Question

Under the standard (x, y)-coordinate system, a grid of points with integer coordinates is given in the picture below. Here, the bottom-left point is the origin (0, 0) and the topright point has coordinate (6, 3). The coordinates of the remaining points can easily be computed accordingly. 2 During the 74th Hunger Game, Katniss and Peeta are separated inside a grid maze. Katniss is currently at the point (0, 0) and Peeta is (badly injured) at the point (x, y) where x and y are positive integers. Due to a defect in her navigation system, Katniss can only go east (or right) and north (or up) along the points on this grid. (a) (6 points) In terms of x and y, what is the number of paths that Katniss can take to get to Peeta? (b) (12 points) Let a, b be integers with 0 < a < x and 0 < b < y. Suppose President Snow destroys the node (a, b) so that Katniss can no longer travel through this node on her path. In terms of a, b, x, and y, what is the number of paths that Katniss can take to get to Peeta in this case? Remember that Katniss can only go east or north along the points. (c) (Optional - Hard) Think about the number of “valid” paths that Katniss can take if Snow destroys another point on the grid.

Under the standard (x, y)-coordinate system, a grid of points with integer coordinates is given in the picture below. Here, the bottom-left point is the origin (0,0) and the top- right point has coordinate (6,3). The coordinates of the remaining points can easily be computed accordingly. During the 74th Hunger Game, Katniss and Peeta are separated inside a grid maze. Katniss is currently at the point (0,0) and Peeta is (badly injured) at the point (x, y) where z and y are positive integers. Due to a defect in her navigation system, Katniss can only go east (or right) and north (or up) along the points on this grid. (a) (6 points) In terms of r and y, what is the number of paths that Katniss can take to get to Peeta? (b) (12 points) Let a, b be integers with 0 〈 a 〈 x and 0くb 〈 y. Suppose President Snow destroys the node (a, b) so that Katniss can no longer travel through this node on her path. In terms of a, b, x, and y, what is the number of paths that Katniss can take to get to Peeta in this case? Remember that Katniss can only go east or north along the points. c) (Optional - Hard) Think about the number of "valid" paths that Katniss can take if Snow destroys another point on the grid.

Answer 1

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