Solution
If 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
- D.Wells, The Penguin Book of Curious and Interesting Puzzles, Penguin Books, 1992
- Does It Blink?
- Apparent paradox
- Set of all subsets
- An Impossible Page
- Russell's paradox
- An Impossible Machine
- A theorem with an obvious proof
Copyright © 1996-2009 Alexander Bogomolny