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?

onyuIee Jul 26, 2024

#1**+1 **

Let's just count.

We have

\((1,1) \\\to (13, 19)\\(\text{2 steps in between})\\\to (1, 19)\\\text{(3 steps in between)}\\\to(1, 3)\\\to(15,23)\\ \text{(2 steps in between)}\\\to(3, 23)\\\text{(4 steps in between)}\\\to(3, 3)\\\to (17,25)\\\text{(3 steps in between)}\\\to (1, 25)\\\text{(5 steps in between)}\\\to(1, 1)\)

Adding all of these up, we find that there are 28 points.

Thanks! :)

NotThatSmart Jul 26, 2024