Problem

Source: India Postals 2015 Set 1

Tags: combinatorics



For each point $X$ in the plane, a real number $r_X > 0$ is assigned such that $2|r_X - r_Y | \le |XY |$, for any two points $X, Y$ . (Here $|XY |$ denotes the distance between $X$ and $Y$) A frog can jump from $X$ to $Y$ if $r_X = |XY |$. Show that for any two points $X$ and $Y$ , the frog can jump from $X$ to $Y$ in a finite number of steps.