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Question Number 831 by malwaan last updated on 23/Mar/15
can you solve the hardest logic puzzle in the world
$${can}\:{you}\:{solve}\:{the}\:\:{hardest}\:{logic}\:{puzzle}\:{in}\:{the}\:{world} \\ $$
Commented by prakash jain last updated on 24/Mar/15
three gods and three questions?
$$\mathrm{three}\:\mathrm{gods}\:\mathrm{and}\:\mathrm{three}\:\mathrm{questions}? \\ $$
Commented by malwaan last updated on 21/Mar/15
yes
$${yes} \\ $$
Answered by prakash jain last updated on 24/Mar/15
Let say three gods are A, B and C. Ask B a question. If I ask you if A is random will you say ′ja′. If B is True or False. Response ′ja′ will imply ′A′ is random. Response ′da′ will imply ′A′ is not random. So if B answer ′ja′ either B or A is random. ⇒ C is not random. So if B answer ′da′ either B is random or if B is not random then A is not random. ⇒A is not random. Next 2 question to the god identified to be not random (true or false) Q1. If I ask you if A is True will you say ′ja′. Response ′ja′ will imply A is True. Response ′da′⇒ A is false. Q2. If I ask you if B is random will you say ′ja′. These 2 questions along with the first question will establish the identities.
$$\mathrm{Let}\:\mathrm{say}\:\mathrm{three}\:\mathrm{gods}\:\mathrm{are}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}. \\ $$$$\mathrm{Ask}\:\mathrm{B}\:\mathrm{a}\:\mathrm{question}. \\ $$$$\mathrm{If}\:\mathrm{I}\:\mathrm{ask}\:\mathrm{you}\:\mathrm{if}\:\mathrm{A}\:\mathrm{is}\:\mathrm{random}\:\mathrm{will}\:\mathrm{you}\:\mathrm{say}\:'\mathrm{ja}'. \\ $$$$\mathrm{If}\:\mathrm{B}\:\mathrm{is}\:\mathrm{True}\:\mathrm{or}\:\mathrm{False}. \\ $$$$\:\:\:\:\mathrm{Response}\:'\mathrm{ja}'\:\mathrm{will}\:\mathrm{imply}\:'\mathrm{A}'\:\mathrm{is}\:\mathrm{random}. \\ $$$$\:\:\:\:\mathrm{Response}\:'\mathrm{da}'\:\mathrm{will}\:\mathrm{imply}\:'\mathrm{A}'\:\mathrm{is}\:\mathrm{not}\:\mathrm{random}. \\ $$$$\mathrm{So}\:\mathrm{if}\:\mathrm{B}\:\mathrm{answer}\:'\mathrm{ja}'\:\mathrm{either}\:\mathrm{B}\:\mathrm{or}\:\mathrm{A}\:\mathrm{is}\:\mathrm{random}. \\ $$$$\:\:\:\:\:\Rightarrow\:\mathrm{C}\:\mathrm{is}\:\mathrm{not}\:\mathrm{random}. \\ $$$$\mathrm{So}\:\mathrm{if}\:\mathrm{B}\:\mathrm{answer}\:'\mathrm{da}'\:\mathrm{either}\:\mathrm{B}\:\mathrm{is}\:\mathrm{random}\: \\ $$$$\:\:\:\:\mathrm{or}\:\mathrm{if}\:\mathrm{B}\:\mathrm{is}\:\mathrm{not}\:\mathrm{random}\:\mathrm{then}\:\mathrm{A}\:\mathrm{is}\:\mathrm{not}\:\mathrm{random}. \\ $$$$\:\:\:\:\Rightarrow\mathrm{A}\:\mathrm{is}\:\mathrm{not}\:\mathrm{random}. \\ $$$$\mathrm{Next}\:\mathrm{2}\:\mathrm{question}\:\mathrm{to}\:\mathrm{the}\:\mathrm{god}\:\mathrm{identified}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{not}\:\mathrm{random}\:\left(\mathrm{true}\:\mathrm{or}\:\mathrm{false}\right) \\ $$$$\mathrm{Q1}.\:\mathrm{If}\:\mathrm{I}\:\mathrm{ask}\:\mathrm{you}\:\mathrm{if}\:\mathrm{A}\:\mathrm{is}\:\mathrm{True}\:\:\mathrm{will}\:\mathrm{you}\:\mathrm{say}\:'\mathrm{ja}'. \\ $$$$\:\:\:\mathrm{Response}\:'\mathrm{ja}'\:\mathrm{will}\:\mathrm{imply}\:\mathrm{A}\:\mathrm{is}\:\mathrm{True}. \\ $$$$\:\:\:\mathrm{Response}\:'\mathrm{da}'\Rightarrow\:\mathrm{A}\:\mathrm{is}\:\mathrm{false}. \\ $$$$\mathrm{Q2}.\:\mathrm{If}\:\mathrm{I}\:\mathrm{ask}\:\mathrm{you}\:\mathrm{if}\:\mathrm{B}\:\mathrm{is}\:\mathrm{random}\:\mathrm{will}\:\mathrm{you}\:\mathrm{say}\:'\mathrm{ja}'. \\ $$$$\mathrm{These}\:\mathrm{2}\:\mathrm{questions}\:\mathrm{along}\:\mathrm{with}\:\mathrm{the}\:\mathrm{first}\:\mathrm{question} \\ $$$$\mathrm{will}\:\mathrm{establish}\:\mathrm{the}\:\mathrm{identities}. \\ $$
