3. Three foxes: Alice, Larisa, and Inessa were talking on a meadow. Larisa: "Alice is not the most cunning." Alice: "I am more cunning than Larisa." Inessa: "Alice is more cunning than me." It is known that the most cunning fox lied, and the others told the truth.

a) Can Alice be the most cunning fox? Why?

b) Which fox is the most cunning? Provide an answer and explain why the other options do not work.
Answer. a) Cannot, b) Inessa.

## Solution.

a) Alice cannot be the smartest, because if she is the smartest, then she is smarter than Larisa, i.e., Alice told the truth. But the smartest fox should have lied.
b) The smartest fox is Inessa. Let's prove this. We have already established in part a) that Alice cannot be the smartest fox. Larisa also cannot be the smartest, because she told the truth about Alice, and the smartest fox should have lied. Therefore, the only remaining option is that the smartest is Inessa.

## Grading Criteria.

- Correct solution for part a) - 3 points, part b) - $\mathbf{4}$ points.
- Only correct answers for each part - 2 points.