7.1. Riding along a forest road, Ivan-tsarevich met a bear, a fox, and a wolf. The bear always tells the truth, the fox always lies, and the wolf alternates between truth and lies, always starting with the truth. Each of the animals said two sentences to Ivan-tsarevich. The first: "You will save the horse. But you will perish yourself." The second: "You will remain unharmed. And you will save the horse." The third: "You will remain unharmed. But you will lose the horse." Determine which animal gave each response, and what awaits Ivan-tsarevich ahead. Justify your answer.
Solution: The first parts of the statements are: "you will save the horse," "you will remain unharmed," "you will remain intact." Among them, two should be true and one false, so Ivan survives, but his horse does not. This means that both parts of the first statement are false, and the first speaker was the fox. Similarly, we find that the second was the wolf, and the third was the bear.

Answer: The first statement belongs to the fox, the second to the wolf, and the third to the bear. Ivan will survive, but without his horse.

Recommendations for checking:

| included in the work | points |
| :--- | :--- |
| Correct and fully justified answer | 7 points |
| Only Ivan's fate is correctly determined | 4 points |
| The correct answer is provided, and it is shown that it is possible, but it is not shown that other cases are impossible | 2 points |
| Answer without justification and/or incorrect answer | 0 points |