What brings you down but never up?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

Can you find out a way through which you can make five squares out of the given figure by moving just six match sticks?

In a football game, Christina defeated Teresa by 2 - 0 but no man from either side scored. How can this be possible?

A murder has been committed in a house. You are a detective and have to find out the murderer.

You investigate by asking three questions to each of the six suspects. Out of those six suspects, four are liars. It is not necessary that they speak everything a lie. But in their answers, there must be at least one lie. One of the six is the murderer.

There are eight rooms in the house in which the murder has been committed: Kitchen, Living Room, Bathroom, Garage, Basement, 3 Bedrooms.

At the time of the murder, only the murderer was present in the killing room. Any number of people can be present in any of the other rooms at the same time.

Can you identify the murderer and the four liars? Also, can you find out who was in which room?

The responses of all the suspects are mentioned below.

Joseph:
Peter was in the 2nd bedroom.
So was I.
David was in the bathroom.

Mandy:
I agree with Joseph that David was in the bathroom and Peter was in the 2nd bedroom.
But I think that Joseph was in the living room, OH MY GOD!

Peter:
Mandy was in the kitchen with Christopher.
But I was in the bathroom.

David:
I still say Peter was in the 2nd bedroom and Jennifer was in the bathroom.
Joseph was in the 1st bedroom.

Jennifer:
Peter was in the bathroom with Christopher.
And Mandy was in the kitchen.

Christopher:
David was in the kitchen.
And I was in the 2nd bedroom with Peter.

PS: The corpse was found in the Living Room.

I have some blue and red sock in my drawer. I have a total of 4 socks. I pick 2 socks and the chance that I get a pair of red socks is 1/2.

What is the chance of picking a pair of blue socks?

what does the below math rebus puzzle mean?

Evil warlock dislikes dwarfs and therefore he selects four of them and buries them. The dwarfs are buried in the ground and they are in such a way that except for their heads, their body is inside the ground. The dwarfs cannot move their body and they can view only forward. They are all buried in a line, and amongst the four, one of the dwarfs is separated by a wall. All the dwarfs are in the same direction. The last dwarfs can see two heads of friends in the front and a wall. In the last second dwarf can see one head of his friend and a wall. The second dwarf can see only the wall. The dwarf can see nothing.
Warlock comprehends the situation and tells the dwarfs that he has placed hats on their heads. There are two blue hats and two red ones. In all four dwarfs, one of them has to say what colour hat he is wearing. If the dwarf says the correct colour of the hat, they will be left free. If the answer is wrong, then they will be dug inside the ground till the very end.

What will be the answer by the dwarf and how will they answer?

A tourist visits a small town for his research. While in the town, he decides to get a haircut. Since the town is quite small, there are only two barbers in the town � one on the North Street and one on the South Street. The barbershop on the North Street is a mess and the barber has a weird and pathetic haircut. While the barbershop at the South Street is pretty tidy and the barber as well has an impressive haircut.

Which barbershop will the tourist visit for his haircut and why?

At a bar, three friends, Mr Green, Mr Red and Mr Blue, were having a drink. One man was wearing a red suit; one a green suit; and the other a blue suit. 'Have you noticed,' said the man in the blue suit, 'that although our suits have colours corresponding to our names, not one of us is wearing a suit that matches our own names?' Mr Red looked at the other two and said, 'You're absolutely correct. What colour suit is each man wearing?