prob·lem /ˈprɑbləm, bṃ, ˌblɛm/
1. A question proposed for solution; a matter stated for examination or proof; hence, a matter difficult of solution or settlement; a doubtful case; a question involving doubt.
2. Math. Anything which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular; or, in algebra, to find an unknown quantity.
Note: ☞ Problem differs from theorem in this, that a problem is something to be done, as to bisect a triangle, to describe a circle, etc.; a theorem is something to be proved, as that all the angles of a triangle are equal to two right angles.
Plane problem Geom., a problem that can be solved by the use of the rule and compass.
Solid problem Geom., a problem requiring in its geometric solution the use of a conic section or higher curve.
n 1: a state of difficulty that needs to be resolved; "she and
her husband are having problems"; "it is always a job to
contact him"; "urban problems such as traffic congestion
and smog" [syn: job]
2: a source of difficulty; "one trouble after another delayed
the job"; "what's the problem?" [syn: trouble]
3: a question raised for consideration or solution; "our
homework consisted of ten problems to solve"