I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

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?

A 3 digit number is such that it's unit digit is equal to the product of the other two digits which are prime. Also, the difference between it's reverse and itself is 396.

What is the sum of the three digits?

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

There was an aeroplane crash, every single person died, but two people survived. How is this possible?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

A cat had three kittens: Snophy, Topsy and Jorden. What was the mother's name?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

My location can be determined by the below rebus.
So where am i ?

What runs around the whole yard without moving?