Which number should replace the question mark?

What is the riddle which can be asked all day with a different correct answer each time.

By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.

In the four images below, can you find the odd one out?

Vin Diesel is pulling a theft and has planned to run away with all the cash kept in the safe. But the only way to open the safe is the 13 character password. He has a set of five clues given to him by a trustworthy source.

Exactly two of the below statements are false.
The password is contained within this sentence.
The password is not in this hint.
The password is within only one of these statements.
At least one of the above statements is a lie.

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 ?

What number when divided in half becomes zero?

What occurs twice in a week, once in a year but never in a day?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

There are two beautiful yet remote islands in the South Pacific. The Islanders born on one island always tell the truth, and the Islanders from the other island always lie.
You are on one of the islands and meet three Islanders. You ask the first which island they are from in the most appropriate Polynesian tongue, and he indicates that the other two Islanders are from the same island. You ask the second Islander the same question, and he also indicates that the other two Islanders are from the same island.
Can you guess what the third Islander will answer to the same question?