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

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

You have two buckets - one holds exactly 5 gallons and the other 3 gallons. How can you measure 4 gallons of water into the 5 gallon bucket?

(Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

In 1990, a person is 15 years old. In 1995, that same person is 10 years old. How can this be?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

What Does this text mean:

important=important

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

Eight Chelsea player makes the following statements :

1. Seven of us are lying here.
2. Six of us are lying here.
3. Five of us are lying here.
4. Five of us are lying here.
5. Four of us are lying here.
6. Three of us are lying here.
7. My name is Torres.
8. My name is Lampard.

The last two are Lampard and Torres or maybe Torres and Lampard.
So can you deduce which of the last two is Lampard or Torres?

What is red and smells like blue paint?

John is looking at Jenifer, but Jenifer is looking at Jacob. John is married, but Jacob is not.

Is a married person looking at an unmarried person ?