Question

Starting from the point (0,0), a grasshopper makes a series of leaps on the coordinate plane. The grasshopper's first leap takes her to (3,4). After a move which adds (x,y) to the grasshopper's coordinates, her next move adds either (x,y-1) or (x-1,y) to her coordinates. Thus her second move adds either (3,3) or (2,4) to her position, landing her at (6,7) or (5,8) accordingly.

If the grasshopper's x and y coordinates never decrease, and if she ends at the point (a,a) where a is as large as possible, then what is the value of a?

Give an explanation with the answer. Thanks!!!! :)

Answer 1

14