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2011启智杯真题

2011启智杯真题
2011启智杯真题

2011启智杯真题

1.今天是2011年12月03日,请在20111203八个数字之间添加+、-、×、÷四种运算符号中的某些符号,使得下面等式成立。

2□0□1□1□1□2□0□3=9

2.汉字“数”、“学”、“好”分别表示不同的数字,根据下列所给算式,则“数”表示数字,“学”表示数字“好”表示数字

学好

学好

学好

学好

+学好

数字

3.“启”、“智”、“杯”各表示一个数字,同时满足下列等式:

(l )启+智+杯=22

(2 )启-智+杯=4

( 3 )启+智-杯=6

则“启”表示,“智”表示,“杯”表示。

4.有一个孤岛,那里的人们在商品交易时有如下特殊的要求:

( l )所有商品价格(单位:元)为整数,目不超过31元

( 2 )消费者支付款项时每—砷币值的钱币最多只能使用1枚,而且商家不找零钱。

问:为了保证公平交易(照实支付),至少应该生产种不同面值的钱币,请具体列举出。

5.按照下图规律,写出第四个图中x ,y ,z 所表示的三位数x= ,y= ,z= . 说明理由。

请写出你发现的规律:

第一个图 第二个图 第三个圈 第四个图

6.在同一个布袋里有红色、黄色、蓝色袜子各15只,最少要拿 只才能保证其中至少有2双颜色不同的袜子(注意:袜子不分左右)。

7.如图所示是2011

年12月份的日期,现用一矩形在日历中任意框出6个数

,请

用一个等式表示a 、

b 、

c 、

d 、

e 、

f 这6个数之间的关系。

将答案写在下列横线上:

8、如图所示是,长方形的长:宽=4:3,将该长方形划分为四个三角形,其面积分别是S 1、S 2、、S 3、S 4。若S 1=S 2、+ S 3=S 4 ,则S 2 : 、S 3 = .

9、a 、b 、c 、d 为整数,满足等式,4330

1

1

1

1=+++d

c b a 则d= 。

10、观察下面的算式:

0×0=0-0,1×31

21

31

21

,32

232

2,21121-=?-=?-=,……

根据算式反映出的规律,再写出满足这个规律的两个算式。

将答案写在下列横线上: , 。

D

C

11、半径为1的圆沿着半径为3的圆的内侧与外侧无滑动地滚动(如下图),当他们回到开始滚动的位置时:

(1)哪个圆滚动的圈数多?为什么?

(2)若点A 是内侧滚动圆上的一个定点(如左图),请在甲图中画出点A 的运动路线。

(甲) (乙)

12、有一家公司董事长从他四个得力助手中挑选一名担任策划部经理,他给他们出了一下问题;把一闲置的圆形土地平均分成四块,要求每块都与其他三块相连(即有公共边),请你在下列所给图中至少画出2个符合要求的分割方法。

13、A 、B 、C 、D 四个盒子中分别放有6,5,4,3个球,第一个小朋友找到放球最少的盒子,从其它的盒子中各取1个球放入这个盒子中,然后第二个小朋友又找到一个放球最少的盒子,从其他的盒子中各取1个球放入这个盒子中,……如此进行下去,当第2011个小朋友放完后,A 、B 、C 、D 四个盒子中的球数依次是多少个?

将答案写在下列横线上: 。

A

A

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