2007 AMC 12A Problems/Problem 11
Problem
The function f is defined on the set of integers and satisfies
Find .
Solution
Define , where the function is performed times. We find that . . So we now need to reduce .
Let’s write out a couple more iterations of this function:
So this function reiterates with a period of 2 for . It might be tempting at first to assume that is the answer; however, that is not true since the solution occurs slightly before that. Start at :
See also
1984 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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All AIME Problems and Solutions |