to every point $X$ in the plane is assigned a real number $r(x) > 0$ such that for any two points $X$ and $Y$ in the plane $2|r(x)-r(y)|<|XY|$ where $|XY|$ is the linear distance between the two points $X$ and $Y$. A frog on the plane can jump from point $X$ to point $Y$ if $r(x) = |XY|$. Prove that given any two points $X$ and $Y$ the frog can move from $X$ to $Y$ in a finite number of steps.

  • $\begingroup$ Hey. Is your condition for the frog being able to jump correct? $\endgroup$
    – Mankind
    Aug 9, 2015 at 7:53
  • $\begingroup$ i dont know ... that's what i was confused about! however this problem was taken from a very reliable source, that was all the more reason why i posted it here...in the hope that someone could make sense out of it. :P $\endgroup$ Aug 10, 2015 at 18:32


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