C41=20

hitlzc

以下是引用jennysxjing在2006-2-8 18:36:00的发言：

gwd 21 17题

  There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 cars red, 1 is blue, and 1 is yellow. If the cars are identical except for color （意思是相同颜色的车不能放一块?), how many different display arrangements of the 5 cars all possible?

key :20

先给蓝车找个位C51，再给黄车找个位C41，余下的都是红车的，就是C51*C41=20

这种方法好，简单

rixianglanren

hitlzc 发表于 2006-2-8 18:41
以下是引用jennysxjing在2006-2-8 18:36:00的发言：gwd 21 17题  There are 5 cars to be displa ...

嗯，真得非常清晰明了