1》 an unwelcome or harmful matter needing to be dealt with and overcome.
↘a thing that is difficult to achieve.
2》 Physics & Mathematics an inquiry starting from given conditions to investigate or demonstrate something.
3》 (in chess) an arrangement of pieces in which the solver has to achieve a specified result.
ME: from OFr. ~e , via L. from Gk problēma , from proballein 'put forth', from pro 'before' + ballein 'to throw'.