On the island of knights and knaves

Question

On the island of knights and knaves you come across a group of 30 people wearing tags numbered 1 to 30. Person 1 says exactly one of us is a knave. Person 2 says exactly two of us are knaves, person 3 says exactly 3 of us are knaves, and so on. Who is a knight and who is a knave?

Answer 1

First, person 30 claims that all 30 are knaves. If this is true, then person 30 is a knave, which means that the statement of person 30 is a lie. This is a contradiction. Hence, there is at least 1 knight.

Since each person's statement contradicts all of the other people, at most 1 person can be a knight. Which person claimed that there is 1 knight? The person who says exactly 29 our of 30 are knaves, claimed that there was 1 knight. Therefore, person 29 is a knight and the rest are knaves.