# Who stole the jam?February 17, 2005 8:27 PM   Subscribe

I need help solving a logic puzzle.

My fiance was given a reading assignment, which included a riddle. Both of us have tried and failed to solve it, and google has been no help. Oh AskMe, please bestow your wisdom and tell me: Who stole the jam?

The riddle:
``How about making us some nice tarts?" the King of Hearts asked the Queen of Hearts one cool summer day.

``What's the sense of making tarts without jam?" said the Queen furiously. ``The jam is the best part!"

``Then use jam," said the King.

``I can't!" shouted the Queen. ``My jam has been stolen!"

``Really!" said the King. ``This is quite serious! Who stole it?"

``How do you expect me to know who stole it? If I knew, I would have had it back long ago and the miscreant's head in the bargain!"

Well, the King had his soldiers scout around for the missing jam, and it was found in the house of the March Hare, the Mad Hatter, and the Dormouse. All three were promptly arrested and tried.

``Now, now!" exclaimed the King at the trial. ``I want to get to the bottom of this! I don't like people coming into my kitchen and stealing my jam!"

``Did you by any chance steal the jam?" the King asked the March Hare.

``I never stole the jam!" pleaded the March Hare.

``What about you?" the King roared to the Hatter, who was trembling like a leaf. ``Are you by any chance the culprit?" The Hatter was unable to utter a word; he just stood there gasping and sipping his tea.

``If he has nothing to say, that only proves his guilt," said the Queen, ``so off with his head immediately!"

``No, no!" pleaded the Hatter. ``One of us stole it, but it wasn't me!"

``And what about you?" continued the Kind to the Dormouse. ``What do you have to say about all of this? Did the March Hare and the Hatter both tell the truth?"

``At least one of them did," replied the Dormouse, who then fell asleep for the rest of the trial.

As subsequent investigation revealed, the March Hare and the Dormouse were not both speaking the truth. Who stole the jam?
posted by thewittyname to Grab Bag (17 answers total) 1 user marked this as a favorite

This is rather revealing...
posted by Specklet at 8:34 PM on February 17, 2005

Theory 1: The Mad Hatter or the Dormouse stole it.
Theory 2: The March Hare, the Dormouse, or the Mad Hatter stole it.

These are the two claims made which we have a logical conclusion for. Both (or one of) are not true. If neither was telling the truth, it was not the Mad Hatter or the Dormouse, as they appear in both theories. Therefore, it was the March Hare. That's my guess anyway, probably wrong!
posted by wackybrit at 8:37 PM on February 17, 2005

It can only be the Hare..
posted by rajbot at 8:38 PM on February 17, 2005

Ha!

I recognized the source of that puzzle right away! Its from Raymond Smullyan's Alice in Puzzleland!

Here's another and a whole book of them.

The answer to the posed question is not hard. Just work through the different cases.
posted by vacapinta at 8:45 PM on February 17, 2005

If the Doormouse is telling the truth, then the Hare is lying so he had to stolen the jam. If the Doormouse is lying then neither the Hare nor the Hatter is telling the truth. That would imply that both the Hare and the Hatter stole the jam together, which seems wrong somehow. Off with the Hare's head!
posted by aspo at 8:47 PM on February 17, 2005

The March Hare stole it with one or more accomplices.

We know that the Dormouse was lying, so it must be true that neither the March Hare nor the Mad Hatter was telling the truth (since the Dormouse's claim "at least one of them is telling the truth" is equivalent to "one or both of them is telling the truth", the only other option, if the Dormouse was lying, is that neither of them was telling the truth).

The Mad Hatter says "one of us stole it, but it wasn't me". If two of them stole it, that would be falsified. It would also be falsified if all three of them stole it, or if only the Mad Hatter stole it.

The March Hare says he didn't steal the jam, so he must have stolen the jam.

So the question is: was it the March Hare and the Hatter, the Hare and the Dormouse, or all three?
posted by kenko at 8:48 PM on February 17, 2005

(The following assumes only one culprit)

If the March Hare told the truth:
- March Hare told the truth and didn't steal the jam.
- Doormouse didn't tell the truth, and for Doormouse's statment to be false, both Mad Hatter and March Hare must be lying.
- But this is illogical, because part of the stipulation of this solution is that March Hare is telling the truth.
- Therefore this solution is no good.

