There are five people - Sarah, Bill, Eric, Molly, Nick - scheduled for appointments at a doctor's office on a specific morning, plus a walk-in, Katie. There are five appointment slots: 9:30, 10:00, 10:30, 11:00, and 11:30. The following conditions apply. Katie will only get a slot if one of the five people with an appointment does not show up. Sarah is not scheduled for 10:00 or 11:00. Eric is scheduled for 11:30. Molly's appointment is immediately before Nick's. If Eric switches appointment times so that his appointment is now at 11:00, if none of the other conditions change, who now has the 11:30 appointment slot?

Explanation: Eric's appointment is moved from 11:30 to 11:00. Molly's appointment is immediately before Nick's, which must take up two consecutive slots. The possible pairs for (Molly, Nick) are (9:30, 10:00) or (10:00, 10:30). If (M,N) is (9:30, 10:00), Sarah cannot be at 10:00/11:00, so Sarah must be at 10:30. The slots are M(9:30), N(10:00), S(10:30), E(11:00). 11:30 is left for **Bill**. If (M,N) is (10:00, 10:30), Sarah cannot be at 10:00/11:00, so Sarah must be at 9:30. The slots are S(9:30), M(10:00), N(10:30), E(11:00). 11:30 is left for **Bill**. In both possible scenarios where the remaining conditions hold true, **Bill** must have the 11:30 slot. Therefore, Sarah or Bill is an accurate list of the possibilities, although only Bill is possible.