MathDB

A frog is jumping between lattice points on the coordinate plane in the following way: On each jump, the frog randomly goes to one of the

8

closest lattice points to it, such that the frog never goes in the same direction on consecutive jumps. If the frog starts at

(20, 19)

and jumps to

(20, 20)

, then what is the expected value of the frog’s position after it jumps for an infinitely long time?

Problem Statement