Truth-tellers and liars: consistent statements

What you’ll solve

These puzzles focus on consistency: deciding whether a set of statements can all hold together given truth-tellers (always true) and liars (always false). You’ll practice translating language into logic and checking whether assumptions lead to contradictions.

Every question uses 4 options and there’s no timer, so you can slow down and verify each implication. Before you start, choose your preferred question count and difficulty to match a quick warm-up or a longer mixed challenge.

Skills you’ll practice

• Identifying contradictions and “impossible” statement sets
• Tracking who must be a truth-teller vs a liar from minimal clues
• Handling nested statements like “A says that B lies”
• Testing cases systematically without losing track of assumptions
• Spotting hidden quantifiers (always/never/at least one/exactly one)

Common pitfalls (and how to avoid them)

Many wrong answers come from flipping only part of a liar’s statement instead of negating the whole claim. Another frequent trap is assuming roles too early - try a case split, push it until it contradicts, then switch.

Difficulty balance

Mixed difficulty means you’ll see straightforward one-step consistency checks alongside denser multi-person scenarios. The progression is balanced so easier items build confidence, while tougher questions reward careful bookkeeping and clean logic.