You have broken up a ring of seven apparently identical aliens who have been plotting to blow up four planets in a solar system.
You apprehended them while they were implementing their plans, but you don’t know how far they got, so each of the planets may or may not be blowing up tomorrow. All of the aliens know which planets are safe, and which are doomed. You need to determine which planets will blow up and evacuate them, but, because evacuation is so costly, you do not want to evacuate any planets that are safe.
However, you can ask only one yes/no question of each alien, and you know that all will tell the truth except for one of them, and that one may chose to lie or not to lie, but you don’t know which one that one is. What seven questions do you ask?
Are we restricted to yes/no questions? Cause if not, I’d put them in separate rooms* and ask each one which planets are safe.
- not strictly necessary for the ones that always tell the truth, but it’s standard operating procedure for interrogations, so what the heck.
btw, ask each of them “Will you answer this question with the word ‘no’?” and watch what happens.
I’ll assume we know which four planets may or may not blow up. That is, they’re aren’t, say, twelve planets in the system, any four of which they may have been targetting.
Ask the first alien about planets 1, the seocnd about planet 2, and so on. Ask alien 5 if 1, 2 and 3 gave the correct answers. If yes, you ask the last two aliens about planet 4. If no, ask alien 6 if 1 and 2 gave the correct answers. If alien 6 says yes, ask 7 about planet 3. If no, you know either alien 1 or alien 2 lied, but not both, so ask alien 7 about either planet 1 or planet 2.
You now have enough information.
Off to MPSIMS.
-
I’d ask the first three whether it was necessary to evacuate any planets at all. If two or more said yes, then I would assume their plan was in an advanced state.
-
Assuming that it was, I’d ask the next three whether I needed to evacuate MY planet, and again, if tow or more said so, I would.
-
At this point I either have 1 or 4 questions left. I’d probably want to know about the existence of God, or more practically, whether or not to buy Cisco stock.
As for the other three planets, let them catch their own aliens.
Actually, now that I re-read this, I could ask questions of two aliens rather than three, and one or more “yes” would indicate true. Sorry.
Zenbeam’s scheme would seem to work. But how about if we add the condition that you have to formulate all 7 questions before you ask any of them? E.g. the aliens are all in a room somewhere, and you must send them your list of 7 questions which they answer in order. Only then do you receive the answers.