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:

If you are thinking to hold one chocolate from each box in hand and then balancing weight in bare hands, you are thinking all wrong.

Let us begin by labelling boxes as 1, 2, 3 and so on till 10.

Now pick one chocolate from box 1, two chocolates from box 2, three from box 3 and so on. In total, you will have 55 chocolates now. (1 + 2 + 3 + ..... + 10)

The ideal weight of the chocolates should be 55 * 20 = 1100. However, somewhere in there are the defected chocolate/s.

You can judge that clearly by noting down the result of 1100 - total weight of chocolates. If the weight is less than 1 gram, the defected box is box 1, if the weight is less than 2 grams, the defected box is box 2 and so on.

Solution:

Girl

Explanation:
In the House P:
There can be three possibilities.
Older Younger
Boy Girl
Girl Boy
Boy Boy
Since a boy is mentioned, we can't have a Girl-Girl option. Now all these options are equally possible and thus we will take them all into account. Two of the outcome have girls as an option and thus the probability here will be 2/3.

In the House Q:
We know that the elder child is a boy and thus there can be only two possibilities:
Older Younger
Boy Girl
Boy Boy

Here, the probability of having a girl child will be 1/2.

Thus you must choose the house P as we have better probability of having a girl in that house.

Solution:

You can see how we did that in the given picture. The idea is to covert the boundaries first and then move to inner squares. If you have another solution, you can send us that or comment with it below.

Solution:

The murderer is Jack.

Christopher is the seer so exclude him.
Now, if Danny was murderer, then Garry should have been killed.
Now we know that Garry was blocked. Therefore he cannot be the murderer.
Harry can't be the killer as he was killed himself.
This leaves with Jack.

Solution:

The figure shows how we have done it. If you have any other idea in mind, feel free to comment below.

Solution:

4

Explanation:
5 = Five (four letters) => 4
7 = Seven (five letters) => 5
10 = Ten (three letters) => 3
3 = Three (five letters) => 5

Therefore, 9 = Nine (four letters) => 4.

Therefore the missing number is 4.

Solution:

2418

Explanation:
The rule that is being followed here is

P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]

Using the same rule in the incomplete equation,
7 ~ 2 ~ 7 ~ 4 = [first digit of (7 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (7 * 4)]
= 2418

Thus 2418 is the missing number.

Solution:

We have provided you with one of the possible solutions. However, there can be three more solutions to this problem.

Solution:

The figure tells that B is located to the North-East of E.