In how many ways can you color one cell blue and one cell red in the grid below so that the colored cells are not neighbors? Two cells are neighbors if they touch at all, even diagonally.
There are 16 competitors in the MATHCOUNTS Trainer competition, including 3 from Vienna. The gold medal goes to first place, silver to second, and bronze to third.
Suppose that the School decides that exactly one student from Vienna must win a medal (no more and no less). Now how many ways are there to award the medals?