I had the same problem you had, at first, until I noticed the circles in spots 3 and 9 (March and September) in the diagram. I think we can chalk this one up perhaps to a subtle ambiguity in the setup. We’re told that Sarah “will host five out-of-town friends…at her house over the course of seven months – the first ONE in March and the last one in September.
I’m pretty sure Mike intended the word “ONE” (emphasis added) to refer to the friends, though it could be read (and was by both of us) as referring to the months. That is to say, you apparently thought that the first of the months was March and the last was September, and the friends could visit in any five of those months. I believe, though, that the intended implication was that the first friend visited in March, and the last in September.
With that in mind, consider two different cases, one when Q visits in March, and the other when Q visits in June. We know that these are the only possibilities for Q, which has to precede P.
If Q visits in March, then O must visit in June in order to prevent consecutive blank months in May and June. Reading the setup to suggest that the last friend visits in September, there’s nobody left but N.
If Q visits in June, that leaves N and O. But on this reading of the setup, one of them has to visit in March, and that can’t be N. So it’s O who must visit in March, again leaving N as the only friend who can visit in September.
So the short answer is, you’re not crazy! On your interpretation of the setup, your analysis is spot-on.