You have 12 identical-looking balls and a balance scale. One ball is a different weight (heavier or lighter). You have only three weighings to determine which ball is different and whether it is heavier or lighter.

Why this works

At first glance, this riddle may seem insurmountable, as it beckons you to identify a single odd ball among twelve, all while navigating the constraints of just three weighings. However, the clever trick lies in the strategic division of the balls into manageable groups. By weighing four balls against another four, you immediately glean vital information: if the scales tip, you've narrowed your search to one of those eight balls, and if they balance, you know the odd ball resides among the remaining four. The brilliance unfolds as you continue to subdivide your options based on the outcomes of each weighing. With each decision, you're not just isolating a suspect but also determining its weight relative to the others, whether it’s heavier or lighter. This decision tree method turns the riddle into a thrilling game of deduction, where each choice leads you closer to revelation, showcasing the power of logical reasoning and systematic elimination. This riddle reflects an age-old fascination with puzzles and problem-solving that dates back to ancient civilizations, where similar balance scale puzzles were used to test wit and intelligence. The "aha moment" comes when you realize that the methodical approach can yield clarity from chaos, a satisfying resolution that resonates with our innate love for solving mysteries. Fun fact: such balance puzzles are often featured in mathematical competitions and are a favorite among those who enjoy logic games, proving that sometimes the most mind-bending challenges can be tackled with a little creativity and strategy!