Problem \#2. You have n coins that are supposed to be gold coins of the same weight, but you know that one coin is fake and weighs less than the others. There is available a balance scale so that you can put any number of coins on each side of the scale at one time, and it will tell you whether the two sides weigh the same, or which side weigh less than the other. Outline an efficient algorithm to find the fake coin. Determine the number of weighings as a function of n using the O notation