a Gordian knot

a Gordian knot

  (formal)
a difficult problem
Usage notes: In an old story, King Gordius of Phrygia tied a complicated knot which no one could make loose, until Alexander the Great cut it with his sword.
Homelessness in the inner cities has become a real Gordian knot.
See also: Gordian, knot
References in classic literature ?
To her mind this complicated tangle of the affairs of life was a Gordian knot impossible to untie and which genius ought to cut.
Last year, ManpowerGroup revealed that Human Age forces had strengthened, becoming more intertwined and difficult to separate - like a Gordian Knot.
Houdini Brown escaped from a Gordian knot he'd unnecessarily tied himself.
This tiny country is held fast by a Gordian knot of unusual complexity, one whose many strands lead to such places as Israel, Syria, America and Iran.
MacKenzie explains that in many process-oriented organizations, "intricate patterns of effective behavior have grown around lessons of success and failure, creating a Gordian Knot of Corporate Normalcy.
The whole question of electronic privacy is like a Gordian knot," Casti said.
For some time the pornography issue has been a Gordian knot in which free speech, feminism, free enterprise, violence against women, child sexuality, and gay rights are knitted into a tightly balled mess.
Far from the Global Village that media visionary Marshall McLuhan once predicted-in which everyone would communicate in the same language-worldwide business, currently taking place in more than three dozen languages, is more of a Gordian Knot.