Dobble – how does it work?

For background: read this page on Permutations and Combinations

How does Dobble work? 

I want you to figure out how you design Dobble so that every single time you turn over a card it has one and only one match between any 2 cards.
Let’s start with some guesses and then begin working up.

1. Guesstimation

Grab a notebook or start a note on a computer dedicated to this task. Write down your guessed answers to these questions:

  1. How many images are there per Dobble card?
  2. How many different images are used in total in a Dobble set?
  3. How many Dobble cards are there?
  4. Could there be any more Dobble cards?
  5. How would you go about making the cards so that you always have one and only 1 match between any 2 cards?

2. Starting small

Now let’s start tackling this in a small and simple way:

  • What’s the smallest number of images you could have on a card to play Dobble?
    • Obviously 1 wouldn’t work. I mean you could have any number of cards in a set with 1 image on them and you could always guarantee each card would have 1 and only 1 match on it. But you’d also have more than one identical card in the pack, and the real Dobble never has 2 totally identical cards.
    • So what about 2 images?
      • How many cards could we produce? (n)
      • How many different images would you need? (r)
      • Draw the cards. How can you know that you have all the cards you need?