difficulty - a condition or state of affairs almost beyond one's ability to deal with and requiring great effort to bear or overcome; "grappling with financial difficulties"

race problem - a social and political problem caused by conflict between races occupying the same or adjacent regions

balance-of-payments problem - an economic problem caused by payments for imports being greater than receipts for exports

difficulty - a factor causing trouble in achieving a positive result or tending to produce a negative result; "serious difficulties were encountered in obtaining a pure reagent"

can of worms - a source of unpredictable trouble and complexity

deep water - serious trouble

growing pains - problems that arise in enlarging an enterprise (especially in the early stages)

hydra - trouble that cannot be overcome by a single effort because of its many aspects or its persistent and pervasive quality; "we may be facing a hydra that defies any easy solution"

matter - a problem; "is anything the matter?"

question, head - the subject matter at issue; "the question of disease merits serious discussion"; "under the head of minor Roman poets"

mystifier, puzzle, puzzler, teaser - a particularly baffling problem that is said to have a correct solution; "he loved to solve chessmate puzzles"; "that's a real puzzler"

case - a problem requiring investigation; "Perry Mason solved the case of the missing heir"

homework problem - a problem that students are assigned to do outside of class

brain-teaser, conundrum, riddle, enigma - a difficult problem

stumper, toughie, poser, sticker - a particularly difficult or baffling question or problem

Gordian knot - any very difficult problem; insoluble in its own terms

crossword, crossword puzzle - a puzzle in which words corresponding to numbered clues are to be found and written in to squares in the puzzle

koan - a paradoxical annecdote or a riddle that has no solution; used in Zen Buddhism to show the inadequacy of logical reasoning

acrostic, word square - a puzzle where you fill a square grid with words reading the same down as across

pons asinorum - a problem that severely tests the ability of an inexperienced person

rebus - a puzzle where you decode a message consisting of pictures representing syllables and words