# A puzzle

#### StephenPrivitera

Noting their locations I place two aces and a jack face down on a table in a row. You do not see which card is placed where. Your problem is to point to one of the cards and ask me a sinlge yes or no question, from the answer to which you can, with certainty, identify one of the three cards as an ace. If you pointed to one of the aces, I will answer your question truthfully. If you pointed to the jack, I will answer yes or no at random. Remember, you get only one question.

From the problem, I can guess that the answer to the question I ask must expose only one of the aces, for if it exposed the jack or two aces, the location of all the cards would be known, and the problem only asks to find one ace. That's not hard reasoning, but a good guess.
The problem that I run in to in this problem is that the answer to the question is ambiguous. It is difficult to distinguish between an honest answer and a false answer which are the same. I must find a question for which the answer "yes" unambiguously identifies a card as does the answer "no."

#### Inquiring_Mike

Puzzle Solved.

Hmm... I'm not sure if I'm breaking any of the rules, because i'm not sure if I understand the game... However, this is my solution.

When you ask your question, point at the card on the left hand side and ask "Is the middle card a jack?"

Therefore, if you say "no"... the possible positionings of the cards include: A A J(since you pointed at the ace, they must tell the truth)and J A A (since you pointed at the jack they could lie, therefore the jack would have to be in the left hand position)... As you can see, either way, if they say no then the middle card must be an ace.

If you say "Yes"... then the possible positionings of the cards include: A J A(since you pointed at the ace, they are telling the truth) and J A A(since you pointed at the jack they could lie meaning the left would be the jack)... leaving only the right card that has to be an ace.

I'm not sure, is this right?

#### StephenPrivitera

Yes, that's right....
Hmmm....
I feel defeated.
I was too concerned with knowing whether I was pointing to the ace of the jack. But it doesn't matter. Only the answer matters.

#### Inquiring_Mike

hehehe...... No problem. :)

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