reasoning Maths Puzzle undefined

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

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reasoning Other Question
There is one and only one Dracula
This Dracula is locked in three and only three caskets
One is solid red, one is solid yellow, one is solid blue
The caskets have inscriptions
Red says, Dracula is here (meaning inside the casket)
Yellow says, Dracula is not here (not inside the casket)
Blue says, Dracula is not in the red casket
At most one inscription is true

Where must Dracula be I want to weigh 10 people. What is the minimum number of times I must use the scale?