What is the next number in this series?

4,12,84,3612....

what does the below math rebus puzzle mean?

You need to complete the maze by entering from the entrance marked below in the figure near the yellow circle, bottom left and leaving from the exit point near the green circle, bottom middle.

Rule of Game: You can move only by exchanging green and yellow circles.

You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles, and 2 empty bowls. He then says, 'Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die.'

How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?

If a shopkeeper can only place the weights on one side of the common balance. For example, if he has weights 1 and 3 then he can measure 1, 3 and 4 only. Now the question is how many minimum weights and names of the weights you will need to measure all weights from 1 to 1000? This is a fairly simple problem and very easy to prove also.

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside.
The man said, "Oh! I am really sorry, I thought this was my room."
He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man.
What made her suspicious of that man? He might have been genuinely mistaken.

A mad serial killer kidnaps people and forces them to play the game of 2 pills with them, In this game, there are pills in the table and one of them is normal pill while the other one is deadly poisonous.
The victim will choose one pill and the killer will pick the other pill and both simultaneously will swallow the pill with water.
victim dies every time.

One day the serial killer kidnaps the Joseph and forces him to play the same game with him.

Joseph solves the mystery of the two pills and remains alive.

Explain?

Let's play a word game. Following are some meaningless words that can be completed by adding random letters on either side of the word.

For example, the word "rdo" can be formed into "pardon".

Using the same technique, can you complete the given words?
ecalc
airb
rinci
tibac
uidel
gorit
igna
eyho

You are stuck on an island where you have nothing. You find four pieces of paper somewhere on the island. What will be your strategy to escape from the island safely?

PS: No other resource is available to you on the island, neither can you build anything.

A pregnant woman is preparing to name her seventh child. Her children's names so far are Dominique, Regis, Michelle, Fawn, Sophie, and Lara. What will she name her next child -- Jessica, Katie, Abby or Tilly?