What is both possible and impossible at the same time?

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

If you drop me I’m sure to crack, but give me a smile and I’ll always smile back. What am I?

A girl says this to her best friend: “I was born in 1955, and I celebrated my 17th birthday last weekend.” Her best friend thinks she’s lying, but she’s actually correct. How is that possible?

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 ?

Replace each alphabet with the number (1-9) to make the below equation correct.

AB * C = DE - F = GH / I

A rain drop fell from one leaf to another leaf and lost 1/4th of its volume. It then fell to another leaf and lost 1/5th of the volume. It again fell on another leaf and lost 1/5th of the volume.



This process kept repeating till it fell on the last leaf losing 1/75th of its volume.



Can you calculate the total percentage of loss from the initial volume when the drop has fallen to the last leaf accurate up to two decimal places?

French Police inspects a room where there are no windows, no doors, no tables and is almost empty expect there is just a puddle of water. They found a dead man who obviously hung herself from the ceiling, but they are not able to figure out how this had happened.

John and Jacob entered the crime scene and easily able to solve the case.

How did the man die?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

A man in a car saw a Golden Door, Silver Door and a Bronze Door. What door did he open first?