What is the largest amount of money that you can possess in change and still if someone asks you for a dollar, you won't be able to give?

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?

They are three errirs in this question. Can you find them?

While sitting in the Car, John suddenly finds that one of the wheels was missing. John noticed that a killer is approaching towards him. John cannot get out of the car.

How will John escape?

Two boys wish to cross a river. The only way to get to the other side is by boat, but that boat can only take one boy at a time. The boat cannot return on its own, there are no ropes or similar tricks, yet both boys manage to cross using the boat.

How?

What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ?

1 dollar = 100 cent
= 10 cent x 10 cent
= 1/10 dollar x 1/10 dollar
= 1/100 dollar
= 1 cent

=> 1 dollar = 1 cent

solve this tricky problem?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

Which is the smallest number that you can write using all the vowels exactly once?

Can you discover the missing number in this series?

37, 10, 82
29, 11, 47
96, 15, 87
42, ?, 15