What is both possible and impossible at the same time?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

A quarter is one-fourth of a dollar but Mr. John has changed the equation as below :

DOLLAR * 4 = QUARTER

Can you replace each letter with a digit to make the above solution correct?

Out of three Friends John, Jacob and Jonny one of them is a king, one is a bureaucrat, and one is a Spy.

The king always tells the truth, the bureaucrat always lies, and the Spy can either lie or tell the truth.

John says: Jonny is a bureaucrat
Jacob says: John is a king
Jonny says: I am a Spy

Tell me, Who is the king, who is the bureaucrat, and who is the Spy?

What is the probability of choosing the correct answer at random from the options below?

a) 1/4
b) 1/2
c) 1
d) 1/4

In a town, there are over 100 flats.
Flat-1 is named first flat.
Flat-2 is named second flat.
Flat-3 is named third flat.

A visitors 'Victor' decides to walk through all the flats, he finds all the flats except flat-62.
Victor later founds that the local of the town have given it another name.

What is the name of the Flat?

You are in a land where thirty men and two women were dressed in classic black and white dresses.
They begin to fight as soon as any of them move.

Where are you?

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

It is an eleven letter word.
The first, second, third and fourth letters form a banquet's name.
The fifth, sixth and seventh letters form a car's name.
The eighth, ninth, tenth and eleventh letters form a mode of transport.

Can you identify what word it is?

The ages of a father and son add up to 66.
The father's age is the son's age reversed.
How old could they be?
(3 possible solutions).