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"tangled problem" is a correct and usable phrase in written English.
You would generally use this phrase in the context of a complex issue that is difficult to solve. For example, you could say, "The jury had a tangled problem to solve when determining the verdict."
Exact(2)
Taylor, W. R. & Lin, K. Protein knots: a tangled problem.
That will present a tangled problem for the reinforcements to the UN monitoring force (Unifil) and Lebanese government troops who are supposed to take control of the border region.
Similar(58)
Ultimately, each country presents its own set of tangled problems and predicaments, with no easy answers.
And so he has devised one-dimensional solutions to tangled problems like homelessness and welfare.
It had taken sixty years to resolve the tangled problems to which FDR devoted one frantic, memorable summer.
That their tangled problems end up being reduced to the title question is a measure of the play's bitter humor (1 25).
General Clark, landing in Korea, made it clear he also had scant hope the truce would go far to solve the tangled problems of a divided Korea.
Friends of the younger Mr. Pinault recalled recently that he had complained privately that his father, in handing over the reins of the empire, also bequeathed two tangled problems at Executive Life and Gucci.
"In fact, one might almost feel that if they could keep it up, there is hardly anything they could not do, either in the field of war or in the not less tangled problems of peace".
Knotty problem: You're a knitter and your yarn is hopelessly tangled — who you gonna call?
They obtained the existence results for the tangled lexicographic problem via the study of a related sequential problem.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com