A puzzle from the October 1962 issue of Eureka, the journal of the Cambridge University Mathematical Society:
(a) At least two of these statements, apart from this one, are true.
(b) At least two of these statements, apart from this one, are false.
(c) At least one of these statements is false.
(d) x of these statements are true.
Given that, if you knew the value of x, you could determine uniquely which statements are true and which are false, determine the value of x.
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The journal states only that x = 3, but here’s an attempt. We’re told that the value of x in (d) is vital, so (d) must be true; otherwise its claim about x would be useless. It’s impossible for all four statements to be true, because then (a) and (b) would contradict one another. This means that at least one statement is false, which means that (c) is true. And if (c) and (d) are both true, then (a) is true, which means that (b) is false:
(a) true
(b) false
(c) true
(d) true
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