synonyms: difficulty, issue, trouble, worry, complication, difficult situation, mess, muddle, mix-up;

snag, hitch, drawback, stumbling block, obstacle, hurdle, hiccup, setback, catch;
catch-22, vexed question, quandary, the rub;
predicament, plight, can of worms, hornets’ nest, Gordian knot;
misfortune, mishap, misadventure;
informal dilemma, headache, prob, hassle, pickle, fix, tight spot, fly in the ointment, how-do-you-do, job, gremlin, facer;
informal katzenjammer;
rarenodus
“he’s been under increasing stress due to business and personal problems”

nuisance, source of difficulty, bother, pest, source of trouble, irritant, thorn in one’s side/flesh, vexation;
informaldrag, pain, pain in the neck;
informalfair cow;
vulgar slangpain in the arse
“‘I don’t want to be a problem,’ Lucy said”

a thing that is difficult to achieve.
“motivation of staff can also be a problem”
denoting or relating to people whose behaviour causes difficulties to themselves and others.
“practitioners help families develop strategies for managing problem behaviour in teens”

Geometry
a proposition in which something has to be constructed.

(in chess) an arrangement of pieces in which the solver has to achieve a specified result.