I'm sure htis is a chestnut... but I'm stumped

[Macros]

Trapped in a room
Are 7 men
Holding 7 keys
To Seven doors
3 tell lies
3 tell truth
The one that you want tells both.
Seven questions you can spare.
To find out who he is and where.

What are your questions? Note that you can't direct a single question at everybody (that would be cheating), and that each man holds the key to the door he is standing next to
_________________
oh hello

[ralphmerridew]

Assuming each one will answer a question if he can:
Ask each one "Are the statements 'You always tell the truth.' and 'You will answer this question "No.".' both true or both false?"

The liars and truth-tellers will be unable to answer. The one who does answer has the right key.

[/dev/joe]

You didn't specify yes-no questions. Assuming all the men know the behavior of the other men, and without requiring questions that are unanswerable for some people:
Pick any man, and ask him how many others of the 7 men holding keys answer questions in the same way he does. If he gives any answer other than 2, he is not a truthteller, so pick another man and ask him this question (until this question has been asked four times). If the first four all give answers other than 2, pick any remaining man, who must be a truthteller, and ask him which man both lies and tells the truth.

When one of the first four men questioned says 2, ask him which two. If he indicates a man you've already questioned, the man who gave this answer is the one you want. Otherwise, ask one of the 2 indicated men how many others of the 7 men holding keys answer questions in the same way he does. If he says any number other than 2, he is a liar and the man who indicated him is the one you want. If he says 2, he is a truthteller; ask him which man both lies and tells the truth.

[ralphmerridew]

Alternate method: Three yes/no questions.
Define a person to be "consistent" if he is either always truthful or always lying.

Ask A "Are you truthful iff B, C, and D are all consistent?".

If A said "yes", then ask B "Are you truthful iff A and E are consistent? Are you truthful iff A and F are consistent?"

If A said "no", then ask E "Are you truthful iff A and B are consistent? Are you truthful iff A and C are consistent?"


Reasoning:

If you ask a consistent person "Are you truthful if and only if X?", the answer he gives will be the correct answer to "Is X true?".

If A says yes, then B, C, and D are all consistent. If he says no, then E, F, and G are all consistent. (If A is consistent, this follows from the rule above. If not, then A is the only consistent person.)

In any case, you'll have a known consistent person and have limited the suspects to four and can get the full answer in the next two questions.

[Zag]

It seems unclear to me how liars will interpret the partial statements which are part of the assorted boolean logic.

[L'lanmal]

I will try to make this as non-clever as possible, as to not confuse either myself or the seven men.

Pick three men. Ask each a patently true or false question (such as "Are you Elvis Presley?") Follow up with either "Which one of you tells both?" or "Who here is someone that does not tell both?" depending on the answer given to the first question. (I leave as an exercise to the reader which goes with which response to the first question.)

Only the one that you are looking for can dissent. If all three agree, go with the identified person obviously. You may even be able to stop after 2 people and 4 questions.


Edit: Perhaps "Are you Elvis Presley" isn't specific enough. Some people name their children weird things.

[ralphmerridew]

Okay, rephrasing: Change my key question to "Can you claim that X is true?" A consistent person will answer "yes" iff X is true.