What are the mathematical/computational principles behind this game?

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My kids have this fun game called Spot It! The game constraints (as best I can describe) are:

  • It is a deck of 55 cards
  • On each card are 8 unique pictures (i.e. a card can’t have 2 of the same picture)
  • Given any 2 cards chosen from the deck, there is 1 and only 1 matching picture.
  • Matching pictures may be scaled differently on different cards but that is only to make the game harder (i.e. a small tree still matches a larger tree)

The principle of the game is: flip over 2 cards and whoever first picks the matching picture gets a point.

Here’s a picture for clarification:

spot it

(Example: you can see from the bottom 2 cards above that the matching picture is the green dinosaur. Between the bottom-right and middle-right picture, it’s a clown’s head.)

I’m trying to understand the following:

  1. What are the minimum number of different pictures required to meet these criteria and how would you determine this?

  2. Using pseudocode (or Ruby), how would you generate 55 game cards from an array of N pictures (where N is the minimum number from question 1)?

Update:

Pictures do occur more than twice per deck (contrary to what some have surmised). See this picture of 3 cards, each with a lightning bolt:3 cards

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