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?


Book Has 500 Pages
Can any of the pages be true? 6 guesses to Book Has 500 Pages 

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The 499th page.
Every other page is incorrect.
The one that states 499 are false could be true in, and all others false.
Additionally, it does t say that this in the only writing on these pages, so page 499 could include some other false statement making page 500 correct.
But Crabman, if the 500th page was correct, it would also (by its own statement) be false.
Therefore it can only be that the 499th page can be correct.
Max, you are today’s winner!
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.
Max, I suggested that it’s possible that the 500th page may included another unspecified false statement (such as “the earth is flat”). Thus, this page would contain 1 true & 1 false statement, and we all know TRUE AND FALSE = FALSE, therefore all 500 pages would be false.
I’m not arguing that the answer is 499, just explaining the line of thinking on my tangent ;)
Ah. That makes more sense, Crabman….!
Sorry about that, I should consider things with greater perspective than I did earlier….
Cheers.