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# Function

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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?

Apr 7, 2024

#2
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The path in question:

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

Counting directly, there are 28 different points.

Apr 8, 2024

#1
+214
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https://web2.0calc.com/questions/i-need-some-help_8#r1

#2
+9664
+1

The path in question:

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

Counting directly, there are 28 different points.

MaxWong Apr 8, 2024