At a skiing camp, 4 friends arrived from 4 cardinal directions and had the following conversation.

Karel: "I did not come from the north or the south."

Mojmír: "I came from the south."

Pepa: "I came from the north."

Zdenda: "I did not come from the south."

We know that one of these statements is not true. Determine which one it is.

So, who came from the north and who from the south?

(M. Volfová)

Hint. Reformulate the previous statements in terms of cardinal directions (not in terms of individual friends).
Let's imagine where each person could have come from based on the previous statements:

- from the north, Pepa or Zdenda,
- from the east, Karel or Zdenda,
- from the south, Mojmír,
- from the west, Karel or Zdenda.

Now we consider which statements could have been false:

- If Mojmír lied, everyone else would have to be telling the truth, which would mean that no one came from the south. Therefore, Mojmír's statement was true.
- If Zdenda lied, he must have come from the south, which would mean that Mojmír also lied. Therefore, Zdenda's statement was true.
- If Karel lied, he must have come from the north or the south. In the first case, it would mean that Pepa also lied, and in the second case, it would mean that Mojmír also lied. Therefore, Karel's statement was true.

Since Mojmír, Zdenda, and Karel spoke the truth, it was Pepa who lied (which is indeed not in contradiction with anything). Therefore, Zdenda came from the north, and Mojmír came from the south.

Note. Pepa and Karel came from either the east or the west; it cannot be precisely determined from the given information who came from where.