I am wondering which following form is correct:
- Anyone can find the answer himself.
- Anyone can find the answer themselves.
More generally, what reflexive pronoun should I use with anyone/anybody?
Almost all English speakers and writers use "themselves."
This question was studied in 2009 by Collins Dictionaries for the Committee on Bible Translation. The conclusion is that the plural generic is almost universal and increasing, against masculine generic and other alternatives.
Either "himself" or "herself" is most accepted by prescriptive grammarians. "Herself" is increasingly used by itself in academic writing to counterbalance the sexist implications of assuming that everyone is male (by using the male form as the generic for all people).
"Themselves" is probably most common but (practically speaking) could be considered more casual.
I do not believe I have ever seen "themself" and would personally consider it the least appealing of all possible options. A native speaker might use it to make a point or promote language change, but in an obviously non-native speaker it would almost certainly be taken as an error.
If I were you, I would go with "him or herself" or "themselves."
There is no universally accepted "correct" answer: whatever you choose, himself or herself or themselves or themself, you are going to annoy some of your readers.
If you care, the only solution is to find another way of saying it.
—and so forth.
I would go with "themself."
Singular they/them has a long history in the English language, and has come back into style with a lot of mainstream publications as a way to avoid inserting gender into general statements like the one you're making.
"Himself" or "herself" are both correct.
"Themselves" is technically incorrect, but has found common usage lately due to concerns about sexism.
The most practical advice is to avoid the idiom, e.g. with something like
"Anyone can find the answer without help." (slightly changes the meaning)
"One can find the answer oneself." (rather formal)
"One can find the answer on one's own." (still kind of formal)
"Anyone can find the answer using only common sense." (getting casual and changes the meaning somewhat)