An algebra problem by Dharani Chinta

Algebra Level 4

Let \(N\) be any four-digit integer \(\overline{x_1x_2x_3x_4}\), where \(x_1\), \(x_2\), \(x_3\), and \(x_4\) are single-digit positive integers and \(x_1 \ne 0\).

Find the maximum value of \(\left \lfloor \dfrac{N}{x_1 + x_2 + x_3 + x_4} \right \rfloor \), where \(\lfloor \cdot \rfloor\) denotes the floor function.

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