Many problems, especially those whose solution is multi-valued, have no way of finding the answer except by trying every combination. A classic example is the Travelling Salesman Problem or any route-planning puzzle. As the number of values in the solution grows, so the number of trials must grow exponentially and soon take an unreasonable time to evaluate.
Yet other questions have only a best-fit or fuzzy solution. Search, especially for image or video, on Google and other search engines is one such, and now hugely important. A perennial challenge continues to be finding good investments in financial markets. And on a more leisurely note, search, rather than heuristics, may benefit computer game strategies and their artificial intelligence (AI) opponents.
