there are 1000 kids and 1000 lockers. the first kid opens all the lockers, the second kid closes all the even?

Question

please show your work.

Answer 1

Actually...

here are 1000 lockers (all locked) and 1000 kids, who lock the unlocked lockers and unlock the locked ones.

The first kid touches (i.e., opens) each locker. The second kid touches (i.e., locks) all even lockers.

The third kid touches (i.e., opens the locked ones and closes the unlocked ones) all lockers with number divisible by 3.

The fourth kid touches the lockers number 4, 8, 12 etc.

After the 1000th kid locks (or unlocks, if it was locked already) the locker number 1000, how many lockers are open?

ANSWER:

31 will be open (square root of 1000 is 31 point something). 31 doors had an odd number of students come along - 969 doors had an even number of students come along.

Most numbers have an even number of factors.
Example: 18 = 18 x1, 9x2, 6x3. Factors are 1, 2, 3, 6, 9, and 18.

The only exception are perfect squares. The fact that you're multiplying a number of by itself gives it an odd number of factors.

Example: 16 = 1x16, 2x8, 4x4. Factors are 1, 2, 4, 8, and 16.

Since 31 is the largest number that can be squared and still be less than 1000, there are 31 perfect squares between 1-1000 (counting 1 which only has 1 as a factor).

Answer 2

do you want me to draw a picture of what you stated? I don't get what the question is?

Answer 3

And what? Finish the problem.

Answer 4

Huh?

Answer 5

OK, interesting start. So then what happens?

Answer 6

problem statement incomplete