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    OlympiadHardCombinatorics10–12

    How many triples of integers (a,b,c)(a, b, c) with 0≤a,b,c≤30 \le a, b, c \le 3 satisfy a+b+c=5a + b + c = 5?

    Quantos ternos de inteiros (a,b,c)(a, b, c) com 0≤a,b,c≤30 \le a, b, c \le 3 satisfazem a+b+c=5a + b + c = 5?

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    Solution

    Step 1 of 3

    1. 1.Without the upper bound, stars and bars give (72)=21\binom{7}{2} = 21 solutions.