What is the next number in this matchsticks series riddle?

Can you count the number of blocks in the picture below?

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?

Can you name an animal whose killing cannot be performed without spilling your own blood?

A girl rode into a tourist spot out of the city on Thursday. She loved the place and decided to stay for a few days. She stayed for four days and then she left for back home on Thursday.

How can this be possible?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

The dirtier I get, the whiter I look. Who am I?

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.

I am not alive, but I grow; I don't have lungs, but I need air; I don't have a mouth, but water kills me. What am I?

At a party, there are five people and a whole round cake lying at the centre of the table. Only four people will make a cut and take their piece and the last one will get the remaining piece on the table. How can they make sure that everyone gets a 1/5th of the piece?