Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

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?

In a picnic session, a footballer was practicing. During his play, he busted lips and ears and broke ribs and thighs. However, he was still able to play a professional match on the very next day.



How can this be possible?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

Find the next number in the series.
1 10 24 43 67 ?

Can you divide numbers from 1 to 9 (1 2 3 4 5 6 7 8 9) into two groups so that the sum of the numbers of each group is equal?

Note: 9 cannot be turned over to make it 6.

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

Our product and our sum always give the same answer. Who are we?

Can you place six X (crosses) in below board without making three in a row in any way ?