Explore BrainMass

Explore BrainMass

    Number Patterns : Door Problem

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A school had a very unusual tradition involving its 1000 students and its 1000 lockers. On opening day, after the head of the school had closed all the lockers, a student walked by and opened every single one. A second student then closed every second one (#2, 4, 6, 8 etc). A third student then changed every third locker (#3,6,9,12 etc), that is, she opened the ones that were closed and closed the ones that were open. A fourth student then changed every fourth locker, after which a fifth student changed every fifth locker , and so on until all 1000 students had passed by all 1000 lockers. At the end of this strange activity, which lockers were open?

    © BrainMass Inc. brainmass.com February 24, 2021, 2:16 pm ad1c9bdddf
    https://brainmass.com/math/combinatorics/number-patterns-door-problem-11032

    Solution Preview

    A school had a very unusual tradition involving its 1000 students and its 1000 lockers. On opening day, after the head of the school had closed all the lockers, a student walked by and opened every single one. A second student then closed every second one (#2, 4, 6, 8 etc). A third student then changed every third locker (#3,6,9,12 etc), that is, she opened the ones that were closed and closed the ones that were open. A fourth student then changed every fourth locker, after which a fifth ...

    Solution Summary

    A door problem is solved. The expert examines number patterns.

    $2.19

    ADVERTISEMENT