There-are-2-doors-in-a-room-and-only-one-of-them-leads-to-exit-There-is-one-watchman-who-tosses-a-coin-when-you-ask-a-question-and-speaks-truly-or-falsely-based-on-the-toss-Also-watchman-gives-answe

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Question Number 843 by prakash jain last updated on 05/Apr/15

$$\mathrm{There}\mathrm{are}2\mathrm{doors}\mathrm{in}\mathrm{a}\mathrm{room}\mathrm{and}\mathrm{only}$$$$\mathrm{one}\mathrm{of}\mathrm{them}\mathrm{leads}\mathrm{to}\mathrm{exit}.\mathrm{There}\mathrm{is}\mathrm{one}$$$$\mathrm{watchman}\mathrm{who}\mathrm{tosses}\mathrm{a}\mathrm{coin}\mathrm{when}\mathrm{you}$$$$\mathrm{ask}\mathrm{a}\mathrm{question}\mathrm{and}\mathrm{speaks}\mathrm{truly}\mathrm{or}\mathrm{falsely}$$$$\mathrm{based}\mathrm{on}\mathrm{the}\mathrm{toss}.\mathrm{Also}\mathrm{watchman}$$$$\mathrm{gives}\mathrm{answer}{}^{\prime }{\mathrm{da}}^{\prime }\mathrm{or}{}^{\prime }{\mathrm{ja}}^{\prime }\mathrm{one}\mathrm{of}\mathrm{which}\mathrm{means}$$$$\mathrm{yes}\left(\mathrm{you}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know}\mathrm{which}\mathrm{one}\mathrm{means}\mathrm{yes}\right).$$$$$$$$\mathrm{You}\mathrm{are}\mathrm{allowed}\mathrm{to}\mathrm{ask}\mathrm{only}\mathrm{one}\mathrm{question}$$$$\mathrm{to}\mathrm{find}\mathrm{which}\mathrm{door}\mathrm{leads}\mathrm{to}\mathrm{exit}.$$$$$$$$\mathrm{What}\mathrm{question}\mathrm{will}\mathrm{you}\mathrm{ask}?$$

Commented by malwaan last updated on 24/Mar/15

$$Ithinkwenead2questions$$$$the1sttoknow:ja:;da$$$$the2ndtoknowtheexit$$

Commented by prakash jain last updated on 24/Mar/15

$$\mathrm{Only}\mathrm{one}\mathrm{question}\mathrm{is}\mathrm{required}.$$

Commented by malwaan last updated on 01/Apr/15

$$pleasesolveit$$

Answered by prakash jain last updated on 05/Apr/15

$$\mathrm{Let}\mathrm{us}\mathrm{say}\mathrm{dooes}\mathrm{are}\mathrm{A}\mathrm{and}\mathrm{B}.$$$$\mathrm{Watchman}\mathrm{speaks}\mathrm{either}\mathrm{Truly}\mathrm{or}\mathrm{Falsely}.$$$$\mathrm{Q}:\mathrm{If}\mathrm{I}\mathrm{ask}\mathrm{you}\mathrm{if}\mathrm{door}\mathrm{A}\mathrm{is}\mathrm{exit}\mathrm{will}\mathrm{you}\mathrm{say}{}^{\prime }{\mathrm{ja}}^{\prime }?$$$$\mathrm{Case}1:\mathrm{Watchman}\mathrm{speaks}\mathrm{Truly}$$$$\mathrm{A}:\mathrm{exit}\mathrm{ja}:\mathrm{yes}\mathrm{Answe}:\mathrm{ja}$$$$\mathrm{A}:\mathrm{exit}\mathrm{ja}:\mathrm{no}\mathrm{Answe}:\mathrm{ja}$$$$\mathrm{A}:\mathrm{notexit}\mathrm{ja}:\mathrm{yes}\mathrm{Answe}:\mathrm{da}$$$$\mathrm{A}:\mathrm{notexit}\mathrm{ja}:\mathrm{no}\mathrm{Answe}:\mathrm{da}$$$$\mathrm{Case}2:\mathrm{Watchman}\mathrm{speaks}\mathrm{Falsely}$$$$\mathrm{A}:\mathrm{exit}\mathrm{ja}:\mathrm{yes}\mathrm{Answe}:\mathrm{ja}$$$$\mathrm{A}:\mathrm{exit}\mathrm{ja}:\mathrm{no}\mathrm{Answe}:\mathrm{ja}$$$$\mathrm{A}:\mathrm{notexit}\mathrm{ja}:\mathrm{yes}\mathrm{Answe}:\mathrm{da}$$$$\mathrm{A}:\mathrm{notexit}\mathrm{ja}:\mathrm{no}\mathrm{Answe}:\mathrm{da}$$$$\mathrm{So}\mathrm{answer}{}^{\prime }{\mathrm{ja}}^{\prime }\mathrm{from}\mathrm{Watchman}\mathrm{to}\mathrm{Q}\mathrm{will}$$$$\mathrm{indicate}\mathrm{that}\mathrm{A}\mathrm{is}\mathrm{exit}.$$

Commented by malwaan last updated on 07/Apr/15

$$thanksverymuch$$

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