What is both possible and impossible at the same time?

What is next number in the pattern below:

131 517 192 123 ?

How can one talk without saying a single word?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

Before the start of the car race, John and Jacob have the same amount of fuel in their car. With this fuel, John can drive for 4 hours while Jacob can drive five hours.
After a time they realize that the amount of fuel left in John's car is 1/4th of the fuel in Jacob's.

For how long they are racing?

I have two sand hourglasses:
1. A 7 minute one and
2. An 11-minute one.

Using just these 2 sand hourglasses, how can I measure time as 15 minutes?

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

Thirty friends were on a hiking trip when they decided to enjoy the bonfire. They assembled for it and agreed to play a game. For that, they divided themselves into five teams with seven members each, forming five rows.

How did they manage to achieve this formation?

Look at the below sequence of letters and tell us what the next letter should be:

O T T F F S S ?