What is the next number in the series?

15 29 56 108 208 ?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

If we change the South-East direction into North and North-East into West and all others similarly.
Can you find out which direction will be in the place of South-West direction?

Using the clues below, what four numbers am I thinking of?

The sum of all the numbers is 31.
One number is odd.
The highest number minus the lowest number is 7.
If you subtract the middle two numbers, it equals two.
There are no duplicate numbers.

Which digit occurred maximum times between the number 1 and 1000?

If you were to put a coin into an empty bottle and then insert a cork into the neck, how could you remove the coin without taking out the cork or breaking the bottle?

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?

Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

Can you find the missing letter in the sequence?
S - T - I - L - ? - T - F - Y - C

You are a cab driver who pools passengers. You pick 3 people from a destination and drop 1 after an hour. 2 people climb aboard at the same time and you drop 3 at the next destination. After some time, you pick 2 passengers only to drop 1 after a short distance where 3 more passengers climb up the cab. You leave the rest of the passengers one by one to their destination and then come back home.

Can you tell the eye color of the cab driver?