Which one of the following sentences is true or more common?
This is one of the most well-known methods used to solve this problem.
This is one of the well-known methods used to solve this problem.
I want to say that almost every one knows this method. Can we just remove most?
Is there a better expression to say this?
The superlative of "well" is "best":
You should then say:
Note: I reply to your comment with this graph ("best-known" expresses the same concept as "well-known" in the superlative, which is what you seem to want):
Both "most well-known" and "best-known" are completely unambiguous in writing, and mean the same thing. In speech, however, "best-known method" may be heard as "best known method", which instead means "the best of all the methods which are known". Simply for disambiguation while speaking, I would definitely use "most well-known".
In fact, while "better-known" and "best-known" are undoubtedly more common in writing than "more well-known" and "most well-known", as Gustavson's graph indicates, they're both just a little bit more formal than I would hear in everyday usage. Wiktionary lists both forms, but I'm afraid I can't find a more definitive source.
You can also use:
This is one of the more well-known methods used...
This phrase is often found in contexts like this. An example, from a textbook:
One of the more well-known fractals is the Cantor set.
Source: Elements of Quantum Optics.
Using more instead of most gets us away from the hair-splitting angst some might have when you use "most".