Commented by malwaan last updated on 24/Mar/15
I will try to understand soon now I cant
$${I}\:{will}\:{try}\:{to}\:{understand}\:{soon} \\ $$$${now}\:{I}\:{cant} \\ $$$$ \\ $$
Commented by prakash jain last updated on 24/Mar/15
Writing a few cases for first question to B. If B is false, ja means no. If A is random B answer to question ′is A random′ is ja. But the question asked is will you say ′ja′. So B answer to combined question will be ′ja′. If A is not random. B answer to question ′is A random′ is da. But the question asked is will you say ′ja′. So B answer to combined question will be ′da′. If you list all cases you will realize because there is embedded question. False will need to gives false answer twice making False′s answer same as True′s answer. So the first question can be used to filter out random.
$$\mathrm{Writing}\:\mathrm{a}\:\mathrm{few}\:\mathrm{cases}\:\mathrm{for}\:\mathrm{first}\:\mathrm{question}\:\mathrm{to}\:\mathrm{B}. \\ $$$$\mathrm{If}\:\mathrm{B}\:\mathrm{is}\:\mathrm{false},\:\mathrm{ja}\:\mathrm{means}\:\mathrm{no}. \\ $$$$\mathrm{If}\:\mathrm{A}\:\mathrm{is}\:\mathrm{random} \\ $$$$\:\:\:\:\:\mathrm{B}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{question}\:'\mathrm{is}\:\mathrm{A}\:\mathrm{random}'\:\mathrm{is}\:\mathrm{ja}. \\ $$$$\:\:\:\:\:\mathrm{But}\:\mathrm{the}\:\mathrm{question}\:\mathrm{asked}\:\mathrm{is}\:\mathrm{will}\:\mathrm{you}\:\mathrm{say}\:'\mathrm{ja}'. \\ $$$$\:\:\:\:\:\mathrm{So}\:\mathrm{B}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{combined}\:\mathrm{question}\:\mathrm{will} \\ $$$$\:\:\:\:\:\mathrm{be}\:'\mathrm{ja}'. \\ $$$$\mathrm{If}\:\mathrm{A}\:\mathrm{is}\:\mathrm{not}\:\mathrm{random}. \\ $$$$\:\:\:\:\:\mathrm{B}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{question}\:'\mathrm{is}\:\mathrm{A}\:\mathrm{random}'\:\mathrm{is}\:\mathrm{da}. \\ $$$$\:\:\:\:\:\mathrm{But}\:\mathrm{the}\:\mathrm{question}\:\mathrm{asked}\:\mathrm{is}\:\mathrm{will}\:\mathrm{you}\:\mathrm{say}\:'\mathrm{ja}'. \\ $$$$\:\:\:\:\:\mathrm{So}\:\mathrm{B}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{combined}\:\mathrm{question}\:\mathrm{will} \\ $$$$\:\:\:\:\:\mathrm{be}\:'\mathrm{da}'. \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{list}\:\mathrm{all}\:\mathrm{cases}\:\mathrm{you}\:\mathrm{will}\:\mathrm{realize}\:\mathrm{because} \\ $$$$\mathrm{there}\:\mathrm{is}\:\mathrm{embedded}\:\mathrm{question}.\:\mathrm{False}\:\mathrm{will}\:\mathrm{need} \\ $$$$\mathrm{to}\:\mathrm{gives}\:\mathrm{false}\:\mathrm{answer}\:\mathrm{twice}\:\mathrm{making}\:\mathrm{False}'\mathrm{s}\:\mathrm{answer} \\ $$$$\mathrm{same}\:\mathrm{as}\:\mathrm{True}'\mathrm{s}\:\mathrm{answer}. \\ $$$$\mathrm{So}\:\mathrm{the}\:\mathrm{first}\:\mathrm{question}\:\mathrm{can}\:\mathrm{be}\:\mathrm{used}\:\mathrm{to}\:\mathrm{filter} \\ $$$$\mathrm{out}\:\mathrm{random}. \\ $$

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