Mathegoras

Combinatorics › Combinations and selections › Choosing with gaps

Four-element set from its triple sums

High school · ●●○○○ 20 pts

Let A={a1,a2,a3,a4}A=\{a_1, a_2, a_3, a_4\} be a set of four numbers. The set B={−1,3,5,8}B=\{-1, 3, 5, 8\} consists of the sums of the elements of all the three-element subsets of AA. Find the four elements of AA, in increasing order.

Enter the values in any order.

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subset sumssymmetric sumslinear equationsset theory