Solution:

The next three digits will be 138, 150 and 180.

If you analyze, you will find that all the numbers are increasing in order and are surrounded by two prime numbers.

For example, 4 is surrounded by 3 and 5; both are prime numbers.
6 is surrounded by 5 and 7; both are prime numbers.

Solution:

Here is a way to do it. We dont know if it can be done using some other arrangement or not. If you know, do send us.

4 | 3 | 8
9 | 5 | 1
2 | 7 | 6

Solution:

Put one black rock in one sack and put all the rest in the other one. In such manner you will get about 3/4 probability of surviving.

Solution:

8/(1−1/5)

Solution:

Anybody will prefer the shop in the eastern market for sure. There are two reasons for it:
Firstly, since there are only two barbers in the town, the one running the shop in eastern market must have gotten his hair done by the one running the shop in the northern market and vice versa. Thus, if the barber in the eastern market has a shabby haircut, it must be due to the incompatibility.
Secondly, the neat and clean shop can be due to the scarcity of customers as well. While the untidy place refers to the fact that so many customers get their hair done in that shop.

Thus any one will opt for the barber shop in the eastern market.

Solution:

Old password : altered

New Password : distinct

Solution:

Yes, some people are going get really tiny pieces but you were allowed for that right. Also, there is another way of doing it. Can you think of it?

Solution:

You can ask this question to any one person, "if I ask the man who is next you: which is the correct way and the road to the village, what would the person next to you answer?"
If you happened to ask this question to the liar, he will show you the wrong way.
And if you happened to ask this question to the one who says truth, he will also show you the wrong way.
Once you are done with this, take the other way. This will lead you to the village

Solution:

Steps:
1) Light fire on first bar from both the ends and second bar from one end.

2) After 30 seconds(when first bar gets completely burned out) , burn the second bar from second end as well.

3) When second run completely gets burned , you know its 45 seconds.

Solution:

Pages 19, 20, 23, 37, 38, & 42 will also be missing

Solution:

Karate Kid (car + at + tea + kid)