Our product and our sum always give the same answer. Who are we?

There are three Athletes (John, Tarun and Harish) and their individual Coaches (Jacob, Meenaxi and Priyanka) standing on the shore.
No Coach trusts their Athlete to be near any other Coach unless they are also with them.
There is a boat that can hold a maximum of two persons.
How can the six people get across the river?

Cristina leaves home and then she makes exactly 3 left turns and returns home where she found 2 girls wearing the mask.

Who are these two masked girls?

Why Aeroplane windows are round?

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?

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 can a man go eight days without sleep?

You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.
How many remain now?

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 ?