2009 AIME I Problems/Problem 14
Problem
For , define , where . If and , find the minimum possible value for .
Solution
Because the order of the s doesn't matter, we simply need to find the number of s s s and s that minimize . So let and represent the number of s, s, s, and s respectively. Then we can write three equations based on these variables. Since there are a total of s, we know that . We also know that and .
See also
2009 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |