"no solution but" is a correct and usable phrase in written English.
It is typically used to introduce a statement or action that is the only option or course of action available, despite not being desirable. Here is an example: "There seemed to be no solution but to sell the family farm, which had been in their family for generations, in order to pay off their mounting debts."
Gilbert said, "I'm telling you there's no solution, but there's a technique...
I finally decided that there was no solution but to start all over again — this time, using iMovie.
As curtain time approaches and Merelli remains comatose, it appears there's no solution but for Max himself to slap on the blackface and slip into the tights, resulting in mayhem when the original recovers and does the same.
But those reforms were already stalled out, with no solution but an indefinite series of temporary extensions of the existing system in sight.
The correct answer is that there is no solution, but how many people have the confidence in their math ability to make that choice?
The president decried what he called the "deeply pessimistic" vision of America that emerged from Mr. Trump's convention in Cleveland last week — saying it offered no solutions but rather fanned "resentment and blame and anger and hate.
For example, the equation 6x − 9y = 29 has no solutions, but the equation 6x − 9y = 30, which upon division by 3 reduces to 2x − 3y = 10, has infinitely many.
The committee offered no solutions, but it did call for a large, federally funded study of urban water use and issues to help planners and managers cope with the problem.
Ultimately, we are pushing and pulling in a fluid space, creating no solutions, but only violent movement.
Manager Folkert Koopmans told Hamburger Morgenpost: "In view of the high deficits, there is no solution left but closure, if you want to act responsibly.
There is no other solution but to share the Holy City.
