My square patio is tiled with square tiles, all the same size. All the tiles are gray, except the tiles along the two diagonals, which are all yellow. (The corners are yellow, the center is yellow, and all the tiles along the diagonal in between are yellow.) If there are 21 yellow tiles, how many gray tiles are there?
If there are 21 yellow tiles, then there are 21 tiles along one diagonal. Since the tiles are square, the total number of tiles along one side of the square is 21 + 1 = 22. Therefore, the total number of tiles in the square is 22 * 22 = 484. Since there are 21 yellow tiles, there are 484 - 21 = 463 gray tiles. So the answer is 463