We started off by playing the card game Dobble. If you haven’t seen it before, the game consists of a set of cards like the one above with 8 symbols on each card. You compete in a small group of people to be the first to spot a common symbol with your topmost card and a card in the middle.
The question is, what is the maximum number of cards you could have in the Dobble pack so that there is always exactly one identical symbol between any two given cards, and this identical symbol is not the same for all the cards (that would be a boring game!).
We used these questions to guide us to the answer …
1 Is Dobble a game of chance (stochastic game) or a speed game?
2 Take two random cards from the deck. How many symbols do they have in common? Is this number the same for any two cards?
3 Take two random symbols. Can you find a card which has both of these symbols ? Could there be another card with these two symbols?
4 Now try and create a mini dobble game following these rules. (It will be easier to use letters or numbers rather than fancy symbols!):
- each card contains 3 symbols
- each pair of cards share exactly one symbol
- each pair of numbers appear together on some card
How many symbols did you need ?
How many cards have a particular symbol on them ?
5 Now try to calculate the number of cards in the game of Dobble given that there are 8 symbols per card.
Here is a great article on the maths behind Dobble.