Usowan (うそワン) is one of Nikoli's most clever deduction puzzles. The presence of a known liar in every room turns standard counting logic on its head!

• Liar Detection: If a clue claims a count that is mathematically impossible (for example, claiming 3 black neighbors when 2 are already known white), that clue MUST be the liar for its room!
• Truth Cascade: Once the liar in a room is identified, EVERY other clue in that room is guaranteed to be 100% truthful.
• Contradiction Elimination: If assuming a clue is truthful forces a room to have two liars, that clue must be false.
• White Connectivity: Never isolate any white cells into enclosed islands; white cells must always connect back to the global network.