Algebra · Extremal values · Linear systems · Integer constraints
Each of the numbers \(x_1, x_2, \ldots, x_{2023}\) belongs to the set \(\{-1, 0, 1, 2\}\), and together they satisfy
\[ x_1 + x_2 + \cdots + x_{2023} = 111, \qquad x_1^2 + x_2^2 + \cdots + x_{2023}^2 = 999 . \]
Determine the largest possible value of
\[ x_1^3 + x_2^3 + \cdots + x_{2023}^3 . \]
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Serbian National Competition (Drzavno takmicenje) 2023, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source