What is the shortest route to walk every corridor in my school?

Research question

What is the shortest closed route that walks every corridor of my school at least once (the Chinese postman problem), and how much shorter is it than the route the caretaker or duty staff actually use?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Anyone who checks every corridor — a caretaker, a security guard, a teacher on duty — faces this problem. Measuring your own school and solving it with graph theory produces an answer someone could use.

The mathematics you'll need

Graphs, vertex degrees and Eulerian circuits
Pairing odd vertices to minimise repeated edges
Shortest paths between odd vertices
Comparing with a real route

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Draw your school's corridors as a graph and measure edge lengths by pacing or from a floor plan (with permission).

GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Model the building as a weighted graph; explain choices.
Identify odd vertices.
Find the best pairing and total route length.
Construct an actual route.
Compare with the real route and reflect on stairs, locked doors and time vs distance.

Pitfalls that cost marks

Too many odd vertices to pair by hand without a systematic method — explain yours.
Unclear graph (label everything).
Ignoring that stairs take longer than corridors.

Showing personal engagement

Walk and time your optimal route.
Interview the person who does the route now.
Extend to a route that does not have to return to the start.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Weight edges by time (stairs slower) and see whether the optimal route changes.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).