The Locker Problem

The pattern is 1 open, 2 shut, 1 open, 4 shut, 1 open, 6 shut...etc
All numbers with a perfect square are open which is like 10 can go into 100 10 times, so like a square root, and a number that can be multiplied by itself to get a number.

Any other numbers are shut.
there are 31 perfect squares from 1-1000
which is like the example of a perfect square.

There are 969 lockers shut and 31 open because there are only 31 perfect squares and those were the ones that were going to be open so 1000-31=969 so then 969 lockers are going to be closed. 16, 81, and 625, are the doors that were only touched 5 times.

"The locker problem"

• Suppose the first student goes along the row and opens every locker.
• The second student then goes along and shuts every other locker beginning with locker number 2.
• 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.)
• The fourth student changes the state of every fourth locker beginning with number 4

I am going to make a small example using

4 students and 20 lockers.

1.

o

c

c

o

o

o

o

o

c

c

o

c

o

c

c

o

o

o

o

o

2.

c

c

o

c

o

c

c

o

o

o

o

o

c

c

o

c

o

c

c

o

3.

o

o

o

o

c

c

o

c

o

c

c

o

o

o

o

c

c

c

o

c

4.

o

c

c

o

o

o

o

o

c

c

o

c

o

c

c

o

o

o

o

o

O=open C=closed

I followed the steps on the locker problem,

so i started off with all of the lockers closed and did what it said i had to do.