+13 Franklin the fly starts at the point (0, 0) in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After 12 steps, how many different points could Franklin end up at?
Franklin can move a maximum of 6 steps to the right, 6 steps to the left, 6 steps up, or 6 steps down. If he moves a maximum in any one direction, he can end up at 6^2 = 36 different points. However, he could also move 5 steps to the right, 5 steps up, and 2 steps to the left. This would give him a different point than if he had moved 6 steps to the right and 6 steps up. In other words, Franklin can end up at 6^2 * 4 = 96 different points.
However, this is not the final answer. Franklin can also end up at the origin after 12 steps. He can do this by taking 6 steps to the right, 6 steps to the left, 6 steps up, and 6 steps down. This gives us a total of 96 + 1 = 97 possible points.
