Defective ball
You have 12 identical balls. One of the balls is heavier OR lighter than the rest (you don't know which). Using just a balance that can only show you which side of the tray is heavier, how can you determine which ball is the defective one with 3 measurements?
Answer
Notes and comments
Comment 1: With no prior information as to whether the defective ball is heavier or lighter, you can identify the defective ball among up to \(\frac{3^n-3}{2}\) balls using only \(n\) weighings.