I was working on creating a card game with a friend, and we wanted to understand how card draws would play out.
We have a set of 18 distinct cards. Each card participates four times in some pre-defined combination of three cards (order doesn't matter) for a total of 24 combinations. How many cards do we need to draw in our opening hand, to ensure that one of the combinations exists in our opening hand?
We thought this had to do with combinatorics, maybe related to this question, but we get stuck thinking about it, because each of our cards is distinct, so we don't actually have 24 identical cards to choose from, but rather 24 different sets of 3 cards out of 18 unique cards.