2002 AIME II Problems
Contents
Problem 1
Many states use a sequence of three letters followed by a sequence of three digits as their standard license-plate pattern. Given that each three-letter three-digit arrangement is equally likely, the probability that such a license plate will contain at least one palindrome (a three-letter arrangement or a three-digit arrangement that reads the same left-to-right as it does right-to-left) is , where
and
are relatively prime positive integers. Find
.
Problem 2
Three vertices of a cube are ,
, and
. What is the surface area of the cube?
Problem 3
It is given that where
and
are positive integers that form an increasing geometric sequence and
is the square of an integer. Find