+608 The function $f(x,y)$ gives an ordered pair as output. It is defined according to the following rules:
* If $x > 4$, $f(x,y) = (x - 4,y)$.
* If $x \le 4$ but $y > 4$, $f(x,y) = (x,y - 4)$.
* Otherwise, $f(x,y) = (x + y + 11, x + 2y + 16)$.
A robot starts by moving to the point $(1,1)$. Every time it arrives at a point $(x,y)$, it applies $f$ to that point and then moves to $f(x,y)$. If the robot runs forever, how many different points will it visit?
+1952 Let's just count.
We have
(1,1)→(13,19)(2 steps in between)→(1,19)(3 steps in between)→(1,3)→(15,23)(2 steps in between)→(3,23)(4 steps in between)→(3,3)→(17,25)(3 steps in between)→(1,25)(5 steps in between)→(1,1)
Adding all of these up, we find that there are 28 points.
Thanks! :)
