2, 3, 5, 9, 17, _ What is the next number in the sequence?

Can you solve this amazing hard number series problem?
7, 8, 10, 12, 16, 18 ?

You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a single loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?

Sherlock Holmes was challenged to make a pre-drawn line smaller without erasing it. He did it in fractions of seconds. How?

Alex is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alex survive the fire? (There are no buckets or any other means to put out the fire)

We have shown you a regular water barrel as below. Without using any measuring device can you check if the barrel is more than half-filled or less than half-filled?

In the Wild West, you are challenged into a death match by two bounty hunters nicknamed Golden Revolver (GR) and Killer Boots (KB). You accept the challenge. None of you want to waste any of the bullet and so a certain rules are laid down:

1) All of you will shoot in a given order till the last man standing.
2) Each of you shoots only once upon his turn.
3) If any one of you is injured, the other two will finish him off with an iron rod.
4) The worst shooter of all (which is you) shoots first and the best one shoots at the last.

Now, how will you plan things if you know that you hit every third shot of yours, KB hits every second shot and GR hits every shot ?

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

Can you find out which options fits best with the missing column?

Write the next letter in this sequence.
O, T, T, F, F, S, S, E, __
**Hint: It is a Number Series Puzzle