GeekDad Puzzle of the Week: The Case of the Shattered Window — Solution

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Photo by: BotheredByBees/FlickrPhoto by: BotheredByBees/Flickr

Photo by: BotheredByBees/Flickr

This weekend a window in the neighborhood was broken and we needed your help figuring out who was the guilty child so we could punish him or her by giving the other children ice cream. We also wanted to punish his or her parents by giving the guilty child a shot of espresso and a puppy. Congratulations to Bob for having his correct answer chosen; he will receive a $50 gift certificate from ThinkGeek! Continue reading for the puzzle and solution.

Puzzle

This weekend a window in the neighborhood was broken and we needed your help figuring out who was the guilty child. There were four children playing in the street at the time. We interrogated each of them until we received the following answers:

Robert: It was Leslie.
Leslie: Jason did it.
Jason: If Leslie says it was me, she’s lying.
Jennifer: I did not do it.

If only one of them is telling the truth, who broke the window? Why?

If only one of them is lying, who is guilty? Why?

Solution

Bob’s answer:

** If only one of them is telling the truth, that person is Jason, and
Jennifer broke the window.

Here’s why:

Assume Robert is telling the truth, and Leslie broke the window.
Jason would also be telling the truth (Leslie did say it was Jason,
and she was in fact lying), so that’s two truth tellers and this
scenario doesn’t work.

Assume Leslie is telling the truth, and Jason broke the window.
Jennifer would also be telling the truth as she did not break the
window, so again, this scenario doesn’t work.

Assume Jason is telling the truth. Leslie does in fact say it’s
Jason, and so for Jason to be telling the truth, Leslie has to be
lying, so that means Jason could not have broken the window. Jennifer
must also be lying (otherwise we have two truth tellers) and so that
would imply that Jennifer in fact broke the window. Again, by the
same logic, Robert must be lying (it’s not Leslie) and Leslie must be
lying (it’s not Jason). So, this scenario works, we can have one
person telling the truth (Jason), everyone else lying, and the person
who broke the window is Jennifer.

Assume Jennifer is telling the truth, and she did not break the
window. Everyone else has to be lying. The problem with this is that
someone had to break the window! For Robert to be lying, Leslie can’t
have broken the window. For Leslie to be lying, it can’t be Jason.
For Jason to be lying, he has to have broken the window, but that
would mean that Leslie is telling the truth, which would give two
truth tellers.

More generally, “Jason: If Leslie says it was me, she’s lying.” can be
simplified, because she does say it’s Jason, to “Leslie is lying” or
even more simplified “Jason: Leslie is lying, and I did not do it.”

It seems to me the puzzle really revolves around Jason’s statement.

** If only one of them is lying, it’s Leslie, and she broke the window.

Assume Robert is lying, and everyone else is telling the truth. The
problem with this scenario is that both Leslie and Jason cannot be
telling the truth. Leslie does say it’s Jason, so Jason is saying
Leslie is lying. For Jason to be telling the truth, Leslie has to be
lying.

Assume Leslie is lying, and everyone else is telling the truth.
Robert states Leslie did it, that works. Jason says Leslie is lying,
and that works too. Jennifer says she did not do it, that works as
well, so this scenario works. Leslie broke the window.

Assume Jason is lying and everyone else is telling the truth. This
doesn’t work as Robert and Leslie contradict each other.

Assuming Jennifer is lying and everyone else is telling the truth.
This doesn’t work at all as Jennifer would have to be the one who
broke the window, and Robert and Leslie also indicate other folks.

** Given what I know about children (I have three, aged nine, six, and
three) I’m certain Leslie broke the window. Most kids will tell the
truth all the time, except when it directly involves their own
wrongdoing. It’s rare to find more than one kid telling coordinated
falsehoods… at least at this age.

Thanks for playing! Please come back for the next puzzle. And don’t forget to take $10 off a $40 or more purchase from ThinkGeek by using the code, GEEKPUZZLER.

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