Question 57
At the round table, 50 inhabitants of the island "Loud Mouths" are sitting at equal distance from one another and discussing something. Each of them is either a knight who always tells the truth, or a liar who lies every time, and people of each type are present at the table. During the discussion, everyone said that the islander sitting directly opposite of him/her across the table and the two neighbours of that person were not all of one type, i.e., not all three knights and not all three liars. Prove that there are no fewer than 10 and not over 25 liars at the table.