51

edits
# Changes

no edit summary

# Only one of these statements is false.

# Statements 2 and 3 are both true or both false.

{{needs_hint}}

{{needs_answer}}

{{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.

}}

[[Category: Liar puzzles]]

[[Category: Logic]]