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Determine the largest possible value of sum involving permut

Source: Balkan MO 1994, Problem 3

April 25, 2006
algebra proposedalgebrainequalitiesn-variable inequality

Problem Statement

Let a1,a2,…,ana_1,a_2,\ldots,a_n be a permutation of the numbers 1,2,…,n1,2,\ldots,n, with n≥2n\geq 2. Determine the largest possible value of the sum S(n)=∣a2−a1∣+∣a3−a2∣+⋯+∣an−an−1∣. S(n)=|a_2-a_1|+ |a_3-a_2| + \cdots + |a_n-a_{n-1}| . Romania
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