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"solves itself" is a correct and usable phrase in written English.
It is often used to describe a situation in which a problem or issue is resolved without any outside intervention or effort. Here is an example: "After a heated debate, the members of the committee came to a unanimous decision. It seemed that the issue had solved itself as each member realized the value of compromise."
Exact(6)
Soon, this problem solves itself.
("I take it," a magistrate asks a doctor called in to advise on the case, "that your clever scientific colleagues have not yet found a way of distinguishing one man's blood from another?" ) So the mystery more or less solves itself at a local inquest and a subsequent trial at the Old Bailey, with the help of some last-minute revelations, including a letter dictated by one character on his deathbed.
The first reason solves itself in time; the successes in L.A. tech just haven't grown to the scale where this level of impact is a reasonable expectation.
To make it work, a Japanese inventor used servo motors and Arduino boards to actuate the cube as it solves itself.
There is a description of the project on DMM-Make and you can watch the little cube scoot around a table as it solves itself in less than a minute.
Unlike the equation a2 + b2 = c2, which requires some algebraic finesse to produce solutions (not to mention its famously unsolvable cousin a n + bn = cn with exponent n greater than two), the equation a + b = c essentially solves itself: Just pick two numbers a and b, add them together, and voilà.
Similar(54)
It won't solve itself.
That solved itself without lasting effects.
"By then, the problem had solved itself".
Now, the problem has solved itself.
The housing crisis will not solve itself.
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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