**Question: **A sheet of paper has statements numbered from 1 to 100. Statement N says "Exactly N of the statements on this sheet are false." How many statements are true?

**Answer:**Only One statement is true - Statement 99

If they are all false, statement 100 would be true i.e. "Exactly 100 of the statements on this sheet are false", which is contradictory.

If total of 99 statements are false, statement 99 would be true i.e. "Exactly 99 of the statements on this sheet are false". That's the answer - total 99 statements are false, and statement 99 is true.

Try out for all remaining statements, they all will contradict itself.