## Task 4 - 100914

In an old collection of problems, the judgment of Paris is described as follows:

The goddesses Hera, Aphrodite, and Athena ask the wise Paris who among them is the most beautiful. They make the following statements:

```
Aphrodite: I am the most beautiful.
Athena: Aphrodite is not the most beautiful.
Hera: I am the most beautiful.
Aphrodite: Hera is not the most beautiful.
Athena: I am the most beautiful.
```

Paris, who is resting by the roadside, does not consider it worth the effort to remove the cloth that protects his eyes from the sun. However, he is supposed to determine exactly one of the three goddesses as the most beautiful. He assumes that all statements of the most beautiful one are true, while all statements of the other two goddesses are false.

Can Paris, under this assumption, make the required determination? If so, what is it?
The statements 1., 3., and 5. do not advance Paris's decision, as they are identical and true if spoken by the most beautiful goddess and false if spoken by any other goddess.

Now, let's consider the cases and examine statements 2. and 4.:

1. Case: Aphrodite is the most beautiful. If Athena denies this (2.) and Aphrodite truthfully states that Hera is not the most beautiful, there is no contradiction. $\Rightarrow$ Aphrodite can be the most beautiful.
2. Case: Athena is the most beautiful. The 4th statement would then have to be false, as it is not spoken by the most beautiful goddess, which means Hera is the most beautiful, leading to a contradiction with the assumption.
3. Case: Hera is the most beautiful. The 2nd statement would then have to be false, as it is not spoken by the most beautiful goddess, which means Aphrodite is the most beautiful, leading to a contradiction with the assumption.

Thus, the unique solution is that Aphrodite is the most beautiful, given the conditions set by Paris.