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 Butter Pecan.
I can have:
- Butter Pecan and Vanilla
- Butter Pecan and Cookies & Cream
- Butter Pecan and Espresso Biscotto
- Butter Pecan and M&M Birthday Cake
- Butter Pecan and Caramel
- Butter Pecan and Reese’s Cup
- Butter Pecan and Cherry Cheesecake
- Butter Pecanand White Chocolate Grisbi
- Butter Pecan and Coconut
- Butter Pecan and Lemon
- Butter Pecan and Hazelnut
- Butter Pecan and Mint Stracciatella
- Butter Pecan and Chocolate Sorbet
- Butter Pecan and Pineapple Basil
- Butter Pecan and Chocolate
- Butter Pecan and Strawberry
- Butter Pecan and Blackberry + Raspberry
That’s 17 combinations already!
Now I can pick a different starting flavor and do the same thing. Let’s try Hazelnut.
I can have:
- Hazelnut and Vanilla
- Hazelnut and Cookies & Cream
- Hazelnut and Espresso Biscotto
- Hazelnut and M&M Birthday Cake
- Hazelnut and Caramel
- Hazelnut and Reese’s Cup
- Hazelnut and Cherry Cheesecake
- Hazelnut and White Chocolate Grisbi
- Hazelnut and Coconut
- Hazelnut and Butter Pecan
- Hazelnut and Lemon
- Hazelnut and Mint Stracciatella
- Hazelnut and Chocolate Sorbet
- Hazelnut and Pineapple Basil
- Hazelnut and Chocolate
- Hazelnut and Strawberry
- Hazelnut and Blackberry + Raspberry
But wait… Butter Pecan and Hazelnut is the same as Hazelnut and Butter Pecan 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.
- 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
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.
