you have 1000 lockers all shut.suppose the first student opens every locker the

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you have 1000 lockers all shut.suppose the first student opens every locker the second studentshuts every locker beginning with number 2 the third studentchanges the state of every third locker beginning with number 3 thefourth student changes the state of every fourth locker beginningwith number 4 if this continues until all 1000 students havefollowed the pattern , which lockers will be open and which will beshut at the end ? Why? After the 36 student opens/closes lockerswhich lockers are open? Which are closed? After the 100th studentopens/closes lockers which lockers are open? which are closed? Arethere any relationship among the numbers? Can you find a patternfor any number of lockers?

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