Find the next number in the sequence

1, 2, 6, 21, 88, __?

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

The barber of Town shaves all men living in the town. No man living in the town is allowed to shave himself. The barber lives in that town. Who then shaves the barber of the town?

Find the next number in the series

12, 20, 40, 72, 116, 172 ?

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

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

Can it be possible to build a house that has all its four walls facing towards the South?

What can go up a chimney down, but can’t go down a chimney up?

Which tank will fill first?

I have an eye but still cannot see.

Who am I?