What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

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?

Jenifer and Jesica are having a conversation.

Jenifer: I am definitely not over 30.
Jesica: I am 28 and you are surely 5 years older to me at least.
Jenifer: No, you are at least 29.

You are told that both of them are lying throughout in the conversation. Can you find their respective ages?

You have a basket containing ten apples. You have ten friends, who each desire an apple. You give each of your friends one apple.
Now all your friends have one apple each, yet there is an apple remaining in the basket.
How?

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?

Replace the question mark with the correct number below.

There was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?

You have a three-gallon and a five-gallon measuring device. You wish to measure out four gallons.

How can you tell a raw egg from a hard-boiled egg?

You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a single loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?