Six people were in a house when a murder was committed in the second bedroom; from their statements, two of...
logic/murder.house New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
Six people were in a house when a murder was committed in the second
bedroom; from their statements, two of which come from liars, who did
it?
1. There is a house with: kitchen, living room, 1 bathroom, and 3
bedrooms.
2. There are 6 people in the house: John, Mary, Sam, Terry, Albert,
Sandy.
3. There is also a fresh corpse in the second bedroom.
4. When the inspector (you) arrived, he (you) asked every one 3
questions about who was where. Here are their statements:
John:
Sam was in the living room.
Mary was in the first bedroom.
I was in the kitchen.
Mary:
Sam was in the second bedroom.
Terry was in the first bedroom.
Albert was also in the first bedroom.
Sam:
I was in the living room.
John was in the kitchen.
Sandy was in the bathroom.
Terry:
John was in the kitchen.
Sam was in the living room.
Sandy was in the bathroom.
Albert:
Terry was in the first bedroom.
I was in the bathroom.
Sandy was in the kitchen.
Sandy:
Albert was in the third bedroom.
Sam was in the living room.
John was in the kitchen.
5. It is granted that: 1 of them is the murderer. 2 of them are lying.
Although any number of people could have been in any room at the same
time (even the bathroom), only one of them was present in the second
bedroom where the killing took place.
6. Any statement that someone was somewhere does not mean that someone
else wasn't there as well.
Now, who did it? This problem DOES have a UNIQUE solution.
-- Natalia Berenshteyn <natasha@pluto.sfsu.edu> ("the murder house",
first edition)
[ Editor: the first paragraph is the editor's summary. ]
Show solution
John has an alibi, he was in the kitchen as told by 3 people. Sam has an alibi, he was in the living room, this is also confirmed by 3 people. Mary is lying because she disagrees with EVERYONE on at least one point. Sandy was in the bathroom because two people say so (other than Mary). Albert is lying because he said Sandy was in the kitchen. Now that we know both liars, Albert has an alibi, he was in the 3rd bedroom as stated by Sandy. The only one left is Terry. -- Natalia Berenshteyn <natasha@pluto.sfsu.edu>