"Was denken Sie" vs. "Wie denken Sie"

Question

This could be a duplicate but I haven't found one.

My German-Japanese dictionary lists both Was denken Sie? and Wie denken Sie? as expressions to ask for an opinion. Combined with searches on the web, I think both are actually acceptable forms. But I noticed Langenscheidt has only Was denken Sie?.

My questions are:

1. Are both acceptable as an equivalent to English What do you think?
2. Is there any difference in meaning or occasion where they are used?
3. (If Wie.. is accpetable) In my understanding, How do you think? in English is considered wrong. If Wie denken Sie? is grammatically wrong in the same way, why is it acceptable?

Answer 1

Was means what and is asking for an object.

Was denken Sie?
What do you think?

So that's an open question about your thoughts (e.g. your opinion).

Wie means how and is asking for a method, a manner, a way - in German Art und Weise.

Wie denken Sie?
How do you think?

is therefore not asking for an opinion or your thoughts. It's rather asking about the subject of thinking itself.

However, for a given subject you can ask:

Wie denken Sie darüber?
(or Was halten Sie davon?)

That would mean something like: Do you think, it's a good idea? / Do you think, I am right? ...

There is nothing wrong with the grammar. Wie denken Sie is just not asking for an opinion.

Answer 2

As you wrote, "was" means "what" and "wie" means "how". So I would prefer "was".

I can imagine using "how" when the question ask more about the though process and less about the result.

There may also be regional differences.