During which month do people sleep the least?

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

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

What does this rebus riddle means ?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

What two things can you never eat for breakfast?

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

A crime was committed at baker street. Ibrahim Dakota who was shot in the stomach was the main suspect. Sherlock questioned the suspect. The conversation started as:
Sherlock: What's your story, Ibrahim?
Ibrahim: I was walking around baker street and suddenly a man from the back shot me. I ran as fast as I could to save my life".
Sherlock: That is enough (and ask the police to arrest him).

Why does Sherlock think he is the murderer?

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()