I would suggest that a similar phrase would be: Average Joe
An excerpt from Wikipedia's page on the term includes:
used primarily in North America to refer to a completely average person, typically an average American. It can be used both to give the image of a hypothetical "completely average person"
In the example given in your question, it would be used like:
The average Joe can solve this problem.
Or some similar phrasings:
Your average Joe can solve this problem.
Any average Joe can solve this problem.
Kirt mentions "Joe" in their answer, but I think that specifically an average Joe is equivalent.
"Average Joe" is the first item listed in the "See also" section of the Wikipedia page for "Tom, Dick, and Harry".
"Average Joe" is on this list of terms referring to an average person, on which is also found "Tom, Dick, and Harry": https://en.wikipedia.org/wiki/List_of_terms_referring_to_an_average_person