MathDB

An array

(a_1,a_2,...,a_{13})

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.

Problem Statement