Suppose the first sign, THIS ROOM CONTAINS A TIGER, is on the door of Room I. If a lady is in the room, the sign is false, violating the conditions given us. If a tiger is Room I, the sign is true, which again violates the conditions of the puzzle. Therefore, this sign can't be on the door of Room I; it must be on the door of Room II.This means that the sign for Room I reads: BOTH ROOMS CONTAIN TIGERS. Then Room I can't contain a lady, or the sign would be true, which would mean that both rooms contain tigers - an obvious contradiction. Therefore, Room I contains a tiger. From this it follows that the sign is false, so Room II must contain a lady.