Question 25
Let $S=\{1,2,3,\ldots,16\}$. In each of the following subsets of S, $\{6\}$, $\{1,2,3\}$, $\{5,7,9,10,11,12\}$, $\{1,2,3,4,5,6,7,8,9\}$, the sum of all the elements is a multiple of 3. Determine the total number of non-empty subsets A of S such that the sum of all elements in A is a multiple of 3.
