Gordian
Etymology
From the Gordian knot, an impossibly complex knot tied at Gordium in Phrygia; an oracle promised that whoever undid it would rule Asia. According to legend, Alexander the Great, rather than fumbling with the strands, simply sliced it in two with his sword. The adjective names such intractable tangles, and "to cut the Gordian knot" means to solve one with a single decisive act.
adjective · /GOR-dee-un/
Extremely intricate or seemingly impossible to resolve by ordinary means.
What it names
A problem so tangled that patient untangling will never work — use it for the knotty situation that demands a bold, unexpected stroke rather than careful analysis.
Example
The contract dispute had become a gordian mess of countersuits until the two founders met privately and just agreed to split the company.
Related idea
Intractable means stubbornly resistant to any solution; gordian implies the tangle can be resolved, but only by a bold shortcut rather than conventional effort.