Which number should replace the question mark?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

John is asked to stand behind Jacob and Jacob is asked to stand behind John. Both of them feel confused about it and don't know what to do?

But it is quite possible, do you know how?

If one and a half boys, eat one and a half burgers in one and a half hours.

How many burgers can 9 boys eat in 3 hours?

What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see? What is it?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

You board a train. The train will have to enter a tunnel soon. You are claustrophobic. Which place is the best for you to sit?

Can you find out which triangle will have a bigger area among the following?
1. A triangle with sides 300, 400 and 500
2. A triangle with sides 300, 400 and 700