Question 836806: 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 \le 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?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Note that the maximum x-coordinate the robot can reach is 9, and the maximum y-coordinate is 10. Try a few steps:
(1,1) --> (6,7) --> (2,7) --> (2,3) --> (7,9) --> (3,9) --> (3,5) --> (3,1) --> (8,7) --> (4,7) --> (4,3) --> (9,9) --> (5,9) --> (1,9) --> (1,5) --> (1,1)
We're back to where we started! The robot will visit 15 different points.
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