I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

Three friends decide to distribute the soda cans they had among them. When all of them had drunk four cans each, the total number of cans that remained was equal to the cans each one of them had after they had divided the cans.

Can you calculate the total number of cans before distribution?

There are three light switches outside a room. One of the switches is connected to a light bulb inside the room.
Each of the three switches can be either 'ON' or 'OFF'.

You are allowed to set each switch the way you want it and then enter the room(note: you can enter the room only once)

Your task is to then determine which switch controls the bulb?

What does below science rebus mean?

Ag Ag Ag
Ag SPOON Ag
Ag Ag Ag

By including only four matchsticks in below picture, you have to make "Four Triangles And Two Squares"

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.

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

Look at the picture and find out which square is not linked with any of the other squares.

What Does this text mean:

important=important

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.