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October 1, 2014

October 1, 2014

Posted by **arianna** on Sunday, November 1, 2009 at 2:51pm.

- 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?

- 9th grade -
**bobpursley**, Sunday, November 1, 2009 at 4:35pmThere 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.

- 9th grade -
**david**, Friday, January 1, 2010 at 1:33pm@bobpursley

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

- 9th grade -
**hArnoZlLt**, Tuesday, May 8, 2012 at 8:50pmYeah, that's the tkciet, sir or ma'am

- 9th grade -
**Anonymous**, Sunday, February 17, 2013 at 7:23amSide of a triangle are in the ratio 2:3:4 if shortest side is 45mm find the length of the the other sides

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