Pow #2 locker vandalismLong ago,Aptos wasn’t the nice,friendly school as we know of today.One day,these wicked adolescents decided to play a trick on the principal.They decided to vandalize the school’s 1,000 lockers by opening and closing them o

Pow #2 locker vandalismLong ago,Aptos wasn’t the nice,friendly school as we know of today.One day,these wicked adolescents decided to play a trick on the principal.They decided to vandalize the school’s 1,000 lockers by opening and closing them o
Pow #2 locker vandalism
Long ago,Aptos wasn’t the nice,friendly school as we know of today.One day,these wicked adolescents decided to play a trick on the principal.They decided to vandalize the school’s 1,000 lockers by opening and closing them one after another.They had a love of mathematics,so they devised a plan to open and close the lockers in a systematic pattern.
Here was their plan:the lockers were numbered 1-1,000.The first student would start with locker #1 to open every locker.The second student would then go to locker #2 and close every other locker all the way to locker #1,000.The third student would then take her turn.Starting with locker #3,she would change the position of the door to every third locker all the way to #1,000.That is,if the door were open,she’d close it,and if it were closed,she’d open it.Then the fourth student could go to locker #4,change its position,and change its position,and change its position of every fourth locker through #1,000.This pattern continued until all 1,000 students had taken a turn.
When they finished,they looked over what they had done,hoping to see utter chaos… But they were shocked!
What did they see?
Which lockers were open and which lockers were closed?

Pow #2 locker vandalismLong ago,Aptos wasn’t the nice,friendly school as we know of today.One day,these wicked adolescents decided to play a trick on the principal.They decided to vandalize the school’s 1,000 lockers by opening and closing them o
最后打开的锁为平方数:1,4,9,16,25 ,.
关闭的锁为其他锁
因为完全平方数的因子个数为奇数,相当于奇数次打开,最后为打开的状态
而非完全平方数的因子个数为偶数,相当于偶数次打开,最后为关闭的状态

这里是他们的计划：储物柜被编号1-1,000。第一个学生将首先在更衣室＃1打开每间更衣室。第二个学生然后去更衣室＃2，关闭所有其他更衣室一直到更衣室＃1000。第三个学生，然后作出轮到她了。与更衣室＃3开始，她将改变门的位置每三更衣室一直到＃1000。也就是说，如果门都敞开着，她会关闭它，如果它被关闭，她就打开它。那么第四个学生可以去更衣室＃4，改变其立场，并改变其立场，并改变其通过＃1000每第...

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这里是他们的计划：储物柜被编号1-1,000。第一个学生将首先在更衣室＃1打开每间更衣室。第二个学生然后去更衣室＃2，关闭所有其他更衣室一直到更衣室＃1000。第三个学生，然后作出轮到她了。与更衣室＃3开始，她将改变门的位置每三更衣室一直到＃1000。也就是说，如果门都敞开着，她会关闭它，如果它被关闭，她就打开它。那么第四个学生可以去更衣室＃4，改变其立场，并改变其立场，并改变其通过＃1000每第四个更衣柜的位置。这种模式一直持续，直到所有1000名学生采取了转机。
当他们做完以后，他们看了看他们的所作所为，希望能看到一片混乱...但他们被震惊了！
他们看到了什么？
其中哪些储物柜是公开的，哪些是封闭的储物柜？

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