An array (a1,a2,...,a13) of 13 integers is called tame if for each 1≤i≤13 the following condition holds: If ai 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. combinatorics unsolvedcombinatorics