RobDaasch first pointed out to me the difference between problems and difficulties, especially as they relate to computers. A problem is something that is interesting to think about and whose solution you can savor. Compare this with difficulties, especially computer difficulties, like getting your printer to work, your program to compile, or your machine to stop crashing. -- WardCunningham
I'm reminded of a distinction drawn by Peter Gomes (Harvard University Theologian) between a "Problem" and a "Mystery". He describes a "Problem" as "Something you solve and then leave behind". He describes a "Mystery" as "Something you enter, that usually reveals further mysteries". Most of us, especially in this industry, spend a lot of time solving problems. Some of us also enjoy entering mysteries. -- TomStambaugh
Here are some well-studied computer problems, some with cool animations available on the net.