any question or matter involving doubt, uncertainty, or difficulty.
a question proposed for solution or discussion.
Mathematics. a statement requiring a solution, usually by means of a mathematical operation or geometric construction.
difficult to train or guide; unruly: a problem child.
Literature. dealing with choices of action difficult either for an individual or for society at large: a problem play.
no problem, (used as a conventional reply to a request or to express confirmation, affirmation, or gratitude).

1350–1400; Middle English probleme < Latin problēma < Greek próblēma orig., obstacle, (akin to probállein to throw or lay before), equivalent to pro- pro-2 + -blē-, variant stem of bállein to throw (cf. parabola) + -ma noun suffix of result

subproblem, noun

1, 2. puzzle, riddle, enigma.

1. certitude. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
problem (ˈprɒbləm)
1.  a.  any thing, matter, person, etc, that is difficult to deal with, solve, or overcome
 b.  (as modifier): a problem child
2.  a puzzle, question, etc, set for solution
3.  maths a statement requiring a solution usually by means of one or more operations or geometric constructions
4.  (modifier) designating a literary work that deals with difficult moral questions: a problem play
[C14: from Late Latin problēma, from Greek: something put forward; related to proballein to throw forwards, from pro-² + ballein to throw]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

1382, "a difficult question proposed for solution," from O.Fr. problème (14c.), from L. problema, from Gk. problema "a problem, a question," lit. "thing put forward," from proballein "propose," from pro "forward" + ballein "to throw" (see ballistics). Problem child first recorded 1920.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
But it turns out that these machines may cause problems worse than hanging
His two guests do indeed face two similar and linked problems.
Voters around the country are experiencing problems this morning as voting
  machines break down and long lines form.
Pro: the points will provide the bribe many of them seem to need to work
  practice problems.
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