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Math Help - Problem Three

  1. #1
    Newbie Mr`Fantasy's Avatar
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    Lightbulb Problem Three

    Problem Three

    An Open And Shut Case

    In a particular corridor of a school there are 25 lockers numbered from 1 to 25.
    At recess, a class of 25 students decided to try an experiment.

    Each student is to walk along the corridor one at a time.
    • The first student will open all of the locker doors.
    • The second student will close all of the locker doors with even numbers.
    • The third will change all the locker doors with numbers that are multiples of three. This means to close any open doors and open any closed doors.
    • The fourth will change all the locker doors with numbers that are multiples of four and so on.


    1. Which locker doors will be left open after the tenth student has passed through the corridor? Explain.
    2. Which locker doors will be left open after 25 students have all passed through the corridor? Explain.
    3. If there were 1000 students are 1000 lockers which locker doors will now be left open? Explain.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Mr`Fantasy View Post
    Problem Three

    An Open And Shut Case

    In a particular corridor of a school there are 25 lockers numbered from 1 to 25.
    At recess, a class of 25 students decided to try an experiment.

    Each student is to walk along the corridor one at a time.
    • The first student will open all of the locker doors.
    • The second student will close all of the locker doors with even numbers.
    • The third will change all the locker doors with numbers that are multiples of three. This means to close any open doors and open any closed doors.
    • The fourth will change all the locker doors with numbers that are multiples of four and so on.
    1. Which locker doors will be left open after the tenth student has passed through the corridor? Explain.
    2. Which locker doors will be left open after 25 students have all passed through the corridor? Explain.
    3. If there were 1000 students are 1000 lockers which locker doors will now be left open? Explain.
    Discussed here a number of times, see this.

    RonL
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