An unusual die has the numbers $2,2,3,3,5$, and 8 on its six faces. Two of these dice are rolled. The two numbers on the top faces are added. How many different sums are possible?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
We make a chart to determine the sum of each possible combination of top faces. In the chart, the numbers across the top are the numbers from the first die and the numbers down the side are the numbers from the second die. For example, the number in the fourth column and fifth row is the sum of the fourth possible result from the first die and the fifth possible result from the second die, or $3+5=8$.

|  | 2 | 2 | 3 | 3 | 5 | 8 |
| :---: | :---: | :---: | :---: | :---: | :---: | :---: |
| 2 | 4 | 4 | 5 | 5 | 7 | 10 |
| 2 | 4 | 4 | 5 | 5 | 7 | 10 |
| 3 | 5 | 5 | 6 | 6 | 8 | 11 |
| 3 | 5 | 5 | 6 | 6 | 8 | 11 |
| 5 | 7 | 7 | 8 | 8 | 10 | 13 |
| 8 | 10 | 10 | 11 | 11 | 13 | 16 |

So the possibilities are $4,5,6,7,8,10,11,13,16$, or nine possibilities in total.

(We could have cut down the size of our table since we didn't have to include both 2's and both 3's either across the top or down the side. As well, we could have also calculated only the numbers on the diagonal and above, since the chart is symmetric.)

ANSwER: (D)