Problem

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Tags: Putnam, Putnam 2018, Hi



Let $S$ be the set of sequences of length 2018 whose terms are in the set $\{1, 2, 3, 4, 5, 6, 10\}$ and sum to 3860. Prove that the cardinality of $S$ is at most \[2^{3860} \cdot \left(\frac{2018}{2048}\right)^{2018}.\]