puzzle over

I puzzled over the problem for ages before the light suddenly dawned on me.

我对这个问题冥思了很才豁然开朗。

They puzzled over the question for quite a while.

这问题他们了很。

She puzzled over the postmark on the letter.

她信封上的邮戳。

The old general was puzzling over the old map.

老将军对着那张旧图思索着。

He puzzled himself over the matter.

他对那件事绞尽脑汁。