Can we call something a "problem" if it has no solution at all?

Yes, an unsolved problem.

One that waits to be resolved.

Crimes for example can remain unsolved and this is a great problem for law makers and community.

If a problem has no solution, then either the problem was not given ample time to find a solution, or the parameters for finding a solution are too narrowly defined.

For instance, if someone in the 17th century wanted to talk to another person who lived on another continent immediately, there was no solution at the time. Obviously we can do that today. What seemed impossible yesterday is possible today. And what seems impossible today will be possible tomorrow.

Now if you were to say my problem is I want to fly. Well a solution would be to board a jet, balloon, etc. But if you say my problem is I want to fly without the help of technology, then you have eliminated all solutions except for wait until evolution decides to give you wings.

well.. I would theorize that ***error*** recursion too deep. System halt.

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[edit] no. this is a funny answer. at least to me. It illustrates the point very well if you understand it. :)

Yes. The concept of a problem is of a state of affairs that is in some way a barrier to a different and more preferred state of affairs. You may not be able to see how to reconcile these states but they do still exist, and you do have a problem.

Well, judging by the other answer , we got a problem here, that being the question of the definition of "problem." I looked it up and here present one definition ( no problem, it was easy);
problem; noun: a question raised for consideration or solution ( http://www.onelook.com/?w=problem&ls=a )
No mention is made in any definition of there being a requirement of a solution.

Aha! ( I hear you say) We now have another problem, the actual question "Can we call something a 'problem' if it has no solution at all? " The question is, by definition, definitely a "problem", considering that it was presented for solution ( solution; noun: a statement that solves a problem or explains how to solve the problem [ http://www.onelook.com/?w=solution&ls=a ]) I do not know if the problem, or question, was presented for consideration, but as I did consider the question to be a problem, I will consider it to be so considered. Therefor this problem does have a solution; a problem without a solution is, by definition, a " problem". Aside from the lack of solution being a problem in it's own right. Indeed the lack of solution may actually be the solution. Since we have no solution, perhaps we are asking the wrong question. If we can determine the proper question and arrive at a solution, that may be the solution to the original problem.
We now have the problem of whether or not the definition of "problem" is a solution to the original problem,ie. "Can we call something a 'problem' if it has no solution at all? " If this is not a solution, is the original question still a question? If not it needs no solution and the problem arises as to why it was asked, indeed, HOW was it asked? That is, how does one ask something which is not a question?
I propose that we take this question out back to my shed and attempt to dissolve it in one or more of the various solvents, acids, and other hazardous chemicals I keep back there for just such occasions as this problem presents and just see if it does go into solution. If the problem of being or not being a problem dissolves, the problem is resolved and no further consideration is required. However, if the problem of being or not being a problem is not resolved due to not dissolving into solution, I think there is still a mathematician piled with some other dusty junk in the corner. Perhaps the use of the proper formula by the mathematician will arrive at the solution.
Do not disturb the other pile of junk, last time I looked that Zen philosopher was still in there and next thing ya know we'll be considering the problem of "Can we call something a "solution" if there is no problem at all?" I tell ya, ever time I talk to him I wind up wantin to give him a one handed slap upside the head.

Then you have a big problem dont you?

Oh yes it happens of course - unresolved problem. Or... sometimes it may require investing a lot money to solve it. So, one can not call it totally unsolvable.

Obese people who can not lose weight no matter what they do, try an only solution - a surgery - that required a lot of money.
5+

Learning to it see it as a non-problem is a solution.

Just because a problem has no immediate solution does not mean it is incapable of being solved. It has been said that necessity is the mother of invention. If a problem necessitates a solution on a grand scale, then every resource available should be used to solve it.

i think god wouldn't gave you a problem that can't be solved... or maybe he would ...

No we can'nt we should call it life

it only becomes a problem when some one is threaten or insure about the situation... it' takes one!!! and that ruins it all!!!!

Can we call something a solution if there is no problem?

Yes. In fact I'd say a problem is defined by the apparent lack of a solution (to a difficulty). Once the solution is found, it ceases to be a problem.