Can you find a number that lies one third of the distance between 1/3 and 2/3?

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?

There is a unique number which when multiplied by any number from 1 to 6, we will get the new number that contains the same digits only.

Can you find that number?

The more you take me, the more you leave me behind.
Who Am I?

In the given figure, move three matchsticks so that the resulting figure contains two rectangles.

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?

John was writing his first book. After saving the document, he locked his laptop with a password and mentioned some phrases for the hint box.

A friend of his tried opening his laptop but found out that it was password protected. Following is the hint that appeared.
1 mobile 3 books 2 roars 1 night 4 balls 2 lighters 1 ghost 1 hat 3 watches.

Can you help him in cracking the password?

By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.

I’m orange, I wear a green hat and I sound like a parrot. What am I?

What Adam and Eve do not have but the rest of the people have?