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Wednesday, July 23, 2008

Silly Statements

Below are a number of statements:

1. Precisely one of these statements is untrue.
2. Precisely two of these statements are untrue.
3. Precisely three of these statements are untrue.
4. Precisely four of these statements are untrue.
5. Precisely five of these statements are untrue.
6. Precisely six of these statements are untrue.
7. Precisely seven of these statements are untrue.
8. Precisely eight of these statements are untrue.
9. Precisely nine of these statements are untrue.
10. Precisely ten of these statements are untrue.

The Question: Which of these statements is true?

Answer: The ten statements all contradict each other. So there can be at most one statement true. Now suppose there is no statement true. That would mean that statement 10 indeed would be true, which results in a contradiction. This means that exactly nine statements must be untrue, and thus only statement 9 is true.

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