I played a few games of Dobble with my niece and got curious about the algorithm used to generate the cards. It turns out it’s not trivial and one of the best ways to interrogate it is as a finite projective plane.
I got the most useful information from www.101computing.net/the-dobble-algorithm which has actual code although the clearest explanation was on www.petercollingridge.co.uk/blog/mathematics-toys-and-games/dobble
The maximum number of possible cards is n^2 + n + 1 where n is the number of symbols per card minus one.
| Number of Symbols on Card | Max Number of Cards |
| 2 | 3 |
| 4 | 13 |
| 5 | 21 |
| 8 | 57 |
| 12 | 133 |
The number of symbols on the card doesn’t have to be a prime number plus one but the algorithms found online require that.
I thought it was pretty interesting that 8 symbols per card allows 57 cards but the game itself comes with 55 cards. Presumably because once you put one card in the center 54 is divisible by both 2 and 3 for even number of cards per player in the common cases. I wonder which two cards are missing but not enough to look through them all!