LG-007

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

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

Try each possibility:

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