Meaning of PROBLEM in English

n.1 a doubtful or difficult matter requiring a solution (how to prevent it is a problem; the problem of ventilation).

2 something hard to understand or accomplish or deal with.

3 (attrib.) a causing problems; difficult to deal with (problem child). b (of a play, novel, etc.) in which a social or other problem is treated.

4 a Physics & Math. an inquiry starting from given conditions to investigate or demonstrate a fact, result, or law. b Geom. a proposition in which something has to be constructed (cf. THEOREM).

5 a (in various games, esp. chess) an arrangement of men, cards, etc., in which the solver has to achieve a specified result. b a puzzle or question for solution.

Etymology: ME f. OF probleme or L problema f. Gk problema -matos f. proballo (as PRO-(2), ballo throw)

Oxford English vocab.      Оксфордский английский словарь.