Can you find a number that lies one third of the distance between 1/3 and 2/3?

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

f you were running a race, and you passed the person in 2nd place, what place would you be in now?

If I remove one from eleven it becomes Ten and if I remove one from nine also becomes Ten. How?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

No matter how little or how much you use me, you change me every month. 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?

Cristina was born in 1888. She just had her 30th birthday today how did that happen?

I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?