Home Competitions RU-ALLRUSSIAN 1991 Problem 23
RU-ALLRUSSIAN 1991 Problem 23
The real numbers x 1 , x 2 , … , x 1991 \mathbf{x}_1,\mathbf{x}_2,\ldots ,\mathbf{x}_{1991} x 1 , x 2 , … , x 1991 ∣ x 1 − x 2 ∣ + ∣ x 2 − x 3 ∣ + … + ∣ x 1990 − x 1991 ∣ = 1991 \left|\mathbf{x}_1 - \mathbf{x}_2\right| + \left|\mathbf{x}_2 - \mathbf{x}_3\right| + \ldots +\left|\mathbf{x}_{1990} - \mathbf{x}_{1991}\right| = 1991 ∣ x 1 − x 2 ∣ + ∣ x 2 − x 3 ∣ + … + ∣ x 1990 − x 1991 ∣ = 1991 ∣ s 1 − s 2 ∣ + ∣ s 2 − s 3 ∣ + … + ∣ s 1990 − s 1991 ∣ \left|\mathbf{s}_1 - \mathbf{s}_2\right| + \left|\mathbf{s}_2 - \mathbf{s}_3\right| + \ldots +\left|\mathbf{s}_{1990} - \mathbf{s}_{1991}\right| ∣ s 1 − s 2 ∣ + ∣ s 2 − s 3 ∣ + … + ∣ s 1990 − s 1991 ∣ s n = ( x 1 + x 2 + … + x n ) / n \mathbf{s}_n = (\mathbf{x}_1 + \mathbf{x}_2 + \ldots +\mathbf{x}_n) / n s n = ( x 1 + x 2 + … + x n ) / n
Dataset text NuminaMath olympiads . Quoted with source.
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