According to question #15, Alice takes Statistics at 3pm and Geography.

If she takes Statistics at 3pm, she does not take statistics at 9am (according to the setup, “no one is allowed to take any course more than once per semester”).

If she does not take statistics at 9am, then she does not take psychology (this is the contrapositive of the fourth rule).

If she takes Geography, then according to the last rule she does not take World History.

At this point, there are three courses that she isn’t taking: Statistics at 9am, World History, and Psychology. Since she takes four courses, there are only four available spots for courses that she doesn’t take, so now there is only one spot left. Combining the first two rules shows that if she doesn’t take Russian then she takes Japanese, and if she takes Japanese then she doesn’t take Macroeconomics. Thus, if she doesn’t take Russian, then she also doesn’t take Macroeconomics.

Since there is only one spot left for a course that Alice doesn’t take, it can’t be the case that she doesn’t take Russian, because if she doesn’t take Russian then she also doesn’t take Macroeconomics, which means that there would be *five *courses that she isn’t taking. But that’s one course too many. So she must take Russian.

Hope that helps 🙂