问题 解答题

将分别写有数码1,2,3,4,5,6,7,8,9的九张正方形卡片排成一排,发现恰是一个能被11整除的最大的九位数.请你写出这九张卡片的排列顺序,并简述推理过程.

答案

我们知道,用1,2,3,4,5,6,7,8,9排成的最大九位数是987654321.但这个数不是11倍的数,所以应适当调整,寻求能被11整除的最大的由这九个数码组成的九位数.

设奇位数字之和为x,偶位数字之和为y.

则x+y=1+2+3+4+5+6+7+8+9=45.

由被11整除的判别法知

x-y=0,11,22,33或44.

但x+y与x-y奇偶性相同,而x+y=45是奇数,所以x-y也只能取奇数值11或33.

于是有①

x+y=45
x-y=11

解得:

x=28
y=17

x+y=45
x-y=33

解得:

x=39
y=6

但所排九位数偶位数字和最小为1+2+3+4=10>6.

所以②的解不合题意,应该排除,由此只能取x=28,y=17,987654321的奇位数字和为25,偶位数字和为20,

所以必须调整数字,使奇位和增3,偶位和减3才行.为此调整最后四位数码,排成987652413即为所求.

阅读理解

阅读理解。

  "How are you?" is a nice question. It's a friendly way that people in the

U.S.A greet each other. But "How are you?" is also a very unusual question. It's a

question that often doesn't need an answer. The person who asks "How are you?"

hopes to hear the answer"Fine", even if the person's friend isn't fine.The reason

is that "How are you?" isn't really a question and "Fine"isn't really an answer.

They are simply other ways of saying"Hello"or "Hi".

  Sometimes, people also don't say exactly what they mean. For example,

when someone Asks "Do you agree?", the other person might think, "No, I

disagree. I think you're Wrong..."But it isn't very polite to disagree so strongly,

so the other person might say"I'm not sure." It's a nicer way to say that you don't

agree with someone.

  People also don't say exactly what they are thinking when they finish talking

with other people.For example, many talks over the phone finish when one

person say "I've to go now."Often,the person who wants to hang up gives and

excuse:"Someone's at the door.""Something is burning on the stove."The excuses

might be real,or not. Perhaps the person who wants to hang up simply doesn't

want to talk any more,but it isn't polite to say that. The excuse is more polite,and

it doesn't hurt the other person.

  Whether they are greeting each other, talking about an idea, of finishing a

talk, people don't say exactly that they are thinking. It's an important way that

people try to be nice to each other, and it's part of the game of language.

1. When a person in America asks"How are you?", he or she wants to hear

"        "

A. How are you?

B. Hello

C. I don't know.

D. Fine

2. When a person disagree with someone, it is polite to say"        "

A. You are wrong.I disagree.

B. I'm not sure.

C. I'm sure I disagree.

D. No, I disagree.

3. A polite way to finish talk is to say"       "

A. You have to go now.

B. I want to hang up.

C. I have to go now.

D. I don't want to talk any more.

4. When a person says"I've to go now. Someone's at the door.", the person may

be         .

A. giving an excuse

B. hurting someone's feeling

C. ill

D. asking you a question

5. The rule of the game of language is probably       .

A. "Always say what you mean"  

B. "Don't disagree with people."

C. "Never say exactly what you're thinking."    

D. "Be polite."

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