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!).
This is a hard question to answer straight away, try first to create a “Dobble” set of cards with just 2 symbols per card.
Then try and create a set with 3 symbols per card.
Any patterns you spot should help you to answer the hard question!
Here is a nice blog on the maths behind Dobble.