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MathNet 2002 — Part 01 Question 144

Math Olympiad Vault · MathNet 2002 — Part 01

Question 144

It is known that male Martians always tell the truth, while female Martians always lie; on the contrary, male Venusians lie and Venusian women 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 declarations the employee can determine:
  1. Ark's planet and sex, but not Bark's
  2. Bark's planet and sex, but not Ark's
  3. only the planet of both (but not sex)
  4. only the sex of both (but not the planet)
  5. planet and sex of both.