Idiom for "trying to figure something out"?

Question

In Swedish, we have an idiom that goes, "to suck on the/that caramel [for a while]" and is used either when you need to contemplate a decision ("I'll have to suck on that caramel for a while before deciding.") or to try and figure something out ("He had been sucking on that caramel just as long as I had, but neither of us had an answer.")

I can't find a good English equivalent to the second meaning of the idiom, but I'm sure there is one. So, I need an idiom for trying/having tried to figure something out (without luck, so far.)

Answer 1

A similar idiom in English: "I'll have to chew on that for a while."

How it may affect your dental health compared to sucking caramal is debatable.

Less interesting, but gets the job done: to mull something over.

Answer 2

I think rack one’s brain may fit in your context:

to strain in mental effort, esp to remember something or to find the solution to a problem.

(Collide Dictionary)

Answer 3

think something over TFD an idiom:

• to think about something and whether one will choose to do it.

• I need a few minutes to think it over. Let me think over your request for a day or so.