Dobble

You have 7 colored pens (red, orange, yellow, green, blue, indigo, purple) and 7 cards. Let’s think about the following rules:

• Each card has 3 different colors drawn on it.
• Any two cards share exactly one color in common.

[Question] Is it possible to draw on the cards using the 7 colors so that both rules are satisfied?

Comment

I recently bought Pokémon Dobble. The instruction says: “There are 55 cards, each with 8 Pokémon. Every pair of cards shares exactly one Pokémon. Try to find it faster than anyone else!”

While I was playing Dobble with my nephew and sister, my sister suddenly asked: “Why do any two cards always have only one Pokémon in common?”

I had no idea at that moment. Later, I looked it up and found an explanation in a book I had read before: Introduction to University Mathematics through Games written by Prof. Yasuda (in Japanese).

By the way, the instructions for Pokémon Dobble say that there are 57 different Pokémon in total, and actually, the game would still work fine even if there were 57 cards instead of 55.

By the way, my lab is full of Pokémon stuff — not only Dobble, but also many Pokémon plushies. You’re welcome to visit and take a look anytime.