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?

What number divided by 4 is the same as that number minus 4?

I am a three digit number.
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I?

Eight of us go fourth, not back, to protect our king from an attack. What are we?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

Thirty friends were on a hiking trip when they decided to enjoy the bonfire. They assembled for it and agreed to play a game. For that, they divided themselves into five teams with seven members each, forming five rows.

How did they manage to achieve this formation?

A sundial has the fewest moving parts of any timepiece. Which has the most?

I had an infinite supply of water and 5 litres and 3 litres jars.

How would you measure exactly 4 litres in the least number of steps?