25. In one book, the following 100 statements were written:
1) “In this book, there is exactly one false statement.”
2) “In this book, there are exactly two false statements ...”
3) “In this book, there are exactly one hundred false statements.”

Which of these statements is true?
25. If we assume that the first statement is true, this would mean that there is exactly one false statement in the book, and all the others are true, i.e., the second, third, and so on are true, which contradicts the first statement, since, for example, the second statement claims that there are exactly two false statements, the third claims exactly three, and so on. Conducting such reasoning up to the 98th statement inclusive, we will come to the same conclusion. If, however, the 99th statement is true, this means that there are exactly 99 false statements, i.e., all except the 99th statement. Therefore, it is false that there is exactly one, two, ..., 98, or 100 false statements. The hundredth statement cannot be true, because in this case all statements (according to the hundredth statement) are false. Thus, the true statement is the 99th.