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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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