Solution:

First Case:
The possible combinations of the adjacent bullets placed in the chambers are:
1, 2
2, 3
3, 4
4, 5
5, 6
6, 1

Now if you don't spin the barrel:
The first shot was empty and thus the combinations of (6, 1) and (1, 2) surely don't have bullets. This means that the bullets are present in some other possible 4 slots.

Therefore P (Death) = 1/4 = 0.25
P (Survival) = 3/4 = 0.75

If you chose to spin the barrel:
P (Death) = 2/6 = 1/3 = 0.33
P (Survival) = 4/6 = 2/3 = 0.77

Therefore you must not ask to spin the barrel and you will have a better chance at surviving.

Second Case:
If you don't spin it:
You were not hit in the first shot. Thus,
P (Death) in second hit = 2/5 = 0.4
P (Survival) in second hit = 3/5 = 0.6

If you spin the barrel
P (death) in the second hit = 2/6 = 1/3 = 0.33
P (Survival) in second hit = 4/6 = 2/3 = 0.77

Thus in this case, you have better survival rate if you chose to spin the barrel.

Solution:

The three errors are as follows:
a) fynd is spelled wrong. The correct spelling is 'find'.
b) that is not appropriate to use here. It should be 'this'.
c) There are only two errors in the question and that is the third error because the questions asks us to find three.

Solution:

You can see how we did it in the given picture.

Solution:

60

Explanation:
You can encode MM in the first digit leaving the bottom segment MM (6^2=64>=60).
You will need some order so that they can represent the MM in binary.
Every single element of the display is a binary digit:
"On"=1
"Off"=0

Now, the seconds can be encoded in the similar fashion by using the second digit.

You can now use the remaining four elements of display (two bottom segments and two dots) to encode HH (4^2=16>=12).

Solution:

Donald had divorced his wife and had remarried. The doctor had operated on his ex-wife.

Solution:

The stranger said that he thought the room was his. If so, he must have had the keys to the room and thus he must not have knocked.

Solution:

Bob hacked the server.

You can solve this mystery by assuming every one of them as a hacker turn wise. Suppose Timothy is the hacker. Then, his first and last statement will be lies. But that cant be true as he can speak just one lie.

You will find the same result while assuming Christopher, Maggie and Beatrice as the hackers but will see that while assuming Bob as the hacker, only his first statement is false.

Thus Bob is the hacker.

Solution:

This is what Birbal said after bowing in front of the real king:
"Your majesty, the other kings were watching you closely in order to imitate you accurately while you were sitting with your calm and composed demeanor. This is how I found out that you are the real king."

His Quick wit flabbergasted the king and he was rewarded with luxurious gifts and jewels in return.

Solution:

22

Its is sequence of prime numbers and adding 5 to theb number

As we know, 1st seven Prime numbers are :
2 , 3 , 5 , 7 , 11 , 13 , 17

Adding 5 to each number =>
7 , 8 , 10 , 12 , 16 , 18 , 22(Ans)

Solution:

In such questions, the best thing is to assume each one of them as his sister till you can find all the conditions fulfilled. According to our assumptions, Megan is Alex's sister. We will discuss only this case therefore.

Assuming that Megan is Alex's sister, she has told a lie. This also means that Maggie is not Alex's girlfriend.
If Katie is the truth speaking girl, Megan is lying and it proves our assumption.
Now, if Charlize is Alex's girlfriend, she has also told a lie. This further tells that Katie is speaking the truth which also supports our assumption.
Maggie stated that Charlize is not his sister and that is also true because according to our assumption, Charlize is his girlfriend.

Taking that into account, we can conclude that Megan is Alex's sister and Charlize is his girlfriend.

In any other assumption, you will find the data conflicting with the conditions.