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1/31/2013 12:49:26 AM
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The Hardest Logic Puzzle Ever

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.
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    • Edited by Dropship dude: 1/31/2013 1:04:52 AM
      Line up the three individuals, front to back, and number them #1, #2, and #3. I'll abbreviate as you do, T for truth-teller, L for liar, and R for random answerer. (Question 1) Ask #1, "Is R immediately behind L?" If he answers yes, then either he is T and the order is TLR, or he is L and the order is LTR, or he is R and the order can be either RTL or RLT. Thus we have divided the 6 states like this: Q1 yes Q1 no ------ ----- TLR TRL LTR LRT RLT RLT RTL RTL Notice that if the answer was yes, then #2 cannot be R. So (Q2y) ask #2, "Are you R?" If the answer is yes, you know this is a lie, so #2 must be L. This leaves two possible states: TLR or RLT. To distinguish between these states, (Q3yy) ask #2, "Is #3 T?" You know he will lie, so an answer of yes means TLR, and an answer of no means RLT. If the answer to Q2y was no, then you know this is the truth, and #2 must be T, leaving two possible states: LTR or RTL. To distinguish between these states, (Q3yn) ask #2, "Is #3 L?" You know he will tell the truth, so an answer of yes means RTL, and an answer of no means LTR. If the answer to Q1 was no, then #3 cannot be R (see the table above). You can follow exactly the same procedure as above, except that you switch #2 and #3. In summary, here is a flow chart of the questions you ask: (Q1) #1, Is R immediately behind L? Yes --> (Q2y) #2, Are you R? Yes --> (Q3yy) #2, Is #3 T? Yes --> TLR No --> RLT No --> (Q3yn) #2, Is #3 L? Yes --> RTL No --> LTR No --> (Q2n) #3, Are you R? Yes --> (Q3ny) #3, Is #2 T? Yes --> TRL No --> RTL No --> (Q3nn) #3, Is #2 L? Yes --> RLT No --> LRT After three questions, we know who is who. EDIT: Wait, they speak in another language? Impossible to solve with the above solution... Must try again.

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      • Invite them all over for whiskey and xbox.

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      • Hmmmm...

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