What number comes next in the series?

5 15 5 18 5 24 14 20 _

What comes
Once in a Year
Twice in a Month
4 times in a Week
6 times in a Day

Count the number of squares in the picture below.

A woman lives in a skyscraper thirty-six floors high and is served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

There once were seven dwarfs who were all brothers. They were all born two years apart. The youngest dwarf is seven years old. How old is his oldest brother?

How many words can a pen with half refill write?

I have four wings but can't fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.

Do you know what am I?

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?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?