Maths of Dobble
Graph Theory
Every pair of cards in Dobble shares exactly one matching symbol. Work out why, and how many cards a deck like this can have.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Dobble decks are built from a mathematical structure called a finite projective plane, which guarantees that any two cards share exactly one symbol. The full theory sits outside the IB syllabus, so this exploration works best as an enrichment topic: build small decks by hand, find the pattern connecting symbols-per-card to deck size, and use counting principles to explain why some deck sizes are impossible.
Guiding Questions
- In Dobble, every pair of cards shares exactly one symbol. How is that possible? Try to build a small version yourself.
- How many cards and symbols does a Dobble-style deck need? Find the pattern for different symbols-per-card.
- Connect the structure to finite projective planes — what fails when the number of symbols per card is 7?
- Design and test your own working mini-deck, then explore which deck sizes are impossible.