The teacher gave us so difficult a problem as we couldn't so

as
这是一道陷阱题,很容易误选that
The teacher gave us so difficult a problem (as) we couldn't solve.这道题里,as在句中引导的是一个定语从句,修饰先行词problem,并在从句中作 solve的宾语.
The teacher gave us so difficult a problem (that) we couldn't solve it.
如果从句中不缺宾语的话,就用that,与之前的so 组合成 so ...that...如此...以至于这样一个结构作结果状语.