2. 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, three octopuses had the following conversation.

Green octopus: “We have 24 legs together.”

Blue octopus: “You are right!”

Red octopus: “Nonsense, Green is talking rubbish!”

How many legs did each octopus have? (Justify your answer.)
Answer. The Green Octopus has 7 legs, the Blue Octopus has 7 legs, the Red Octopus has 8 legs. Solution. From the condition of the problem, it follows that the number of legs and the truthfulness of the statements are uniquely related. The Blue and Red Octopuses made contradictory statements about the words of the Green Octopus. This means that one of them told the truth, and the other lied. And this, in turn, means that one of them has 7 legs. Thus, the words of the Green Octopus are a lie (otherwise, each of the three octopuses should have 8 legs, otherwise the total number of legs would be less than 24). Let's summarize: The Green Octopus lied, he has 7 legs; then the Blue Octopus lied, he has 7 legs, and the Red Octopus told the truth, he has 8 legs. Evaluation criteria.

- A complete and correct analysis of the situation in the problem and a correct answer given - 7 points.
- A correct analysis of the situation is provided, but for some reason an incorrect answer is given (for example, the connection between the number of legs and the truthfulness of the statements is confused) - 5-6 points.
- A correct answer is provided and it is shown that it satisfies the condition of the problem (a check is performed) - 3 points.
- Only a correct answer is provided - $\mathbf{1}$ point.
- A correct answer is provided with incorrect reasoning - $\mathbf{0}$ points.