Flavors of ice

What this combinatorics puzzle tests

This is an easy combinatorics puzzle that asks you to reason about the number of ways to choose items from a set. It rewards setting up the combinatorial equations carefully and solving for an unknown parameter — a skill that appears frequently in quant interviews, where you need to translate a word problem into mathematical notation quickly.

The key insight is recognizing that two different selection scenarios (choosing from different set sizes) can yield the same number of possibilities. To solve it, you'll need to express each scenario as a binomial coefficient, set them equal, and solve for the number of sold-out flavors. The problem tests whether you can handle small cases fluently without a calculator and spot the solution through systematic enumeration or algebraic reasoning.

• Binomial coefficients and combinations
• Setting up equations from word constraints
• Solving for unknowns in combinatorial contexts