The phrase "guess how many" is correct and usable in written English.
You can use it whenever you want to ask someone to guess a number, for example: "Guess how many jellybeans are in the jar!".
Guess how many he killed.
I won't even guess how many millions that cost.
I wouldn't like to guess how many books Aaron's read.
We can only guess how many years remain.
The problem now, though, was that South had to guess how many hearts his partner held.
Looking around us, we try to guess how many other cancer survivors are in the audience.
Guess how many administrative bodies regulate Indian higher education, to take one example?
You can guess how many cars there will be in the extremely limited production run.
Using the company's average selling price, investors can guess how many chips that $1.1 billion represents.
Care to guess how many times it has been invoked in the half-century of NATO?
Agencies and charities sometimes try to guess how many women work in this way.
