What number when divided in half becomes zero?

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 ?

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

what does the below rebus means?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

Be active and find the killer in the picture Riddle below.

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

On rolling two dices (six-sided normal dice) together, what is the probability that the first one comes up with a 2 and the second one comes up with a 5?

A man lives on the fifteenth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator, or if it was raining that day, he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up five flights of stairs to his apartment. Can you explain why he does this?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?