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Question Number 848 by 123456 last updated on 25/Mar/15

in a street was two way road that leads to city A and city B, at the street you find two people, one lie and one tell truth if you can talk one question to each people only, how you go to city A?

$$\mathrm{in}\:\mathrm{a}\:\mathrm{street}\:\mathrm{was}\:\mathrm{two}\:\mathrm{way}\:\mathrm{road}\:\mathrm{that}\:\mathrm{leads}\:\mathrm{to} \\ $$$$\mathrm{city}\:\mathrm{A}\:\mathrm{and}\:\mathrm{city}\:\mathrm{B},\:\mathrm{at}\:\mathrm{the}\:\mathrm{street}\:\mathrm{you}\:\mathrm{find} \\ $$$$\mathrm{two}\:\mathrm{people},\:\mathrm{one}\:\mathrm{lie}\:\mathrm{and}\:\mathrm{one}\:\mathrm{tell}\:\mathrm{truth} \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{can}\:\mathrm{talk}\:\mathrm{one}\:\mathrm{question}\:\mathrm{to}\:\mathrm{each} \\ $$$$\mathrm{people}\:\mathrm{only},\:\mathrm{how}\:\mathrm{you}\:\mathrm{go}\:\mathrm{to}\:\mathrm{city}\:\mathrm{A}? \\ $$

Answered by prakash jain last updated on 25/Mar/15

Let us say roads are X and Y Person S (Truth) and T (lie) Q: Does road X lead to city A? Question asked to any person: E(Q)=If I ask you Q will you say YES. Assume X leads to A S′s answer to Q yes ⇒S′s answer to E(Q)=yes T′s answer to Q no ⇒ T′s answer to E(Q)=yes Assume X leads to B S′s answer to Q no ⇒S′s answer to E(Q)=no T′s answer to Q yes ⇒ T′s answer to E(Q)=no So answer ′yes′ to E(Q) by any person means X leads to A.

$$\mathrm{Let}\:\mathrm{us}\:\mathrm{say}\:\mathrm{roads}\:\mathrm{are}\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y} \\ $$$$\mathrm{Person}\:\mathrm{S}\:\left(\mathrm{Truth}\right)\:\mathrm{and}\:\mathrm{T}\:\left(\mathrm{lie}\right) \\ $$$$\mathrm{Q}:\:\mathrm{Does}\:\mathrm{road}\:\mathrm{X}\:\mathrm{lead}\:\mathrm{to}\:\mathrm{city}\:\mathrm{A}? \\ $$$$\mathrm{Question}\:\mathrm{asked}\:\mathrm{to}\:\mathrm{any}\:\mathrm{person}: \\ $$$$\mathrm{E}\left(\mathrm{Q}\right)=\mathrm{If}\:\mathrm{I}\:\mathrm{ask}\:\mathrm{you}\:\mathrm{Q}\:\mathrm{will}\:\mathrm{you}\:\mathrm{say}\:\mathrm{YES}. \\ $$$$\:\mathrm{Assume}\:\mathrm{X}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{A}\:\:\: \\ $$$$\:\:\:\:\:\:\mathrm{S}'\mathrm{s}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{Q}\:\mathrm{yes} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\mathrm{S}'\mathrm{s}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{E}\left(\mathrm{Q}\right)=\mathrm{yes} \\ $$$$\:\:\:\:\:\:\mathrm{T}'\mathrm{s}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{Q}\:\mathrm{no} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\mathrm{T}'\mathrm{s}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{E}\left(\mathrm{Q}\right)=\mathrm{yes} \\ $$$$\mathrm{Assume}\:\mathrm{X}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{B} \\ $$$$\:\:\:\:\:\:\mathrm{S}'\mathrm{s}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{Q}\:\mathrm{no} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\mathrm{S}'\mathrm{s}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{E}\left(\mathrm{Q}\right)=\mathrm{no} \\ $$$$\:\:\:\:\:\:\mathrm{T}'\mathrm{s}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{Q}\:\mathrm{yes} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\mathrm{T}'\mathrm{s}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{E}\left(\mathrm{Q}\right)=\mathrm{no} \\ $$$$\mathrm{So}\:\mathrm{answer}\:'\mathrm{yes}'\:\mathrm{to}\:\mathrm{E}\left(\mathrm{Q}\right)\:\mathrm{by}\:\mathrm{any}\:\mathrm{person} \\ $$$$\mathrm{means}\:\mathrm{X}\:\mathrm{leads}\:\mathrm{to}\:\mathrm{A}. \\ $$

Answered by malwaan last updated on 25/Mar/15

T=true F=false Q to anyone [T or F] If I ask that person which road leads to city A ; what will he say ? the right road to city a is the other road

$${T}={true}\:\:{F}={false} \\ $$$${Q}\:{to}\:{anyone}\:\left[{T}\:{or}\:{F}\right] \\ $$$${If}\:{I}\:{ask}\:{that}\:{person}\:{which}\:{road}\: \\ $$$${leads}\:{to}\:{city}\:{A}\:;\:{what}\:\:{will}\:{he}\:{say}\:? \\ $$$$ \\ $$$${the}\:{right}\:{road}\:{to}\:{city}\:{a}\:{is}\:{the}\:{other}\:{road} \\ $$

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