Difference between revisions of "2002 AIME II Problems"
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== Problem 2 == | == Problem 2 == | ||
| + | Three [[vertex|vertices]] of a [[cube]] are <math>P=(7,12,10)</math>, <math>Q=(8,8,1)</math>, and <math>R=(11,3,9)</math>. What is the [[surface area]] of the cube? | ||
[[2002 AIME II Problems/Problem 2|Solution]] | [[2002 AIME II Problems/Problem 2|Solution]] | ||
Revision as of 08:47, 17 April 2008
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 
