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Question Number 902 by 123456 last updated on 18/Apr/15

X is a person that can only one of these  a.only tell truth  b.only tell lie  using a minimal number of question  how to discover what type of people  are X?

$$\mathrm{X}\:\mathrm{is}\:\mathrm{a}\:\mathrm{person}\:\mathrm{that}\:\mathrm{can}\:\mathrm{only}\:\mathrm{one}\:\mathrm{of}\:\mathrm{these} \\ $$$$\mathrm{a}.\mathrm{only}\:\mathrm{tell}\:\mathrm{truth} \\ $$$$\mathrm{b}.\mathrm{only}\:\mathrm{tell}\:\mathrm{lie} \\ $$$$\mathrm{using}\:\mathrm{a}\:\mathrm{minimal}\:\mathrm{number}\:\mathrm{of}\:\mathrm{question} \\ $$$$\mathrm{how}\:\mathrm{to}\:\mathrm{discover}\:\mathrm{what}\:\mathrm{type}\:\mathrm{of}\:\mathrm{people} \\ $$$$\mathrm{are}\:\mathrm{X}? \\ $$

Answered by prakash jain last updated on 18/Apr/15

Only one question is needed.  Q: If I ask you ′Do you speak Truth′ will           you say ′yes′?  If X speak truth:       Answer to Q will be yes.  If X lies      Answer to Q  no.

$$\mathrm{Only}\:\mathrm{one}\:\mathrm{question}\:\mathrm{is}\:\mathrm{needed}. \\ $$$$\mathrm{Q}:\:\mathrm{If}\:\mathrm{I}\:\mathrm{ask}\:\mathrm{you}\:'\mathrm{Do}\:\mathrm{you}\:\mathrm{speak}\:\mathrm{Truth}'\:\mathrm{will} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{you}\:\mathrm{say}\:'\mathrm{yes}'? \\ $$$$\mathrm{If}\:\mathrm{X}\:\mathrm{speak}\:\mathrm{truth}: \\ $$$$\:\:\:\:\:\mathrm{Answer}\:\mathrm{to}\:\mathrm{Q}\:\mathrm{will}\:\mathrm{be}\:\mathrm{yes}. \\ $$$$\mathrm{If}\:\mathrm{X}\:\mathrm{lies} \\ $$$$\:\:\:\:\mathrm{Answer}\:\mathrm{to}\:\mathrm{Q}\:\:\mathrm{no}. \\ $$

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