In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

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

Before Mount Everest was discovered, what was the highest mountain in the world?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

How could a baby fall out of a twenty-story building onto the ground and live?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

A word I know has six letters it contains, remove one letter and 12 remain. What is it?

Until it is measured, not known. Yet how you miss it when it has gone. What is it?

A man hijacks an aeroplane transporting both passengers(8 of them) and valuable cargo. After taking the cargo, the man demands nine parachutes, puts one of them on, and jumps, leaving the other eight behind. Why did he want eight?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?