Four statements are written on a piece of paper: 1. "At least one of these four statements is false." 2. "At least two of these four statements are false." 3. "At least three of these four statements are false." 4. "All four of these four statements are false." Which of these statements are true and which are false?
Statements 1 and 2 are true; Statements 3 and 4 are false.
Statement 4 cannot be true because if it were, it would contradict itself, so 4 is false. This means there is at least one false statement, making Statement 1 true. If Statement 3 were true, there would be 3 false statements and 1 true statement, but that would make Statements 1, 2, and 3 all true, a contradiction. Thus Statement 3 is false. Now we have 2 false statements (3 and 4), which makes Statement 2 true and Statement 1 true.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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