If you’re anything like me, you have a hard time deciding on just two flavors when you go out for ice cream. There are so many flavors and so many combinations!
It begs the question, how many flavor combinations are there?
Let’s start by picking one flavor and seeing how many other flavors I can pair with it. We’ll start with Cherry Cheesecake.
I can have:
- Cherry Cheesecake and Vanilla
- Cherry Cheesecake and Cookies & Cream
- Cherry Cheesecake and Espresso Biscotto
- Cherry Cheesecake and M&M Birthday Cake
- Cherry Cheesecake and Caramel
- Cherry Cheesecake and Reese’s Cup
- Cherry Cheesecake and Chocolate
- Cherry Cheesecake and White Chocolate Grisbi
- Cherry Cheesecake and Coconut
- Cherry Cheesecake and Butter Pecan
- Cherry Cheesecake and Hazelnut
- Cherry Cheesecake and Mint Stracciatella
- Cherry Cheesecake and Chocolate Sorbet
- Cherry Cheesecake and Pineapple Basil
- Cherry Cheesecake and Lemon
- Cherry Cheesecake and Strawberry
- Cherry Cheesecake and Blackberry + Raspberry
That’s 17 combinations already!
Now I can pick a different starting flavor and do the same thing. Let’s try Reese’s Cup.
I can have:
- Reese’s Cup and Vanilla
- Reese’s Cup and Cookies & Cream
- Reese’s Cup and Espresso Biscotto
- Reese’s Cup and M&M Birthday Cake
- Reese’s Cup and Caramel
- Reese’s Cup and Chocolate
- Reese’s Cup and Cherry Cheesecake
- Reese’s Cup and White Chocolate Grisbi
- Reese’s Cup and Coconut
- Reese’s Cup and Butter Pecan
- Reese’s Cup and Hazelnut
- Reese’s Cup and Mint Stracciatella
- Reese’s Cup and Chocolate Sorbet
- Reese’s Cup and Pineapple Basil
- Reese’s Cup and Lemon
- Reese’s Cup and Strawberry
- Reese’s Cup and Blackberry + Raspberry
But wait… Cherry Cheesecake and Reese’s Cup is the same as Reese’s Cup and Cherry Cheesecake right? The order doesn’t really matter to me. So I want to make sure I’m not counting doubles when I’m counting. That means I’ll actually have one less combination this time.
If I do that again, I’ll again have my list of all combinations, but this time I can cross two doubles out.
- Espresso Biscotto and Vanilla
- Espresso Biscotto and Cookies & Cream
- Espresso Biscotto and Chocolate
- Espresso Biscotto and M&M Birthday Cake
- Espresso Biscotto and Caramel
- Espresso Biscotto and Reese’s Cup
- Espresso Biscotto and Cherry Cheesecake
- Espresso Biscotto and White Chocolate Grisbi
- Espresso Biscotto and Coconut
- Espresso Biscotto and Butter Pecan
- Espresso Biscotto and Hazelnut
- Espresso Biscotto and Mint Stracciatella
- Espresso Biscotto and Chocolate Sorbet
- Espresso Biscotto and Pineapple Basil
- Espresso Biscotto and Lemon
- Espresso Biscotto and Strawberry
- Espresso Biscotto and Blackberry + Raspberry
If this pattern continues, then each time I’ll have one less pair to count. So instead of listing them out every time I can use this pattern to get my answer faster!
17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 153 different combinations!
All that math has made me hungry! I think I’ll get White Chocolate Grisbi and Lemon.
