Solution:

Molly

Explanation:
Let us suppose that Patrick was not in the second bedroom. This proposes that Jerry, Molly, Max and Mike are liars. It infers that Patrick and Catherine speak truth. But that is not possible as they do not coincide on Mike's location. Therefore, we are wrong with our assumption and Patrick was in the second bedroom.
So far, we have established the fact that Patrick was in the second bedroom. Additionally, Patrick and Catherine are liars

Now, let us suppose that Jerry speaks truth. This proposes that Max was in the bathroom and Jerry in the second bedroom. This infers that Molly and Max are liars as they told that Jerry was not in the second bedroom. Also it implies that Mike lied, as he said Max was in kitchen. Therefore we have three new liars now, which totals the number of liars to 5, which contradicts the given situation in the question.
Hence, now we have established the fact that Jerry is a liar.

Let us now suppose that Molly speaks truth. This proposes that Jerry was in the living room and Max was in the Kitchen. This infers that Max and Mike are liars. But again, this is contradicting the situation as we have already established the fact that there are again 5 liars (counting above 3 established liars)
Therefore, now we have established that Molly is a liar. Max and Mike speak truth. Catherine was in the bathroom. Jerry was in the first bedroom. Max was in the kitchen. Mike was in second bedroom with Patrick.

The killer has to be Molly as no one else was present in the living room.

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:

Zouma is 3 and has two footballs.
Ake is 1 and has one football.
Kalas is 4 and has three footballs.
Aina is 2 and has four footballs.

Solution:

Selfie
Explanation:
: Selfie = is six letter word
: Self = The first four letter is me.
: e = The second and last letter are the same.
: fee = The fourth second and last letter are payment.

Solution:

For this answer is 3^0, 3^1, 3^2... That is 1,3,9,27,81,243 and 729.

Solution:

192

Explanation:
I started with the number 192.
Adding the reversed 291 to 192 gave me 483.
Similarly,
483 + 384 = 867
867 + 768 = 1635
1635 + 5361 = 6996

Solution:

9 - 8 + 76 - 5 + 4 + 3 + 21 = 100


Other ways of making number 100 (withiout using number 32)
98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100
98 - 7 - 6 - 5 - 4 + 3 + 21 = 100
9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
98 - 7 + 6 + 5 + 4 - 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 + 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 - 3 + 2 + 1 = 100
98 - 7 + 6 + 5 - 4 + 3 - 2 + 1 = 100
98 - 7 + 6 - 5 + 4 + 3 + 2 - 1 = 100
98 + 7 - 6 - 5 + 4 + 3 - 2 + 1 = 100
98 - 7 - 6 + 5 + 4 + 3 + 2 + 1 = 100
9 + 8 + 76 + 5 + 4 - 3 + 2 - 1 = 100
9 + 8 + 76 + 5 - 4 + 3 + 2 + 1 = 100

Solution:

The brain teaser can be solved as shown in the image below.

Solution:

The first step that they will take will be a leap of logic. What it means is that they will deduce that every color must appear twice at least. Why? Because the master logician has assured them that the puzzle will not be impossible for anyone of them. And if a color appears only once in the circle, the person wearing it will have no clue about that color which will not be fair for him.

Then the logicians will follow the same and look for all the colors of hats in the circle. If one of them sees a color just once, he can safely assume that he is also wearing the hat of the same color as by leap of logic, no color can appear just once. Thus when the bell is rung, he will leave.

In the similar fashion, if anyone sees another color just once, he can determine that he is wearing the hat of the same color and will leave when the bell rings or will be disqualified and sent home. Unvaryingly, if a color is seen twice, they will be eliminated after the first bell. Hence, there must be at least three hats of any of the remaining color.

Assume that you are sitting in the circle and you don’t see a color once but see it twice. Then if they were the only two hats of the same color, the logicians must have left at the first bell already. But they did not. Which means that there are three hats of that color and you are wearing one. Thus you will leave after the second bell.

Solution:

'five'

Its the count of alphabet

Solution:

The young lady was presented with a bill which belonged to the elderly woman. She had asked the waiter to collect the bill from her daughter.