A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

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?

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

If we change the South-East direction into North and North-East into West and all others similarly.
Can you find out which direction will be in the place of South-West direction?

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

2 ladies and 2 girls need to cross a river in a boat big enough for 1 LADY or 2 girls. How do they do it?

A journalist was investigating a sacred cult in the jungles of Africa when he was caught by one of the person. He was confined in a cave till the leader arrived. The leader told him that he need to tell him a statement. If he thinks the statement is true, then the journalist head will be chopped off. If he thinks that the statement is false, his head will be smashed with a hammer.

What statement did the journalist make to survive?

A frog is at the bottom of a 30-meter well. Each day he summons enough energy for one 3-meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?