If the Doormouse told the truth:
- For Doormouse's statement to be true, at least one or the other of March Hare and Mad Hatter is telling the truth.
- But it is stipulated that both Doormouse and March Hare cannot be telling the truth at the same time.
- Therefore Mad Hatter is telling the truth, and he didn't steal the jam.
- And March Hare is lying, so he did steal the jam.

So, March Hare stole the jam.

I think.
posted by falconred at 8:55 PM on February 17, 2005

(oh, and because Mad Hatter's statement in theory #2 is true: "one of us stole it, and it wasn't me", March Hare acted alone and not with the aid of Doormouse)
posted by falconred at 8:58 PM on February 17, 2005

The problem can be solved if we only have one culprit.
I vote Hare did it.

Dormouse can only be true; either he stole it -therefore one of the others tells the truth; or he didn't and again one of the others tells the truth.

oh! I don't have to check preview. I am sure someone beat me to it....
posted by carmina at 9:01 PM on February 17, 2005

If the Dormouse is lying, then neither of the others told the truth, and thus:

a) the March Hare stole the jam

b) none of them stole the jam, and the Mad Hatter stole the jam

If the March Hare is lying:

a) the March Hare stole the jam
___________________________________

"B" in the first case isn't possible, so the March Hare is lying, and took the jam.
posted by taz at 9:12 PM on February 17, 2005

As subsequent investigation revealed, the March Hare and the Dormouse were not both speaking the truth. Who stole the jam?

If you interpret this to meant that one of them was lying and one was telling the truth, then the Hare acted alone. If you allow that this may mean both are lying, then the Hare and the Hatter definitely did it, with the Dormouse either helping or not.

Either way, the Hare was definitely involved.
posted by 23skidoo at 9:17 PM on February 17, 2005

A: March Hare: "I never stole the jam!"
B: Mad Hatter: "One of us stole it, but it wasn't me!"
C: Dormouse: "At least one of them is telling the truth." (As in, either or both the Hare and the Hatter are telling the truth.)

(negations/untruths)
~A: The March Hare stole the jam.
~B: The Mad Hatter stole the jam.
~C: Neither the Hare nor the Hatter told the truth.

The untruth of C necessitates the untruth of A. If the Hare claims to not have stolen the jam and this is true, and the Dormouse says at least one of them is telling the truth and this is untrue, meaning none of them are telling the truth, then it is an impossible situation.

However if A is untrue (meaning the Hare really did steal the jam) and C is true, to fulfill the condition of "at least one" of them speaking the truth means that either the Hatter and the Hare are both speaking the truth (implying that the Dormouse did it), or only one of them is. Since we are stipulating the untruth of the Hare's statement in this case, then it is the Hatter's statement that must be true. So, if he says he didn't do it, there can be only one conclusion.

The March Hare stole the jam.
posted by Lush at 9:44 PM on February 17, 2005

falconred, you're right, but you can actually stop sooner. Once you realize your assumption (Hare's telling the truth) leads to an impossibility, you know your assumption is false. Therefore, the hare is lying, and he stole it.
posted by knave at 9:49 PM on February 17, 2005

knave, yeah I know, but I was trying to be clear and/or exhaustive.
posted by falconred at 9:53 PM on February 17, 2005

I think it was the doormouse, and they're all telling the truth.

The March Hare says he didn't steal it.
The Mad Hatter says that one of them did, but that it wasn't him.
The Doormouse says that at least one of them is telling the truth.

So if both of them are telling the truth, the doormouse stole it.
posted by armoured-ant at 2:34 PM on February 18, 2005

I think it was the doormouse, and they're all telling the truth.

They can't be. The last line of the problem states, " As subsequent investigation revealed, the March Hare and the Dormouse were not both speaking the truth".
posted by vorfeed at 2:51 PM on February 18, 2005

Ah.
posted by armoured-ant at 2:58 PM on February 18, 2005

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