You work for a factory making bricks. A coworker accidentally contaminated one of the bricks with lightweight material and it must be removed. Given a pile of 50 bricks and a balance scale, how can you find the one that weighs less? The scale can hold any number of bricks on each side of the scale at one time, and it will tell you if the two sides weigh the same, or which side is lighter if they do not weigh the same. Describe the algorithm to find the contaminated, lightweight brick. How many weighings will you do? Find an algorithm that uses the least number of weighings possible. State and justify your answer as a function of n, the total number of bricks.