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1. Maths a statement requiring a solution usually by means of one or more operations or geometric constructions
2. designating a literary work that deals with difficult moral questions



in the broad sense, a complex theoretical or practical question requiring study and a solution. In science, a problem consists in a contradictory situation that arises in the form of opposing views to the explanation of any given phenomenon, object, or process and that requires an adequate theory for its solution. A key prerequisite for the solution of a problem is its correct statement or formulation. An incorrectly stated problem merely detracts attention from the solution of the real problem. [21–8—4]

References in classic literature ?
The doctor had much difficulty in restraining the balloon; but at length the wind died away with the setting in of nightfall; and the two friends kept watch together in an almost desperate state of mind.
My second difficulty was with regard to my name, or rather A name.
I had difficulty often in securing a satisfactory teacher.
This difficulty for a long time quite confounded me.
And it seems to me that nothing less than a long list of such cases is sufficient to lessen the difficulty in any particular case like that of the bat.
Therefore, I can see no difficulty, more especially under changing conditions of life, in the continued preservation of individuals with fuller and fuller flank-membranes, each modification being useful, each being propagated, until by the accumulated effects of this process of natural selection, a perfect so-called flying squirrel was produced.
Although no graduated links of structure, fitted for gliding through the air, now connect the Galeopithecus with the other Lemuridae, yet I can see no difficulty in supposing that such links formerly existed, and that each had been formed by the same steps as in the case of the less perfectly gliding squirrels; and that each grade of structure had been useful to its possessor.
Even in so extreme a case as this, if the supply of insects were constant, and if better adapted competitors did not already exist in the country, I can see no difficulty in a race of bears being rendered, by natural selection, more and more aquatic in their structure and habits, with larger and larger mouths, till a creature was produced as monstrous as a whale.
Yet reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist; if further, the eye does vary ever so slightly, and the variations be inherited, which is certainly the case; and if any variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real.
With these facts, here far too briefly and imperfectly given, which show that there is much graduated diversity in the eyes of living crustaceans, and bearing in mind how small the number of living animals is in proportion to those which have become extinct, I can see no very great difficulty (not more than in the case of many other structures) in believing that natural selection has converted the simple apparatus of an optic nerve merely coated with pigment and invested by transparent membrane, into an optical instrument as perfect as is possessed by any member of the great Articulate class.
One thing only could and ought to be done, and Vronsky determined upon it without an instant's hesitation: to borrow money from a money-lender, ten thousand roubles, a proceeding which presented no difficulty, to cut down his expenses generally, and to sell his race horses.
According to Al-Yamani, global statistics confirmed that between seven and 10 percent of children have difficulty both reading and writing, and 40 percent of them drop out of school because of this.