9th grade

A new high school has just been completed. There are 1,000 lockers in the long hall of the school and they have been numbered from 1 to 1,000. During lunch, the 1,000 students decide to try an experiment.

- The first student, student 1, runs down the row of lockers and opens every door.
- Student 2 closes the doors of lockers 2, 4, 6, 8 and so on to the end of the line.
- Student 3 changes the state of the doors of lockers 3, 6, 9, 12 and so on to the end of the line. (the student opens the door if it is closed and closes the door if it is opened)
- Studnet 4 changes the state of the doors 4, 8, 12, 16 and so on. Student 5 changes the state of every fifth door, student 6 changes the state of every sixth, and so on until all 1000 students have had a turn.

When the students are finished, which lockers doors are open?

  1. 0
asked by arianna
  1. There won't be a pattern. Take the factors of each number, include 1 and the number itself. Count the number of factors. This is the number of "state" flips. If it is even, the locker is closed. If it is odd, the locker is open.

    posted by bobpursley
  2. @bobpursley

    so you mean we have to do a factor tree for 1000 numbers?!

    posted by david
  3. Yeah, that's the tkciet, sir or ma'am

    posted by hArnoZlLt
  4. Side of a triangle are in the ratio 2:3:4 if shortest side is 45mm find the length of the the other sides

    posted by Anonymous

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algrebra

    A new high school has just been opened, with an enrollment of 1000 students. The school has 1000 lockers, numbered 1 to 1000, to accommodate them. On the first day of school all 1000 lockers are closed. The first student enters
  2. Math

    Newon Middle School has a hall with 500 lockers, all of which are closed. Five hundred students start down the hall. The first student opens every locker. The second student closes all the lockers that are multiples of 2. The
  3. Math

    Reasoning Word Problem: A school's lockers are numbered 1-100. One hundred students enter the school one at a time. The first student opens the lockers. The second student closes the even-numbered lockers. The third student either
  4. Math Word Problem(PLEASE HELP NOW)

    Reasoning Word Problem: A school's lockers are numbered 1-100. One hundred students enter the school one at a time. The first student opens the lockers. The second student closes the even-numbered lockers. The third student either
  5. Math

    A new school has exactly 1,000 lockers and 1,000 students. the student meet outside the building and decide on this plan. The first student will enter and open al the lockers. The second student will enter and colse ever locker
  6. algebra

    the new school has exactly 1000 lockers and 1000 students. on the first day of school, the students meet outside the building and agree on the following plan: the first student will enter the school and open all of the lockers.
  7. algebra

    the new school has exactly 1000 lockers and 1000 students. on the first day of school, the students meet outside the building and agree on the following plan: the first student will enter the school and open all of the lockers.
  8. math

    A school’s gym lockers are numbered from 1 to 150. How many lockers have numbers that contain the digit 6?
  9. geometry

    At Millock Highschool, there are 1,000 lockers and 1,000 students. The first day of school, all the students line up outside of the school and enter one at a time. The first student touches evry locker,the second student touches
  10. Math

    There are 50 lockers, numbered 1 throught 50, in a short hall at Phillips Middle School. Mr. Giannetti hid trears for his class in one of the lockers. He gave the class the following clues about the locker where the treats are

More Similar Questions