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?

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.

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

You see me once in June, twice in November, and not at all in May. What am I?

In which direction should the missing arrow point?

Mr. Buttons was all set to go to the village of Buttonland to meet his friend. So, he packed his bags and left for the village at 5 in the morning. Upon travelling on a road for miles, he came across a point where the road diverged into two. He was confused on which road to take. He gazed around and he saw two owls sitting on a branch. He thought he could ask for directions for the village from the two owls. So he went to the tree. There he saw a sign which read, "One owl always lies, and one is always truthful. They both fly away if you ask them more than 1 question."
Mr. Buttons was caught in the dilemma of what to ask? And from which owl to ask, since he only had one question. What should Mr. Buttons ask?

John went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
He went again to the parrot shop and complaint to the shopkeeper, but the shopkeeper never lied. Explain?

I am dry when I go inside, but wet when I am pulled outside.
The longer I am inside, the stronger I get
When I am completely out, I am wet and I literally sag
Who am I?

A charming young lady was approached by a kind looking old woman in a restaurant. The old woman said to her, 'You look exactly like my younger daughter. Sadly she passed away a couple of months back. Could you do me a favor and say 'Goodbye, mother' with a kind smile on your face when I leave?

The young lady agreed for the same and said, 'Goodbye, mother' when the old woman left. Soon after, she got the most disengaging shock of her life.

Can you guess what the shock was?

Which digit occurred maximum times between the number 1 and 1000?