NL-NWO 1995 Problem 5

An array $(a_1,a_2,...,a_{13})$ of $13$ integers is called $tame$ if for each $1 \le i \le 13$ the following condition holds: If $a_i$ is left out, the remaining twelve integers can be divided into two groups with the same sum of elements. A tame array is called $turbo$ $tame$ if the remaining twelve numbers can always be divided in two groups of six numbers having the same sum. $(a)$ Give an example of a tame array of $13$ integers (not all equal). $(b)$ Prove that in a tame array all numbers are of the same parity. $(c)$ Prove that in a turbo tame array all numbers are equal.