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max sum prod a_{i,j}

Source: Polish MO Second Round 1971 p5

September 8, 2024
algebrainequalities

Problem Statement

Given the set of numbers {1,2,3,…,100} \{1, 2, 3, \ldots, 100\} . From this set, create 10 pairwise disjoint subsets Ni={ai,1,ai,2,...ai,10 N_i = \{a_{i,1}, a_{i,2}, ... a_{i,10} (i=1,2,…,10 i = 1, 2, \ldots, 10 ) so that the sum of the products
∑i=1010∏j=110ai,j \sum_{i=10}^{10}\prod_{j=1}^{10} a_{i,j} was the biggest.
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