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2025 SSMO Speed Round Problems/Problem 3

Revision as of 11:09, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Anna is buying different types of cheese from the local supermarket. Let <math>x,</math> <math>y,</math> and <math>z</math> be the number of pieces of blue, chedd...")
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Problem

Anna is buying different types of cheese from the local supermarket. Let $x,$ $y,$ and $z$ be the number of pieces of blue, cheddar, and mozzarella cheese, respectively, that Anna buys. She can buy any nonnegative integer number of each type, but the total number of pieces must be at most 12. How many different combinations $(x, y, z)$ of cheese can Anna buy? (Anna is allowed to buy 0 pieces of cheese.)

Solution

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