A book has 500 pages:
The 1st page says “Exactly 1 page in this book is false.”
The 2nd page says “Exactly 2 pages in this book are false.”
The 500th page says “Exactly 500 pages in this book are false.”
Can any of the pages be true?
Yes, the 499th page is true. It says “Exactly 499 pages in this book are false.” With this page true, the other 499 pages are false, fulfilling the statement.