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:

-3 -1 1

Explanation:
-3 * 1 * -1 = 3(prime)
-1 - (-3) = 1 -(-1) = 2

Solution:

31

Explanation:
Ramanujan lighting the candles in binary.
11110 =30
11111 =31

Solution:

What must be kept in mind before you start calculating through any method is that the weights can be put on both the pans.

So the weights - 1, 3, 7, 12, 43, 76, 102

The oldest man that can be weighed using these weights is a man aged 122 years

Solution:

This puzzle has no answer if you are considering this figure in a 2d domain. However if you follow it on a three-dimensional plane, you can do it like shown in the figure given.

Solution:

1

Explanation:
4 + 9 = 1
The trick to solve is to assume the first number as the time in AM and the second number is the number of hours you have to add to it. You'll find the time in PM when you do that.

For example
7 AM + 7 hours = 14:00 or 2 PM

4 AM + 9 hours = 13:00 or 1 PM.

Solution:

It can be solve as shown below.

Solution:

The mules is moving in circular path and hence outside legs travels more distance than inner legs.

Solution:

Four

As the window was closed it is obvious that the six candles that were not extinguished were lit till they melted away entirely. Thus only four candles that were extinguished remain at the end.

Solution:

A
D
C
A
B

Solution:

Ms. Britney did it.

We will take up every person and analyze the statements over all of them one by one.

Case 1: Ms. Britney did it, then
Statement 1 => true
Statement 2 => false (as Rihanna did not do it)
Statement 3 => false (as Ms. Britney is lying)
Statement 4 => false (as Ms. Gwyneth is lying)
Our first guess itself was right but let us confirm our analysis by analyzing the statements over others.

Case 2: Ms. Rihanna did it, then
Statement 1 => false (as Ms. Britney did not do it)
Statement 2 => true
Statement 3 => true (as Ms. Britney is not lying)
As per the conditions, three statements had to be wrong but here, we have two statements right which clearly contradict the condition.

Case 3: Ms. Gwyneth did it, then
Statement 1 => false (as Ms. Britney did not do it)
Statement 2 => false (as Ms. Rihanna did not do it)
Statement 3 => false (as Ms. Britney is lying)
Statement 4 => false (as Ms. Gwyneth is lying)
She did not do it as all the statements are false.

Case 4: Ms. Yoon did it, then
Statement 1 => false (as Ms. Britney did not do it)
Statement 2 => false (as Ms. Rihanna did not do it)
Statement 3 => false (as Ms. Britney is lying)
Statement 4 => false (as Ms. Gwyneth is lying)
All four statements are false in her case as well thus she did not do it.

Therefore we have proved that Ms. Britney did it.