Why would you need to read about the characters in the story before
reading the solution to the problem?

Explanation:  you need to read about the characters in the story before  reading the solution to the problem because you need to find out the personalities of your characters so you can infer and contradict what you think will happen later on then continue reading to find out the solution to the problem.

cockroaches and rats often are a symbol for things that are disgusting or vile. though i don't know which play you are talking about, i hope this !