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# Who Dunnit?

## Question

Here's the situation.
There has been a murder in the house, and you must find who dunnit.

You ask three questions of each of six suspects, four of whom are liars.
Liars will give at least one, but not necessarily all three, incorrect answers.
One of the six is the murderer.

The house has eight rooms: Kitchen, Living Room, Bathroom, Garage, Basement, 3 Bedrooms.
Only one person (the murderer) was present in the killing room.
Any number of people could have been in any of the other rooms at the same time.

You must identify the murderer and determine which four are liars, and who was in which room.

Here are the responses to your questions:

John:

Pat was in the 2nd bedroom.
So was I.
Tim was in the bathroom.

Mary:
I agree with John that Tim was in the bathroom
and Pat was in the 2nd bedroom.
But I think that John was in the living room, OH MY GOD!

Pat:
Mary was in the kitchen
with Don.
But I was in the bathroom.

Tim:
I still say Pat was in the 2nd bedroom
and Kelly was in the bathroom.
John was in the 1st bedroom.

Kelly:
Pat was in the bathroom
with Don.
And Mary was in the kitchen.

Don:
Tim was in the kitchen.
And I was in the 2nd bedroom
with Pat.

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has to be Mary

as no one else is present in the living room according to the finding in my first post. she has to be there and be the killer
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question looks incorrect.

the informants are providing info only about who was in which room, so we can at best deduce who was where. The question assumes that by knowing who was where, we will know the murder. The only relationship between a murderer and location information is that the murderer was alone in his room. This must imply that the murderer is the ONLY person who is alone in a room, otherwise we cannot deduce the murderer from the location information alone.

Having said that, additional information on why I think so:

Assume: Pat is not in 2nd bedroom. Implies, John, Mary, Tim and Don are liars. Implies, Pat and Kelly speak truth. But they cannot be as they do not concur on Don's location. Hence our assumption is wrong and Pat is in 2nd bedroom.
Fact established: Pat in 2nd bedroom. Pat and Kelly are liars

Assume: John speaks truth. Implies, Tim is in bathroom and John in 2nd bedroom. Implies Mary and Tim are liars as they imply John is not in 2nd bedroom. Also implies, Don lies, as he says Tim is in kitchen. Hence, there are 3 new liars, totalling 5 liars, which is a contradiction.
Fact established: John is a liar

Assume: Mary speaks truth. Implies, John is in living room and Tim is in Kitchen. Implies, Tim and Don are liars. Contradiction as there are again 5 liars (including above 3 established liars)
Fact established: Mary is a liar.
Fact established: Tim and Don speak truth
Fact established: Kelly is in bathroom. John is in 1st bedroom. Tim is in kitchen. Don is in 2nd bedroom with Pat.
Mary may have or might not have been in kitchen. In any case it will leave at least two people (among Kelly, Tim and John) alone. But to infer the murderer we need only one person alone. Hence I think information is insufficient.

Edited by m00li
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Yes, the missing information is that a corpse was found in the Living Room.

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