2001 AIME II Problems

Problem 1

Let be the largest positive integer with the following property: reading from left to right, each pair of consecutive digits of forms a perfect square. What are the leftmost three digits of ? Solution

Problem 2

Each of the 2001 students at a high school studies either Spanish or French, and some study both. The number who study Spanish is between 80 percent and 85 percent of the school population, and the number who study French is between 30 percent and 40 percent. Let be the smallest number of students who could study both languages, and let be the largest number of students who could study both languages. Find M-m. 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