What is the math behind the game Spot It? I just purchased the game Spot It. As per this site, the structure of the game is as follows:

Game has 55 round playing cards. Each card has eight randomly placed symbols. There are a total of 50 different symbols through the deck. The most fascinating feature of this game is any two cards selected will always have ONE (and only one) matching symbol to be found on both cards.

Is there a formula you can use to create a derivative of this game with different numbers of symbols displayed on each card.
Assuming the following variables:


*

*S = total number of symbols

*C = total number of cards

*N = number of symbols per card


Can you mathematically demonstrate the minimum number of cards (C) and symbols (S) you need based on the number of symbols per card (N)?

I have the game myself.  I took the time to count out the appearance frequency of each object for each card. There are 55 cards, 57 objects, 8 per card.  The interesting thing to me is that each object does not appear in equal frequency with others ... the minimum is 6, max 10, and mean 7.719.  I am left curious why the makers of Spot It decided to take this approach.  Apparently they favor the clover leaf over the flower, maple leaf, or snow man.
