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5

Part of 2020 Argentina National Olympiad

Problems(1)

max S=a_1a_2a_3 + a_4a_5a_6 +⋯+ a_{2017}a_{2018}a_{2019} + a_{2020}

Source: 2020 Argentina OMA L3 p5

12/26/2020
Determine the highest possible value of: S=a1a2a3+a4a5a6+...+a2017a2018a2019+a2020S = a_1a_2a_3 + a_4a_5a_6 +... + a_{2017}a_{2018}a_{2019} + a_{2020} where (a1,a2,a3,...,a2020)(a_1, a_2, a_3,..., a_{2020}) is a permutation of (1,2,3,...,2020)(1,2,3,..., 2020).
Clarification: In SS, each term, except the last one, is the multiplication of three numbers.
inequalitiesSumpermutationalgebra