Which Lockers Stay Open in Percy's Locker Challenge?

[17109007]

Percy went to a school with 900 students with exactly 900 lockers. His principal, who used to be a math teacher, met the students outside the building on the first day of school, and described the following weird plan.
The first student is to enter the school and open all the lockers. The second student will then follow the first and close every even-numbered locker. The third student will follow and reverse every third locker by closing open lockers and opening closed lockers. The fourth student will reverse every fourth locker, and so on until all 900 students have walked past and reversed the condition of the lockers. The students who can predict which lockers will remain open will get the first choice of lockers.
Percy immediately gave the principal the correct answer. Which lockers will remain open?

1. How can you make the problem simpler?
2. Make a chart showing each locker and what happens when each student past by.
3. What does each of the open lockers have in common?
4.What is special about the type of numbers that make-up the open lockers?
5. Use this information to find all of the open lockers between 1 and 900.


This is what I tried...

1. try 1 to 4 first
2.
1 2 3 4
o o o o
o c o c
o c c c
o c c o

3. square #s

4.
1 = 1*1
2= 1*2 or 2*1
3 = 1*3 or 3*1
4 = 2*2
square #s are the only ones that have an odd # of factors

5.
1,4,9,16,25, 36, 49 , 64, 81, 100, ...900




Yet I find no pattern?? Cannot find a proper solution :\ please help!

 

[sandy.bridge]

In regards to number 5, there indeed is a pattern governed by a square relationship. Does that help?

 

[tannerbk]

Try looking at more than the first 4 lockers. Like sandy.bridge said there is a square relationship. Lockers that are squares will be closed once you get to that number (you can figure out why), and will be opened on that round. Nobody will be able to close it afterwards.