题干

设m,n(3≤m≤n)是正整数,数列Am:a1,a2,…,am,其中ai(1≤i≤m)是集合{1,2,3,…,n}中互不相同的元素.若数列Am满足:只要存在i,j(1≤i<j≤m)使ai+aj≤n,总存在k(1≤k≤m)有ai+aj=ak,则称数列Am是“好数列”.

(Ⅰ)当m=6,n=100时,

(ⅰ)若数列A6:11,78,x,y,97,90是一个“好数列”,试写出x,y的值,并判断数列:11,78,90,x,97,y是否是一个“好数列”?

(ⅱ)若数列A6:11,78,a,b,c,d是“好数列”,且a<b<c<d,求a,b,c,d共有多少种不同的取值?

(Ⅱ)若数列Am是“好数列”,且m是偶数,证明:

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答案(点此获取答案解析)

解:(Ⅰ)(ⅰ)∵m=6,n=100,数列A6:11,78,x,y,97,90是一个“好数列”,

∴x=89,y=100,或x=100,y=89,

数列:11,78,90,x,97,y也是一个“好数列”.

(ⅱ)由(ⅰ)可知,数列必含89,100两项,

若剩下两项从90,91,…,99中任取,则都符合条件,有 <

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Tips for Upcoming Senior Two

    People often describe Senior Two as a year with “much more homework, more frequent exams and more fierce competitions”.____

    ⒈Manage your time carefully and make full use of it.

    Try to study not hard but efficiently. Make a to-do-list for your time after school. Don't just spend quite a long time on only one subject.____Remember to take breaks when you feel exhausted.

    ⒉Treat Competition in Class in a right way.

    Don't treat your classmates as potential(潜在的)enemies. Competition cannot be avoided, but everyone wants to study and live in a friendly environment.____By helping others solve problems, you inspire others, enrich your own knowledge and gain lasting friendship.

    ⒊____

    Don't let your former rankings limit you. What really matters is how you treat exams and ranking. Forget the class ranking or grade rankings, but compete with yourself. In a while, you will see yourself climbing in scores and rankings.

    All in all, the coming new school year is sure to be full of challenges. Too much worry only adds to your difficulties in your development.____Wish you the best of luck in the new academic year!

A. Learn for yourself, not for others.

B. Have a right attitude towards your rankings.

C. Good time management skills are very important.

D. Instead, divide the hours into small periods for different subjects

E. When you prepare for the battle, some advice from me may be of help

F. So when they turned to you for help, just share your wisdom immediately

G. If you keep my advice in mind, you will achieve a lot and lead a happy life.

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