Problem:
It is known that male Martians always tell the truth, while female Martians always lie; on the contrary, male Venusians lie and female Venusians always tell the truth. A spaceship full of Martians and Venusians lands; at the immigration office two of the occupants, Ark and Bark, make the following statements:
Ark: "Bark is from Venus".
Bark: "Ark is from Mars".
Ark: "Bark is male".
Bark: "Ark is female".
On the basis of these statements the officer can determine:
Pick one
Solution:
The answer is . If Ark tells the truth, then Bark is a male Venusian, hence he lies, but then Ark must be a male Venusian, a contradiction. Therefore Ark lies, so Bark is a female Martian, who lies, and hence Ark is indeed a male Venusian (who lies). So everything is determined.
Solution:
The answer is (E). If Ark tells the truth, then Bark is a male Venusian, hence he lies, but then Ark must be a male Venusian, a contradiction. Therefore Ark lies, so Bark is a female Martian, who lies, and hence Ark is indeed a male Venusian (who lies). So everything is determined.