From Middle English probleme, from Middle French probleme, from Latin problema, from Ancient Greek πρόβλημα (próblēma, “anything thrown forward, hindrance, obstacle, anything projecting, a headland, promontory”), from προβάλλω (probállō, “to throw or lay something in front of someone, to put forward”), from προ- (pro-, “in front of”) + βάλλω (bállō, “to throw, to cast, to hurl”).

[note the etymologic similarity to word "project":  from Latin projectum ‘something prominent’, neuter past participle of proicere ‘throw forth’, from pro- ‘forth’ + jacere ‘to throw’)]