3. In the underwater kingdom, there live octopuses with seven and eight legs. Those with 7 legs always lie, while those with 8 legs always tell the truth. One day, a conversation took place between three octopuses.

Green octopus: "We have 21 legs together." Blue octopus (to the green one): "You're lying!" Red octopus: "Both of you are lying!"

1) Could the green octopus have told the truth? Why?
2) How many legs did each octopus have? (Justify your answer.)
Answer. 1) Could not.

2) The green octopus has 7 legs, the blue one has 8 legs, and the red one has 7 legs.

Solution.

1) If the green octopus had told the truth, then each octopus would have 7 legs. This means that the green octopus, according to the condition, should have lied. We get a contradiction, so the green octopus lied.
2) Since the green octopus lied, it has 7 legs. The blue octopus told the truth about the green one, so it has 8 legs. The red octopus lied because not both but only one in front of him lied, so the red one has 7 legs.

## Grading Criteria.

- Correct solution for both parts - 7 points.
- Correct solution for the first part + partial solution for the second - 4-5 points.
- Correct solution for the first part - 3 points.
- Partially correct but incomplete reasoning - 1-2 points.
- Only answers for all parts - $\mathbf{0}$ points.