2017 AMC 12A Problems/Problem 7
Problem
Define a function on the positive integers recursively by 
, 
if 
is even, and 
if is odd and greater than 
. What is 
?
Solution
This is a recursive function, which means the function is used to evaluate itself. To solve this, we must identify the base case, 
. We also know that when is odd, 
. Thus we know that 
. Thus we know that n will always be odd in the recursion of , and we add two each recursive cycle, which there are 
of. Thus the answer is 
.
Alternatively, simply download java and run this program: public class Amc12a7 {
public static int f(int n){
if(n == 1)
return 2;
else if(n % 2 == 0)
return f(n-1) + 2;
else
return f(n-2) + 2;
}
}
See Also
| 2017 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
