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Question Number 854 by 123456 last updated on 26/Mar/15
there a room with 3 doors, only one to exit, there are one people, you can talk to her 3 question and he only will answer you truth in only one question talking a lie in the other two question, but you dont know what the question wich he sayed the truth, how a people exit this room if possible?
$$\mathrm{there}\:\mathrm{a}\:\mathrm{room}\:\mathrm{with}\:\mathrm{3}\:\mathrm{doors},\:\mathrm{only}\:\mathrm{one} \\ $$$$\mathrm{to}\:\mathrm{exit},\:\mathrm{there}\:\mathrm{are}\:\mathrm{one}\:\mathrm{people},\:\mathrm{you}\:\mathrm{can} \\ $$$$\mathrm{talk}\:\mathrm{to}\:\mathrm{her}\:\mathrm{3}\:\mathrm{question}\:\mathrm{and}\:\mathrm{he}\:\mathrm{only}\:\mathrm{will} \\ $$$$\mathrm{answer}\:\mathrm{you}\:\mathrm{truth}\:\mathrm{in}\:\mathrm{only}\:\mathrm{one}\:\mathrm{question} \\ $$$$\mathrm{talking}\:\mathrm{a}\:\mathrm{lie}\:\mathrm{in}\:\mathrm{the}\:\mathrm{other}\:\mathrm{two}\:\mathrm{question}, \\ $$$$\mathrm{but}\:\mathrm{you}\:\mathrm{dont}\:\mathrm{know}\:\mathrm{what}\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{wich}\:\mathrm{he}\:\mathrm{sayed}\:\mathrm{the}\:\mathrm{truth},\:\mathrm{how}\:\mathrm{a}\:\mathrm{people} \\ $$$$\mathrm{exit}\:\mathrm{this}\:\mathrm{room}\:\mathrm{if}\:\mathrm{possible}? \\ $$
Answered by prakash jain last updated on 26/Mar/15
Embedded question works in this case also doors A, B nnd C. Q1: Is door A exit? E(Q1): If I ask you Q1 will you say yes. Q2: Is door B exit? E(Q2): If I ask you Q2 will you say yes. The questions E(Q1) and E(Q2) will establish A and B (hence C). So questions E(Q1) qnd E(Q2) are only 2 questions that are need.
$$\mathrm{Embedded}\:\mathrm{question}\:\mathrm{works}\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{also} \\ $$$$\mathrm{doors}\:\mathrm{A},\:\mathrm{B}\:\mathrm{nnd}\:\mathrm{C}. \\ $$$$\mathrm{Q1}:\:\mathrm{Is}\:\mathrm{door}\:\mathrm{A}\:\mathrm{exit}? \\ $$$$\mathrm{E}\left(\mathrm{Q1}\right):\:\mathrm{If}\:\mathrm{I}\:\mathrm{ask}\:\mathrm{you}\:\mathrm{Q1}\:\mathrm{will}\:\mathrm{you}\:\mathrm{say}\:\mathrm{yes}. \\ $$$$\mathrm{Q2}:\:\mathrm{Is}\:\mathrm{door}\:\mathrm{B}\:\mathrm{exit}? \\ $$$$\mathrm{E}\left(\mathrm{Q2}\right):\:\mathrm{If}\:\mathrm{I}\:\mathrm{ask}\:\mathrm{you}\:\mathrm{Q2}\:\mathrm{will}\:\mathrm{you}\:\mathrm{say}\:\mathrm{yes}. \\ $$$$\mathrm{The}\:\mathrm{questions}\:\mathrm{E}\left(\mathrm{Q1}\right)\:\mathrm{and}\:\mathrm{E}\left(\mathrm{Q2}\right)\:\mathrm{will} \\ $$$$\mathrm{establish}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\left(\mathrm{hence}\:\mathrm{C}\right). \\ $$$$\mathrm{So}\:\mathrm{questions}\:\mathrm{E}\left(\mathrm{Q1}\right)\:\mathrm{qnd}\:\mathrm{E}\left(\mathrm{Q2}\right)\:\mathrm{are}\:\mathrm{only} \\ $$$$\mathrm{2}\:\mathrm{questions}\:\mathrm{that}\:\mathrm{are}\:\mathrm{need}. \\ $$

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