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

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

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 solve the maths in the below-given picture equation?

If,
9 * 8 * 7 = 65
8 * 7 * 6 = 50
7 * 6 * 5 = 37

Find
6 * 5 * 4 = ?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

I know a country, If you remove the last alphabet of its name, it will become a part of your body. Do you name it?

If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

I have an apple tree , number of apple in this tree get doubles every week.

On 30th week , the tree gets completely filled with apples :-)



Can you tell me , on what week does my tree is half covered with apples ?

What is next number in the pattern below:

131 517 192 123 ?

The King of a distant land had heard that Birbal was one of the wisest men in the East and so desired to meet Birbal. He sent Birbal an invitation to visit his country.

In due course, Birbal arrived in the distant kingdom. When he entered the palace he was flabbergasted to find not one but six kings seated there. All looked alike. All were dressed in kingly robes. Who was the real king?

The very next moment he got his answer. Confidently, he approached the king and bowed to him.

How did Birbal know who was the real king?