Difference between revisions of "1988 AIME Problems/Problem 2"
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== Problem == | == Problem == | ||
+ | For any positive integer <math>k</math>, let <math>f_1(k)</math> denote the square of the sum of the digits of <math>k</math>. For <math>n \ge 2</math>, let <math>f_n(k) = f_1(f_{n - 1}(k))</math>. Find <math>f_{1988}(11)</math>. | ||
== Solution == | == Solution == |
Revision as of 12:53, 27 March 2007
Problem
For any positive integer , let denote the square of the sum of the digits of . For , let . Find .
Solution
We see that Note that this revolves between the two numbers.
See also
1988 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |