4. In the city of liars and knights, there are 366 residents, all born on different days of a leap year. All residents of the city answered two questions. To the question “Were you born in February?” 100 people answered affirmatively, and to the question “Were you born on the 30th?” 60 people answered affirmatively. How many knights were born in February?
Answer: 29. Solution: To the first question, knights born in February and liars born in other months answered affirmatively. Let $x$ be the number of knights born in February, where $x$ does not exceed 29. Then, $29-x$ liars were born in February, and $100-x$ liars were born in other months. The total number of liars is $129-2x$, which means from 71 to 129 people.

To the second question, knights born on the 30th and liars born on other days answered affirmatively. Let $c$ be the number of knights born on the 30th, where $c$ does not exceed 11. Then, $11-c$ liars were born on the 30th, and $60-c$ liars were born on other days. The total number of liars is $71-2c$, which means from 49 to 71 people.

Therefore, the number of liars is 71, from which $x=29$.