Schön D.…

On the island of knights and liars, a traveler came to visit his acquaintance, a knight, and saw him at a round table with five guests.

- I wonder, how many of you are knights? - he asked.
- Why don't you ask each of us a question and find out yourself, - one of the guests suggested.
- Alright. Tell me each: who are your neighbors? - the traveler asked.

To this question, everyone answered the same.

- Not enough data! - said the traveler.
- But today is my birthday, don't forget about that, - said one of the guests.
- Yes, today is his birthday! - said his neighbor.

And the traveler was able to figure out how many knights were at the table. Indeed, how many of them are there?
If everyone said, "Both of my neighbors are knights," it would be immediately clear that everyone sitting at the table is a knight. Indeed, the traveler's acquaintance, who is a knight, told the truth, meaning that both of his neighbors also told the truth, and so on, which means everyone told the truth.

If everyone said, "My neighbors are a knight and a liar," it would also be immediately clear how many knights there are. Indeed, the traveler's acquaintance told the truth, meaning his neighbors are a knight and a liar. The neighboring knight also told the truth, meaning the other neighbor is a liar. The neighboring liar lied, meaning both of his neighbors are knights. Continuing this way, we get that at the table: there are two pairs of knights sitting next to each other, and two liars between them.

Therefore, everyone said, "Both of my neighbors are liars." This is possible in two cases:

1) Knights and liars sat alternately;
2) The neighbors of the knights are liars, and the neighbors of the liars are a knight and a liar, meaning there are two knights and four liars at the table.

Since two people sitting next to each other said the same thing about their birthday, the first case is impossible. Therefore, there are two knights at the table.

## Answer

Two knights.