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?

Can you solve the below tricky visual equation?

The teacher told the student that if he told a lie then he will be expelled from school and if he told the truth then he still is expelled from school.

What can a student say to prevent his being expelled from school?

What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see?

What does the following represent?

N N N N N N N

A A A A A A A

C C C C C C C

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

My cousin lives in one story house in Antarctica. His house is made the of-of sandstone. what is the color of stairs?

A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?