Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

No matter how little or how much you use me, you change me every month. What am I?

What does this rebus means ?

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 ?

You are in a room that has three switches and a closed door. The switches control three light bulbs on the other side of the door. Once you open the door, you may never touch the switches again. How can you definitively tell which switch is connected to each of the light bulbs?

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

Can you write down eight eights so that they add up to one thousand?

A woman lives in a skyscraper thirty-six floors high and is served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

A man who was outside in the rain without an umbrella or hat didn’t get a single hair on his head wet. Why?

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _