Treebeard's Stumper Answer
Take a grand tour of the science building when you visit the DMS Science Fair on Friday. Below is a sketch of the floor plan showing all rooms and connecting doorways, including the hidden door behind the blackboard and the mysterious "utility room." Closets with only one entry are not shown. That's a lot of doors! Can you find a path through the building that goes through each doorway exactly once, without going through any doorway a second time? Start and end where you like, but there's a bonus if you start on the porch.
You can tour the science building, but only if you start and end in Dorothy's office and the classroom. It's not possible from the porch. If a room has two doorways, then you can enter and leave by different doors. If it has any even number of doorways, then you can pass through it multiple times. But if it has an odd number of doorways, then it must be a place where you either start or finish. There are six entrances from the outside, but the office and classroom each have three doorways. Therefore it's impossible to start on the porch. The real stumper is the layout of the building. How was it used as a home?
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