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Macros
Daedalian Member

 Posted: Fri Mar 06, 2009 5:02 pm    Post subject: 1 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
Daedalian Member

 Posted: Fri Mar 06, 2009 5:46 pm    Post subject: 2 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
Daedalian Member

ralphmerridew
Daedalian Member

 Posted: Mon Mar 09, 2009 6:01 pm    Post subject: 4 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
Tired of his old title

 Posted: Mon Mar 09, 2009 6:05 pm    Post subject: 5 It seems unclear to me how liars will interpret the partial statements which are part of the assorted boolean logic.
L'lanmal
Daedalian Member

 Posted: Tue Mar 10, 2009 10:37 pm    Post subject: 6 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
Daedalian Member

 Posted: Tue Mar 10, 2009 11:52 pm    Post subject: 7 Okay, rephrasing: Change my key question to "Can you claim that X is true?" A consistent person will answer "yes" iff X is true.
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