Difference between revisions of "2002 AIME II Problems"
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== Problem 1 == | == 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 <math>m/n</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. | ||
[[2002 AIME II Problems/Problem 1|Solution]] | [[2002 AIME II Problems/Problem 1|Solution]] | ||
Revision as of 08:46, 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
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 
