I was asked to learn all __ 100 poems by heart within a week,___ task that seemed I impossible to complete.老师给的答案是the和a我想第一个是特指双方都知道特指的100 poems 所以是the,那么第二空呢?为何是a 不是the?有

I was asked to learn all __ 100 poems by heart within a week,___ task that seemed I impossible to complete.
老师给的答案是the和a
我想第一个是特指双方都知道特指的100 poems 所以是the,
那么第二空呢?为何是a 不是the?
有不有可能老师错了呢

我觉得不是特指一个任务,而只是一个这样的任务而已,用A代表整体.