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

我对这个问题冥思苦想了很久才豁然开朗。

《牛津词典》

I puzzled over it for a time and eventually I was able to think of another equation which would get over the logical difficulties of the negative probabilities.

我为此困惑过一段时间，最终我得以想到另一个方程，这个方程可以克服负概率的逻辑困难。

youdao

I puzzled over it for hours before it finally clicked.

我对这一问题茫然不解，几小时后终于顿开茅塞。

youdao

I puzzled over it for hours before it finally clicked.

我对这一问题茫然不解，几小时后终于顿开茅塞。

youdao