Does the form 'penser + noun' exist?

Does the form 'penser + noun' exist?

Or there must be a preposition in between noun and 'penser', which means only either 'penser à + noun' or 'penser de + noun' ?

If 'penser+noun' exist, how to differentiate 'penser+noun' and 'penser à + noun'? 

Let's say I have a Mathematic problem and I am thinking/reflecting on it, hoping to come out with a solution. It should be 'penser' the mathematic problem or 'penser à' the mathematic problem?

If I finally think of the solution, is it correct to use 'penser à' the solution?

Thank you

This question relates to:French lesson "to think of [doing]"
Asked 11 months ago
ChrisC1Correct answer

Hi Joan,

the verb penser always takes either à or de, never just a noun.

Je pense à Anne. -- I think of Anne.
À quoi tu penses? -- What are you thinking of?
This means thinking about something.

Qu'est-ce que tu pense de ce problème? -- What do you think of this problem?
This is in the sense of having an opinion about something.

-- Chris (not a native speaker).

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