Question 1
Farhan says: 'Sanjay has the artifact'
Sanjay says: 'I do not have the artifact'
Sunil says: 'Farhan is lying'
Can all these statements be true simultaneously?
Let's test if all statements can be true:
Assumption 1: If Farhan tells truth, then Sanjay has artifact.
But Sanjay claims not to have it - contradiction if Sanjay tells truth.
If Sanjay lies, then Sanjay DOES have the item - consistent with Farhan.
Then Sunil says Farhan lies - but we assumed Farhan tells truth - contradiction!
Assumption 2: If Farhan lies, then Sanjay does NOT have artifact.
Sanjay says the same thing - consistent if Sanjay tells truth.
Sunil says Farhan lies - consistent if Sunil tells truth.
Therefore, all statements CAN be consistent when Farhan lies, Sanjay and Sunil tell truth.
Thus, the statements are consistent.
Assumption 1: If Farhan tells truth, then Sanjay has artifact.
But Sanjay claims not to have it - contradiction if Sanjay tells truth.
If Sanjay lies, then Sanjay DOES have the item - consistent with Farhan.
Then Sunil says Farhan lies - but we assumed Farhan tells truth - contradiction!
Assumption 2: If Farhan lies, then Sanjay does NOT have artifact.
Sanjay says the same thing - consistent if Sanjay tells truth.
Sunil says Farhan lies - consistent if Sunil tells truth.
Therefore, all statements CAN be consistent when Farhan lies, Sanjay and Sunil tell truth.
Thus, the statements are consistent.