You are given n boxes that can not be opened. Each box contains a secret code. It is possible that two different boxes contain the same secret code. You have a scanner with the following capability: When we place two boxes in the scanner, it tells if the boxes contain the same secret code or not. Each time you do the scanning it costs you a dollar. The goal is to determine if there is a secret message that appears in at least n=2 + 1 boxes. Write an algorithm to solve this problem. The cost of the algorithm is the number of times you uses the scanner. You must use divide and conquer to solve this problem. State the recurrence relation for the cost and solve the recurrence relation.