Question

The function f(x,y) accepts an ordered pair as input and gives another ordered pair as output. It is defined according to the following rules: If x>4, f(x,y)=(x-4,y). If x<=4 but y>4, f(x,y)=(x,y-4). Otherwise, f(x,y)=(x+5,y+6). 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? Thank you.

Answer 1

1,1
6,7
2,7
2,3
7,9
3,9
3,5
3,1
8,7
4,7
4,3
9,6
5,6
1,6
1,2
6,8
2,8
2,4
7,10
3,10
3,6
3,2 this thing is a pretty good vacuum cleaner, keep going until it repeats a point :)