You are called to investigate a murder in a house. There are six suspects of the murder. The corpse was found in the living room. You begin your investigation by asking three questions to all of them. Four people among the six suspects are liars. Thus, they speak at least one lie but not necessarily all lies. It is confirmed that one of them is a murderer.
The responses of all six people are as given below:
Jerry:
Patrick was in the 2nd bedroom.
So was I.
Max was in the bathroom.
Molly:
I agree with Jerry that Max was in the bathroom and Patrick was in the 2nd bedroom.
But I think that Jerry was in the living room, OH MY GOD!
Patrick:
Molly was in the kitchen with Mike.
But I was in the bathroom.
Max:
I still say Patrick was in the 2nd bedroom and Catherine was in the bathroom.
Jerry was in the 1st bedroom.
Catherine:
Patrick was in the bathroom with Mike.
And Molly was in the kitchen.
Mike:
Max was in the kitchen.
And I was in the 2nd bedroom with Patrick.
The house accommodates eight rooms: Living Room, 3 Bedrooms, Kitchen, Bathroom, Garage and Basement. Any number of people could have been present in any of the rooms at the same time.
Can you identity the killer, the four liars and the position of each one of them during murder?
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.
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