Math Is Fun Forum

hotgal24

Member

Registered: 2008-01-12

Posts: 4

Solve this and you are a genius

A Crime Story
An elementary school teacher had her purse stolen. The thief had to be Lilian, Judy , David, Theo, or Margaret. When questioned, each child made three statements :

Lilian :
(1)    I didn’t take the purse.
(2)    I have never in my life stolen anything.
(3)    Theo did it.

Judy :
(4)    I didn’t take the purse
(5)    My daddy is rich enough, and I have a purse of my own.
(6)    Margaret knows who did it.

David:
(7)    I didn’t take the purse.
(8)    I didn’t know Margaret before I enrolled in this school.
(9)    Theo did it.

Theo :
(10)    I am not guilty.
(11)    Margaret did it.
(12)    Lilian is lying when she says I stole the purse.

Margaret:
(13)    I didn’t take the teacher’s purse.
(14)    Judy is guilty.
(15)    David can vouch for me because he knows me since I was born.

Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Solve this and you are a genius

Assume Lilian stole the purse, that makes her first statement false, hence the other two are true, but then that means that Theo stole it. Contradiction therefore Lilian did not steal the purse.

Same argument for David and Theo and Margeret, hence neither David nor Theo nor Margeret stole it.

Hence Judy stole it

Last edited by luca-deltodesco (2008-03-25 04:57:15)

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TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: Solve this and you are a genius

Ignore Lilian's and Judy's responses altogether.  David and Margaret disagreed on when they met, which means one of them must be lying about that.  This in turn means that one of them is telling the truth about who stole the purse, narrowing it down to Judy or Theo.  Theo says that he is innocent and that Margaret took the purse, one of which must be false (it is logically impossible for his third statement to be false).  However, his second statement must be false because we've already narrowed it down to Judy and Theo, so this must mean that he's telling the truth about his innocence, which means Judy is the theif.

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Solve this and you are a genius

Consider the following pair of statements:

(i) I didn’t take the purse
(ii) Some other person did it.

If the first statement is false, then the second statement must be false as well. Since each child only made one false statement, we see that the first statement must be true if accompanied by the second statement.

Judy was the only person who made the first statement but not the second. Therefore Judy was the thief.