Find the next number in the sequence

1, 2, 6, 21, 88, __?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

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

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

Can you spot what's wrong with the following sentence?

PETER WAS ANGRY AT
HIMSELF BECAUSE HE
ACCIDENTALLY LEFT THE
THE KEYS TO HIS CAR
AT HIS FRIEND'S HOUSE.

A boy was driving a car, a girl took a lift from her. She asked his name. The boy said - my name is hidden in my car’s number, find it if you can. After this, she got down Car number was [ WV733N ] Can you guess the name now?

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

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

Sweet & very intelligent katty has 8 puppets(Jane Bird Barbie Angel Colleen Nora Lass Missy).
All puppets are of different size. She arrange all puppets to face towards the guest and tell the guess the following clues :

* Jane has three puppets bigger on its left side
* Bird has two puppets smaller on its left side
* Barbie has one puppet bigger on its right side
* Angel has two puppets smaller on its right side
* Colleen has one puppet bigger on its left side
* Nora has one puppet smaller on its left side
* Lass has four puppets bigger on its right side
* Missy has three puppets smaller on its right side

Also some puppets are inside the bigger puppets.

Assuming you are the guest , can you tell the katty how the puppets are arranged ?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?