Problem 42383. Combined Ages 3 - Non-symmetric, n ≥ 3

Pursuant to the previous two problems ( Symmetric, n = 3 and Symmetric, n ≥ 3 ), this problem will provide n combined ages where n is the number of individuals, though the age sums will not form a symmetric matrix. As an example: If the ages of all four individuals sum to 70; the ages of Alex, Barry, and Chris sum to 65; the ages of Alex and Barry sum to 40; and the ages of Barry and Chris sum to 52, what are their individual ages?

The individuals will be represented by the first n capital letters of the alphabet and the sums will be represented by variables whose string names contain each associated individual (capital letter). In this example problem, the equations would be represented as:

• A+B+C+D = ABCD (= 70)
• A+B+C = ABC (= 65)
• A+B = AB (= 40)
• B+C = BC (= 52)

Write a function to return the individuals' ages based on the supplied sums. See the test suite for examples and the tags for some hints.