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The true phrase

The true phrase

Which of these ten sentences is true?

  1. »Exactly one of these ten sentences is false.
  2. »Exactly two of these ten sentences are false.
  3. »Exactly three of these ten sentences are false.
  4. »Exactly four of these ten sentences are false.
  5. »Exactly five of these ten sentences are false.
  6. »Exactly six of these ten sentences are false.
  7. »Exactly seven of these ten sentences are false.
  8. »Exactly eight of these ten sentences are false.
  9. »Exactly nine of these ten sentences are false.
  10. »Exactly ten of these ten sentences are false.

Solution

The ninth phrase is true. Each of these phrases contradicts the others but at least one of the 10 phrases
it must be true therefore the remaining nine are false.