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IV Lusophon Mathematical Olympiad 2014 - Problem 2

Source:

December 29, 2014

Problem Statement

Each white point in the figure below has to be completed with one of the integers 1,2,...,91, 2, ..., 9, without repetitions, such that the sum of the three numbers in the external circle is equal to the sum of the four numbers in each internal circle that don't belong to the external circle.
(a)(a) Show a solution.
(b)(b) Prove that, in any solution, the number 99 must belong to the external circle.
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