That looks like a hopelessly vague question, and it is unless we’re prepared to clarify it a bit. On the other hand, we already know there are some *impossible* problems so surely there are some that are just *hard*? Again, we’ll need to work out what on earth we’re talking about here. Let’s start with what we actually mean by a *problem* in a *computational* sense …

*(Be warned: There are one or two simplifications and liberties with precision in what follows; it’s well-intentioned but may upset the purist.)*

Well, actually, even *that* isn’t simple and there’s no absolute agreement on what a good definition would be. (We’ve seen previously that mathematicians and computer scientists don’t always see eye-to-eye.) It’s cheating a bit but it’s probably easier to give examples and this should work well enough for us. At least in the context of *computing*, these are all valid *problems*:

- Calculate
*2*x*4 + 9 – 3* - If
*5 – x = 2*what’s*x*? - Find the largest from
*5, 7, 1, 4, 8, 5, 2, 4, 8, 5, 2, 6, 7, 7, 3, 3, 2, 4, 3, 6, 7, 7, 6, 5, 4* - Sort
*25, 44, 66, 72, 12, 45, 56, 90, 45, 69, 11, 10, 12, 42, 88*into ascending order - Arrange
*1, 2, 3, 4, 5, 6, 7, 8, 9*into a magic square - What’s the best way to get to Paris?