What number comes next in this sequence:
7 8 5 5 3 4 4 _

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

The day after tomorrow will be three days before Tuesday. Can you find out what is today?

Can you divide numbers from 1 to 9 (1 2 3 4 5 6 7 8 9) into two groups so that the sum of the numbers of each group is equal?

Note: 9 cannot be turned over to make it 6.

Which number should replace the question mark?

A train full of passengers goes through a tunnel. When the train comes out from the other end, there is no single person on the train.

How did it happen?

Whats the next number in the below number sequence pattern.

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

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 ?