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

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 answer ′da′ or ′ja′ one of which means yes (you don′t know which one means yes). You are allowed to ask only one question to find which door leads to exit. What question will you ask?

$$\mathrm{There}\:\mathrm{are}\:\mathrm{2}\:\mathrm{doors}\:\mathrm{in}\:\mathrm{a}\:\mathrm{room}\:\mathrm{and}\:\mathrm{only} \\ $$$$\mathrm{one}\:\mathrm{of}\:\mathrm{them}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{exit}.\:\mathrm{There}\:\mathrm{is}\:\mathrm{one} \\ $$$$\mathrm{watchman}\:\mathrm{who}\:\mathrm{tosses}\:\mathrm{a}\:\mathrm{coin}\:\mathrm{when}\:\mathrm{you} \\ $$$$\mathrm{ask}\:\mathrm{a}\:\mathrm{question}\:\mathrm{and}\:\mathrm{speaks}\:\mathrm{truly}\:\mathrm{or}\:\mathrm{falsely} \\ $$$$\mathrm{based}\:\mathrm{on}\:\mathrm{the}\:\mathrm{toss}.\:\mathrm{Also}\:\mathrm{watchman} \\ $$$$\mathrm{gives}\:\mathrm{answer}\:'\mathrm{da}'\:\mathrm{or}\:'\mathrm{ja}'\:\mathrm{one}\:\mathrm{of}\:\mathrm{which}\:\mathrm{means} \\ $$$$\mathrm{yes}\:\left(\mathrm{you}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{which}\:\mathrm{one}\:\mathrm{means}\:\mathrm{yes}\right). \\ $$$$ \\ $$$$\mathrm{You}\:\mathrm{are}\:\mathrm{allowed}\:\mathrm{to}\:\mathrm{ask}\:\mathrm{only}\:\mathrm{one}\:\mathrm{question} \\ $$$$\mathrm{to}\:\mathrm{find}\:\mathrm{which}\:\mathrm{door}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{exit}. \\ $$$$ \\ $$$$\mathrm{What}\:\mathrm{question}\:\mathrm{will}\:\mathrm{you}\:\mathrm{ask}? \\ $$

Commented by malwaan last updated on 24/Mar/15

I think we nead 2 questions the 1st to know :ja: ; da the 2nd to know the exit

$${I}\:{think}\:{we}\:{nead}\:\mathrm{2}\:{questions} \\ $$$${the}\:\mathrm{1}{st}\:{to}\:{know}\::{ja}:\:;\:{da} \\ $$$${the}\:\mathrm{2}{nd}\:{to}\:{know}\:{the}\:{exit} \\ $$

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

Only one question is required.

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

Commented by malwaan last updated on 01/Apr/15

please solve it

$${please}\:{solve}\:{it}\: \\ $$

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

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

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

Commented by malwaan last updated on 07/Apr/15

thanks very much

$${thanks}\:{very}\:{much} \\ $$

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