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avatar+736 

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 is less than or equal to 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?

 Jul 21, 2017
 #1
avatar+101088 
+2

 

Moves

 

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  and the cycle  starts again......

 

So...it  visits 15 different points

 

 

 

cool cool cool

 Jul 22, 2017
edited by CPhill  Jul 22, 2017
 #2
avatar+27902 
+1

Here's a visual representation:

 

.

 Jul 22, 2017

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