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# The function \$f(x,y)\$

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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?

Jul 24, 2017

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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 less equal 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 24, 2017
edited by heureka  Jul 24, 2017
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