Advanced Problem Solving Module 21

Advanced Problem Solving Module 21

This module shares a selection of "unusual" STEP and other advanced mathematics examinations questions and offers advice on solving problems that do not fit easily into a topic category.
What is an "unusual" STEP and other advanced mathematics examinations question, and how might you solve such a thing?

Probably a Code? 

Age 16 to 18 Challenge Level:
Is the regularity shown in this encoded message noise or structure?

Torus Patterns 

Age 16 to 18 Challenge Level:
How many different colours would be needed to colour these different patterns on a torus?