2001 AIME II Problems
Contents
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
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Each unit square of a 3-by-3 unit-square grid is to be colored either blue or red. For each square, either color is equally likely to be used. The probability of obtaining a grid that does not have a 2-by-2 red square is , where
and
are relatively prime positive integers. Find
.