As Michael Siefert says, this is both used and immediately recognizable in American English, but it would be generational, with the oldest speakers finding it natural, many or most middle-aged speakers finding it antiquated, and younger speakers likely being unfamiliar with it. The reason you are not seeing it in media is because the mass-media would focus on the middle demographic and so would only use it when they wanted to imply old-fashionedness.
Youth typically use 'literally' as an emphasizer, so young people would say "Literally anyone could solve this". However, that would be too slang to be used in mass media (although common in demographically targeted social media).
More recognizable alternatives include "Any Joe (or any regular Joe or any Joe Shmoe)," "any guy off the street", "any idiot", "any fool", and "anyone with half a brain". The first two emphasize how easy the problem is such that any common person has the ability to solve it, and the second three that even someone of limited ability would be able to solve it.
Other answers and comments have suggested 'everyone and their brother' or 'everyone and their dog'. I think there is a subtle distinction here between anyone and everyone, that is, between saying that the problem is so easy that a single person of the lowest common denominator could solve it, and saying it is so easy that every person in any given group would be able to solve it. I think this is the same distinction that Darrel Hoffman and gotube are drawing between 'Tom, Dick, or Harry' and 'Tom, Dick, and Harry', but I don't know if that distinction is used in Indian English or what the OP's original intent was.
Since I have just finished my yearly re-watch of GATTACA (I show it to my students) I feel I should include a quote from Jerome / Eugene:
That was the company that sell us your hair dye. They sent me ''summer wheat" instead of "honey dawn." Any fool knows it's two shades lighter.