The noun conundrum means a puzzle or problem which is difficult or impossible to solve. 

Synonyms are riddle, mystery, enigma or brain-teaser.

The word origins 1590 and was used probably to describe a person as being pedant (excessively concerned with minor details and rules). The term later developed to whim (sudden change of mind) and in the 17th century it described a word of unknown origin. 1745 it was described as a riddle where the answer often involved a pun.

He is in the conundrum of trying to find a job without any experience.

Balancing wealth accumulation and living life at its fullest is a massive conundrum among millennials nowadays.

The team is struggling to find an answer to this conundrum.