Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

what does the below math rebus puzzle mean?

You walk into a room that contains a match, a kerosene lamp, a candle and a fireplace. What would you light first?

A Doctor always sneezes before the rain. Doctor sneezes, Will it rain?

Give it food and it will live; give it water and it will die.

What goes through cities and fields, but never moves?

There are forty elephants and they have forty-fore heads. How can this be possible?

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?

What number when divided in half becomes zero?

A man plots the murder of his wife. His plan is full proof. Nobody saw them leaving their house. He stabbed her with a knife while driving. She died on the spot. He threw her body in a valley. He threw the knife carefully wiping his finger prints on a random garbage bin. Then he went back to his home and no one was watching him this time as well.

After an hour, he was called by the local police department who informed him that his wife was murdered. They asked him to reach the scene of crime immediately. But as soon as he arrived at the crime scene, he was arrested by them.

How did the police know that he himself is the murderer?