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A problem A reduces to a problem B if we can use a solution to B to solve A. Designing a new divide-and-conquer algorithm from scratch is sometimes akin to solving a puzzle that requires some experience and ingenuity, so you may not feel confident that you can do so at first. But it is often the case that a simpler approach is effective: given a new problem that lends itself to a quadratic brute-force solution, ask yourself how you would solve it if the data were sorted in some way. For example, consider the problem of determining whether the elements in an array are all different. This problem reduces to sorting because we can sort the array, the make a linear pass through the sorted array to check whether any entry is equal to the next (if not, the elements are all different.)