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# Only one of these statements is false.
# Statements 2 and 3 are both true or both false.
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{{solution |
First identify statements with equal vs opposite truth values:
* 1 has opposite truth value to 5 (from statement 1)
* 2 has opposite truth value to 1 (from statement 2), hence equal truth value to 5
* 3 has equal truth value to 4 (from statement 3)
* 5 true only if 2 has equal truth value to 3 (from statement 5)
If 4 false, then:
*3 false (equal value to 4)
*2 has opposite value to 5 (5 true only if 2 false, given 3 false)
But 2 has equal truth value to 5.
So 4 true.
If 4 true, then:
*3 true (equal value to 4)
*2 and 5 true (otherwise they'd both be false, contradicting 4)
*1 false (opposite value from 2, 5)
Hence 1 is false and all other statements are true.
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[[Category: Liar puzzles]]
[[Category: Logic]]
