What is more useful when it is broken?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

You walk into a room and see a bed. On the bed, there are two dogs, five cats, a giraffe, six cows, and a goose. There are also three doves flying above the bed. How many legs are on the floor?

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?

They are the five precious gems of an everyday sort and all can be found on a Tennis Court. Who are they?

A 52% bias toss for head using the 51% tail bias coin was done to obtain a fair result.

Can you find how bias is the floor in this case?

You have three orange, two pink and five purple balls in the drawer beside your bed. There is no electricity and the room is entirely dark. How many balls must you take out to ensure at least one ball of each colour at least?

I am thinking of a five-digit number such that:
The first and last digits are the same, their submission is an even number and multiplication is an odd number and is equal to the fourth number. Subtract five from it and we obtain the second number. Then divide into exact halves and we get the 3rd number.

What number I am thinking of?

There was a strange boy who was born before his father. How can this be possible?

The below mentioned letters have been placed in a order using a logic.

DEAD, BALL, FEAR, SHOP

Can you find the logic?