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Part of 2021 Junior Balkаn Mathematical Olympiad

Problems(1)

Junior Balkan Mathematical Olympiad 2021- P2

Source: JBMO 2021

7/1/2021
For any set A={x1,x2,x3,x4,x5}A = \{x_1, x_2, x_3, x_4, x_5\} of five distinct positive integers denote by SAS_A the sum of its elements, and denote by TAT_A the number of triples (i,j,k)(i, j, k) with 1≤i<j<k≤51 \le i < j < k \le 5 for which xi+xj+xkx_i + x_j + x_k divides SAS_A. Find the largest possible value of TAT_A.
JuniorBalkannumber theorySetsmaximum