Question 49944: We are trying to solve for the number of lockers open.
There are 1000 lockers and 1000 students.
The first student opens every locker.
The second student closes every other locker.
The third student opens or closes every third locker.
The fourth student opens or closes every fourth locker.
This continues until all 1000 students enter and opens or closes lockers.
How many lockers are open?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! This also is a CLASSIC problem!! To do this one, you should write the numbers from 1 to 25 vertically, representing each locker. Leave space at the top of this and write the numbers of each student who is going to open and close the doors, from 1 to 25 (maybe less, since you will probably figure out the pattern way before you get to 25!).
Now, in column 1, label each door with the letter "O" for open. In column 2, label each of the even doors with the letter "C" for closed. In column 3, label the multiples of 3 with the opposite of the previous letter for the status of the door. Continue until you see a pattern emerge. I hate to give you the answer before you have a chance to do this exercise, since it is a truly GREAT discovery problem!!
You are correct that most of the doors will end up closed, but there ARE indeed many doors that will be left open, and it is a GREAT pattern!! If you try this, and want the answer, send me a note, and I'll reply by Email.
The total number of lockers open should be 31.
R^2 at SCC
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