2003 AIME II Problems

Problem 1

The product of three positive integers is 6 times their sum, and one of the integers is the sum of the other two. Find the sum of all possible values of .

Solution

Problem 2

Let be the greastest integer multiple of 8, no two whose digits are the same. What is the remainder when is divided by 1000.

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

See also

• American Invitational Mathematics Examination
• AIME Problems and Solutions
• Mathematics competition resources