The word problem is used for multiple concepts:

• a challenge, especially a mental challenge
• an unhappy state of affairs that exercises the mind
• a seemingly insurmountable difficulty

These may actually be very different things, because some states-of-affairs may be changed, and some may not; but it is often hard to distinguish the former from the latter. Thence we use the same word for all three concepts, and thence we get the famous Serenity Prayer of Reinhold Niebuhr:

God, grant me the serenity to accept the things I cannot change, courage to change the things I can, and wisdom to know the difference.

A good economist is going to note that sometimes the costs of changing what we can would be higher than the benefit. Properly understood, that greater costs would mean that we were trading some greater problem for a solution to the problem under immediate consideration. The Serenity Prayer might lead one to mistake sensible calculation for cowardice, though poetry might have to be sacrificed to provide better guidance.

Still, the distinction between that which we can change and that which we cannot is most fundamental, and confusion between the two is a source of frustration and of anguish. That which displeases us and which we can change is a challenge about which we can usefully exercise the mind, until such time as either we develop a reasonable method of changing things or we recognize that it's not worth the cost. That which displeases us and which we cannot change is an unhappy condition of existence; and — ideally — we ought to come to terms with that condition, to accept it, so that it no longer exercises our minds. (And we ought, similarly, to accept those states the changing of which, though possible, truly would be too costly.)

One seldom-noted root of some of the confusion is a failure to distinguish between what the person in question may change and what someone else may change. The state-of-affairs might be a problem for a person who could change it, or it might not be a problem for that person; but, either way, by someone who cannot change it, it is best treated as a condition of existence.

It may be especially hard to see the distinction when the other person might indeed act to change things and, if that other person did, the first person would want to undertake quickly some course of action. But, likewise, there might be some potential event which would have to be impersonally caused (if at all) and which would call for a prompt response. One should not try to cause that which no person can cause, and one should not try to cause that which only another person can cause, even if there would be things to do should it happen.

It may be too much to hope for serenity from such realizations. It is certainly too much to demand that others be serene in the face of indifference, indecision, or madness on the part of those around them. Sometimes grim acceptance is the best that one can manage.