LG-004

Three people Ethan, Ava, and Liam each make one statement. Exactly one of them is true.

Ethan: “Ava is lying.”
Ava: “Liam is lying.”
Liam: “Ethan is lying.”
Who is telling the truth?

Try each possibility:

1. If Ethan is true, then Ava is lying. That forces Ava's statement to be false, which forces Liam's statement to be true — contradiction.
2. If Ava is true, then Liam is lying. That forces Liam's statement to be false, which forces Ethan's statement to be true — contradiction.
3. If Liam is true, then Ethan is lying, which forces Ethan's statement to be false, which forces Ava's statement to be true — contradiction.

No assignment makes exactly one statement true, so the correct answer is Impossible to determine (the setup is inconsistent).

• Picking the first pattern you see without checking it against all rows/columns.
• Ignoring the simplest rule (counts, rotations, alternations) and jumping to a complex story.
• Not testing your rule on the middle row/column (where many puzzles “break” bad rules).