This course and its predecessor CPSC 128 have focussed exclusively on solving problems using algorithms. An algorithm is a mechanical procedure that is guaranteed to find the correct solution in a finite amount of time. The word mechanical indicates that it doesn't rely on magic, or luck, or involve human judgment or intuition; correct means that it always works; and finite that we won't have to wait forever to get that answer. Those are all desirable properties of a solution methodology, but sometimes they may be overriden by other considerations. For example we may need a solution now (after all finite just guarantees us that an algorithm won't take forever, but it could take years, or for that matter millenia, and still qualify as an algorithm), and be willing to accept an inexact one as long as it is close to the correct one. It might also be that no perfect solution is even possible, i.e. that the solution is not computable, for example because there is insufficient information. In these cases we may turn to heuristics instead of algorithms. Heuristics are solution techniques that give us reasonable answers quickly.
A well-known investing heuristic is that you can find the number of years it will take an investment to double in value by dividing the interest rate into 72. For example money invested at 6% will double in (approximately) 72/6=12 years. (This is an example of an approximation heuristic.)
Email virus scanners use heuristics to flag spam by relying on the presence of certain words to classify messages. The presence of the word "viagra" does not guarantee that the message is spam, but unless you are a medical researcher it is likely. (This is an example where no perfect mechanical solution is possible.)
This week's problem will give you the chance to come up with some heuristics to help with an intractable problem.