I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

I can turn polar bears white.
I can make anyone dance.
I can make everyone cry
I can make your hands clap
I can make you thin.
I can make you smile.
I can make you smile

Can you guess the riddle?

What is the next number in this series?

4,12,84,3612....

How high do you have to count before you use the letter “a” in the English spelling of the whole number?

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

Luis Garavito killed Density x Volume.

Who is Luis Garavito ?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?

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?