As he worked, he became obsessed with solving the problem.

became 是动词 become 的过去式，表示"变得、成为"的状态变化。 obsessed 是形容词，来自动词 obsess（使着迷），表示"着迷的、痴迷的"。 with 在这里是介词，表示"关于、对于"的关联关系。 became obsessed with 是一个固定搭配，表示"变得痴迷于..."，描述某人逐渐对某事产生强烈兴趣或执着状态。