On an island, there live three tribes: knights, who always tell the truth, liars, who always lie, and tricksters, who sometimes tell the truth and sometimes lie. At a round table, 100 representatives of these tribes are seated.

Each person at the table made two statements: 1) “To my left sits a liar”; 2) “To my right sits a trickster.” How many knights and how many liars are at the table, if half of those present are tricksters?
Since knights tell the truth, a liar sits to the left of each knight. Let's now prove that a knight sits to the right of each liar. Indeed, since liars lie, a trickster does not sit to the right of each liar. Moreover, a liar cannot sit to the right of another liar, because then the right liar would have told the truth with the first statement. Therefore, a knight sits to the right of each liar.

Thus, liars and knights are paired, so among the fifty of them, there are an equal number, from which the answer follows.

## Answer

25 knights.