Difference between revisions of "2005 AIME II Problems/Problem 5"

Revision as of 23:20, 8 July 2006

Determine the number of ordered pairs $(a,b)$ of integers such that $\log_a b + 6\log_b a=5, 2 \leq a \leq 2005,$ and $2 \leq b \leq 2005.$

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 == Problem ==
-Robert has 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has an engraving of one face on one side, but not on the other. He wants to stack the eight coins on a table into a single stack so that no two adjacent coins are face to face. Find the number of possible distunguishable arrangements of the 8 coins.
+Determine the number of ordered pairs <math> (a,b) </math> of integers such that <math> \log_a b + 6\log_b a=5, 2 \leq a \leq 2005, </math> and <math> 2 \leq b \leq 2005. </math>
 == Solution ==
 == See Also ==
 *[[2005 AIME II Problems]]