Wednesday, September 10, 2008

The Locker Problem

This is a problem my teacher did with my 6th graders today. I remember doing this problem in college-never in high school, not to mention middle school. They were so adorable counting in their British accents. I was totally impressed with their skills. Definitely above average with critical thinking. Everyone in the class got the answer- and within minutes! They were Brilliant (if you want to use British terms)

Check it out- see if you can solve it!

Here is the famous locker problem:

Imagine you are at a school that has 100 lockers, all shut.
1. Suppose the first student goes along the row and opens every locker.
2. The second student then goes along and shuts every other locker beginning with locker number 2.
3. The third student changes the state of every third locker beginning with locker number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it.)
4. The fourth student changes the state of every fourth locker beginning with number 4.

Imagine that this continues until the 100 students have followed the pattern with the 100 lockers. At the end, which lockers will be open and which will be closed?
What is the pattern?

Post a comment if you found a solution!


Susu said...

Hey U!

I'll take a stab at half open and half shut!

Susu said...

I think the pattern is open,shut,shut,open, etc.

Taylor said...

Nice try! Not quite- Keep going!

Anonymous said...

The answer is the lockers that are open are all perfect squares (1,4,9,16,25,36,49,64,81,100). The lockers that were touched twice are all prime numbers, and the lockers touched three times are the squares of prime numbers.