He left for his summer cottage to puzzle out what he might try next. [VERB PREP. wh]

他动身到他的避暑别墅去想清楚他下一步应该做什么。

Nosenko puzzled out Kutya's surname. [VERB PREP. noun (not pronoun)]

诺先科苦苦思索终于想起了库佳的姓。

The risks can be so complex that banks hire mathematicians to puzzle them out. [VERB noun PREP.]

这些风险太过复杂，因此银行雇请了数学家来破解它们。