2003 AIME I Problems
Contents
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Let be the number of positive integers that are less than or equal to 2003 and whose base-2 representation has more 1's than 0's. Find the remainder when is divided by 1000.
Problem 14
The decimal representation of where and are relatively prime positive integers and contains the digits 2, 5, and 1 consecutively, and in that order. Find the smallest value of for which this is possible.
Problem 15
In and Let be the midpoint of and let be the point on such that bisects angle Let be the point on such that Suppose that meets at The ratio can be written in the form where and are relatively prime positive integers. Find