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Following are ten statements. How many of them are true? If any, which ones?
Copyright © 1996-2008 Alexander Bogomolny
SolutionIf all 10 are false then this is exactly what the 10th asserts. But if it's true, we get a contradiction since then not all 10 are false. Hence, at least one is indeed false. On the other hand, no two of the statements may be true simultaneously; for they make contradictory assertions. Therefore, exactly one of them is true while the remaining nine are false. This is what is claimed by the ninth statement. This is true too. Reference
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