LG-010

Three people Zoe, Mia, and Ivy each make one statement. Exactly one of them is true.

Zoe: “Mia is lying.”
Mia: “Ivy is lying.”
Ivy: “Zoe is lying.”
Who is telling the truth?

Try each possibility:

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