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问题 解答题
有n盏灯排成一排，依次标号1，2，…，n，每盏灯都有一根拉线开关，最初电灯都是关着的．现有n个人，都沿着电灯路线走过，第一个人走过时，把凡是号码是1的倍数的灯的开关拉一下；接着第二个人走过时，把凡是号码是2的倍数的灯的开关拉一下；第三个走过时，把凡是号码是3的倍数的灯的开关拉一下；…；最后，第n个人走过时，把最后那盏灯的开关拉一下．
（1）填空：
n最后第n个人走过后，哪些亮着灯的号码
10
20
（2）猜想n=100时，最后第100个人走过后，哪些亮着灯的号码．说明你猜想的理由．
答案

（1）由于最初所有电灯是关着的，所以只有哪些拉了奇数次开关的电灯才是亮的，而每一盏电灯的拉线开关被拉了多少次取决于这盏灯的编号的数字有多少个不同的正约数，最后亮着的灯的编号只有为完全平方数．所以，n=10时，只有编号为1，4，9亮着，

由于最初所有电灯是关着的，所以只有哪些拉了奇数次开关的电灯才是亮的，而每一盏电灯的拉线开关被拉了多少次取决于这盏灯的编号的数字有多少个不同的正约数，最后亮着的灯的编号只有为完全平方数．所以，n=20时，只有编号为1，4，9，16亮着；

（2）由于最初所有电灯是关着的，所以只有哪些拉了奇数次开关的电灯才是亮的，而每一盏电灯的拉线开关被拉了多少次取决于这盏灯的编号的数字有多少个不同的正约数，最后亮着的灯的编号只有为完全平方数．所以，只有编号为1，4，9，16，25，36，49，64，81，100的电灯最后是亮着的．

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Mon., Nov. 1st, 2011 1:00 P.MNew York Giants vs. Philadelphia Eagles$20~$850Mon
Nov. 1st, 2011 1:00 P.MMiami Dolphins vs. New York Jets$35~$1000Mon
Nov. 8th, 2011 4:15 P.MSam Diego Chargers vs. New York Giants$40~$1500Mon
Nov. 15th, 2011 1:00 P.MJacksonville Kaguars vs. New York Jets$21~$6100Mon
Nov. 22nd, 2011 1:00 P.MAtlanta Falcons vs. New York Giants$40~$19500Mon
Nov. 29th, 2011 1:00 P.MCarolina Panthers vs. New York Jets$10~$12000Mon
Dec. 3rd, 2011 8:20 P.MNew York Jets vs. Buffalo Bills$97~$800 
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    We conduct studies to evaluate new medications for sleep disorder.Both healthy adults and patients
suffering from insomnia are sought to participate in these studies.
You may be qualified to take part as a healthy adult volunteer if you are aged 18 or over and are willing
to have your sleep patterns recorded.Further, if you meet these standards and also suffer from a little
sleep disorder you may be able to sign our register of patients.
     Warnings:
    ☆ Always control your child when he is first learning to skateboard.To best assist a beginner, hold
one of the child's hands and guide him along a smooth and level surface.
    ☆ A safety helmet and elbow, wrist and knee pads must always be worn while your child is
skateboarding.
    ☆ Sneakers must always be worn while your child is skateboarding.Don't let your child skate in
bare feet, sandals or any other open-toed shoes.
    ☆ Never let your child skateboard in the street.
    ☆ Never tow skateboarders with a bicycle or a car.
    ☆ Skateboard only in daylight.
    Parents, there is a Tropical Paradise for kids too!
    The Pacific Islands Club knows something others don't.Kids are on holiday and they want to be
pampered (纵容), too.Our kids' Club of PIC Guam is free of charge and has both indoor and outdoor
activities ensuring a really great time to children aged 4 to 12.Open daily from 09: 00 a.m..Clubmates
will accompany children to all of the exciting play areas.They will also love to join the other children for
the special meals we have prepared just for them.
1. If you want to watch a play by New York Jets but pay the least money, you should go _____.
A. Mon., Nov.15th, 2011 1:00 P.M.
B. Mon., Nov.1st, 2011 1:00 P.M.
C. Mon., Nov.29th, 2011 1:00 P.M.
D. Fri., Dec.3rd, 2011 8:20 P.M.
2. While your child is skateboarding, you should_____.
A. lead him by the hand all the time.    
B. let him put on open-toed shoes
C. require him to skateboard at night
D. forbid him to skateboard at night.
3. We know from the text that PIC Guam______.
A. charges children the least money.
B. offers meals especially to children.
C. only has indoor activities.
D. gets children alone to go to all the play areas.
4. Which of the following is TRUE according to the text?
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单项选择题

宫内节育器的避孕原理不包括：（）

A.阻止卵子与精子的结合

B.铜离子可杀伤精子

C.引起局部炎性改变

D.干扰受精卵着床

E.干扰子宫内膜表面的生理环境
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