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This puzzle is not mine, but I couldn't find an original source. I edited it somewhat.

An elementary school teacher had her purse stolen. The thief had to be Sammy, Karin, Arnold, Harry, or Liza. When questioned, each child made three statements:

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

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

Arnold:
(7) I didn’t take the purse.
(8) I didn’t know Liza before I enrolled in this school.
(9) Harry did it.

Harry:
(10) I am not guilty.
(11) Liza did it.
(12) Sammy is lying when she says I stole the purse.

Liza:
(13) I didn’t take the teacher’s purse.
(14) Karin is guilty.
(15) Arnold can vouch for me because he has known 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?

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4 Answers 4

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It is

Karin

Because

Since 15 and 8 contradict, we have two possibilities
If 15 is False
then 14 is True => then Karin stole the purse.
If 15 is True
then 8 is False
then 9 is True.
However, if 9 is true, then 10, 11 and 12 are False, and we can't have that => 14 is False. So:
Karin did it

The lies are 3, 4, 9, 11 and 15

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    $\begingroup$ Perfect ^^ Well done. that was quick tho. Should try to make more difficult ones haha $\endgroup$
    – Taacoo
    Dec 11, 2014 at 10:04
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I just figured i'd add another reasoning, because i knew without comparing any 2 peoples answers against eachother.

Everyone except Karin makes the statements: "It wasn't me" and "It was someone else" This rules all of them out automatically, since if they did do it, both would be false. So it has to be Karin.

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    $\begingroup$ Wow... Brilliant approach! $\endgroup$
    – dmg
    Nov 13, 2015 at 11:16
  • $\begingroup$ My method exactly. $\endgroup$
    – AndyT
    Nov 13, 2015 at 16:12
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Like @dmg said, the culprit is

Karin

I used a slightly different path to come to this conclusion, though:

Harry said "I am not guilty" and "Liza did it". If he is lying about being innocent, then Liza could not have done it, which would make that statement a lie as well. So Harry must not have done it.

Because Harry did not do it, we know that 9 is Arnold's lie. That means 8 is true.

Because 8 is true, 15 is a lie. That means 14 (Karin is guilty) must be the truth.

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  • $\begingroup$ +1 I started with the contradiction between Liza and Arnold, and only saw that Harry could not have done it before my edit. $\endgroup$
    – dmg
    Dec 12, 2014 at 8:06
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Karin

Reasoning:

Started from last

15 says Karin knows Liza, but in 8 Karin says she doesn't know Liza before enrollment, so one of them is wrong.

If 15 is wrong, 14 is true and Karin is guilty.

If 15 is right, obviously 8 is wrong, and 9 is right which makes Harry the thief. That means Harry's first statement (10) is false, forcing 11 (that states Liza is the thief) to be true, that makes Liza's first statement (13) false, making 14 as true that makes then Karin the thief (This makes the assumption that "15 is right" has been ruled out).

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