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2025 SSMO Relay Round 1 Problems/Problem 1

Problem

Let $x_1, x_2, \ldots, x_7$ be distinct integers such that the mean of $\{x_i,x_{i+1},x_{i+2}\}$ is an integer for all integers $1\le i\le 5$. Find the minimum possible positive value of $x_7 - x_1$.

Solution

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