Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

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?

Make it yours, then agree it with your teacher.

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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

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.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Not a natural fit	The core technique sits in the AI course or at HL; an AA SL student could use it only as clearly explained new mathematics.
AA HL	Not a natural fit	The mathematics is mainly from the AI course; at AA HL the exploration would need an AA-level approach (calculus, proof or probability theory) to reach the top of Criterion E.
AI SL	Not a natural fit	The mathematics is mainly AA or HL (calculus or proof beyond AI SL); an AI SL version would need a data-driven, technology-based approach.
AI HL	Good fit	Graphs, vertex degrees and Eulerian circuits; Pairing odd vertices to minimise repeated edges

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: too many odd vertices to pair by hand without a systematic method — explain yours; and unclear graph (label everything). Say how each one affects your answer.

Use of mathematics (E)

HL: graphs, vertex degrees and Eulerian circuits; pairing odd vertices to minimise repeated edges; shortest paths between odd vertices; comparing with a real route, each explained in your own words and carried out correctly.

How networks & graphs explorations reach the top bands in general: Networks, graphs & algorithms IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

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

Extending it for HL

Add an HL technique the question genuinely needs: what an HL networks & graphs exploration adds.

See a complete IA, marked

What is the quickest way to deliver a leaflet to every house on my estate? (AI HL) explores a question like this one, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Graphs, vertex degrees and Eulerian circuits, pairing odd vertices to minimise repeated edges, shortest paths between odd vertices and comparing with a real route.

Where can I get data for this IA?

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

Turn this idea into your IA

The planner opens with “What is the shortest route to walk every corridor in my school?” filled in: the question, the maths and the data sources.

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Writing it up: how to write a Maths IA, step by step · structure and format · mistakes that cost marks · annotated exemplars, marked on every criterion