A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six " and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said ,"ten" and the man replied, "five." But he was not let in. What was the right answer then?

Three. The doorman lets in those who answer with the number of letters in the word the doorman says.

1
11
21
1211
111221
312211
What is the next number in the sequence?

The next number it: 13112221.
Each number describes the previous number.
Starting with 1, the second line describes it 11 (one 1).
Then the third line describes 11 as 21 (two 1's).
Then the fourth line describes 21 as 1211 (one 2, one 1).
This is the pattern.

An intelligent trader travels from one place to another with 3 sacks having 30 coconuts each. No sack can hold more than 30 coconuts. On the way, he passes 30 check points. At each check point, he has to give one coconut for every sack he is carrying. What is the maximum number of coconuts that he can have with him at the end of his journey?

He will have 25 coconuts with him at the end. The trick is to reduce the number of sacks as you pass checkpoints. The first 10 checkpoints require 3 coconuts each, which empties his first sack. The next 15 checkpoints require 2 coconuts each, which will empty his second stack. Now, he is left with 1 sack and 5 more checkpoints. So, the 5 checkpoints will take 1 coconut each. Therefore, he will be left with 25 coconuts.

Alone I am 24th, with a friend I am 20.
Another friend and I am unclean.
What am I?

The letter 'X'. It is the 24th letter of the alphabet, XX in Roman numerals is 20, and XXX is a label for movies that are very inappropriate (unclean).