I would never jump into a complicated problem without first trying out smaller similar problems. Ask yourself how long does it take to solve for a fifth, fourth, third, and half of that many conditions and estimate the time necessary to solve the whole number of conditions. The estimate won't be exact, but it should tell you if your talking hours, days, or weeks.
You can also time out other approaches as you make the problem grow and see how much time you could save on the big problem by using them.