This problem in part (a) is known as the "Flower of Thymaridas," named after a Pythagorean of the fourth century B.C.
(a) Given the n numbers a1, a2, ... an, solve for x1, x2, ..., xn in the following linear system:
x1 + x2 + ... + xn = a1
x1 + x2 = a2
x1 + x3 = a3
⋮
x1 + xn = an
(b) Identify a problem in this exercise set that fits the pattern in part (a), and solve it using your general solution.