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The phrase "almost impossible to solve" is correct and usable in written English.
You can use it when describing a problem or situation that is very difficult to resolve, but not entirely beyond reach.
Example: "The mathematical equation presented in the exam was almost impossible to solve, leaving many students frustrated."
Alternatives: "nearly unsolvable" or "virtually impossible to resolve."
Exact(11)
Coleman is drawn to the kinds of conflicts that are so complicated and divisive they seem almost impossible to solve.
These challenges are extremely hard to solve one by one, and at the moment they're almost impossible to solve altogether".
Prediction of the flow-generated noise at the design stage is important in engineering, since it is almost impossible to solve the problem after the installation of a ventilation ductwork system.
"The problem of military coups is extremely difficult in terms of jurisprudence, almost impossible to solve — perhaps art and cinema can come up with answers that we as legal scholars cannot provide," Walter Gropp, a German law professor and member of the festival's advisory board, said in Istanbul last week.
Nevertheless, when more than six terms are involved, it becomes almost impossible to solve the problem.
The general RA is a nonlinear, non-convex program so that it is almost impossible to solve it directly for any realistic number of subcarriers, users and antennas.
Similar(49)
Certain problems will be almost certainly impossible to solve through classical optimisation, no matter what 'trick' is sought for or employed to try make the problem solvable.
Live-chat exchanges are cold and it's almost impossible to problem solve with 140-characters on Twitter.
Maybe, as with Candy Crush, the game boards are calibrated to be almost-but-not-quite impossible to solve in the number of moves you get for free … but you can pay for extra moves when you've reached frustrated breaking point.
Actually, the optimal coordination control for MASs depends on the solutions to the coupled Hamilton Jacobi Bellman (HJB) equations which are almost impossible to be solved analytically.
In other words, the color information of an image is also dependent on the imaging characteristics of specific camera; it is almost impossible to be solved only by the adjustment of camera mode.
More suggestions(15)
virtually impossible to solve
almost impossible to eradicate
almost impossible to fix
almost impossible to cope
almost impossible to remove
almost impossible to manage
practically impossible to solve
almost impossible to reconcile
almost impossible to tackle
almost impossible to eliminate
almost hard to solve
almost certain to solve
almost invisible to solve
almost unnecessary to solve
almost singular to solve
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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