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Difference between revisions of "2005 AIME II Problems/Problem 1"

 
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== Problem ==
 
== Problem ==
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Six circles form a ring with with each circle externally tangent to two circles adjacent to it. All circles are internally tangent to a circle <math>C</math> with radius <math>30</math>. Let <math>K</math> be the area of the region inside circle <math>C</math> and outside of the six circles in the ring. Find <math>\lfloor K \rfloor</math>.
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A game uses a deck of <math> n </math> different cards, where <math> n </math> is an integer and <math> n \geq 6. </math> The number of possible sets of 6 cards that can be drawn from the deck is 6 times the number of possible sets of 3 cards that can be drawn. Find <math> n. </math>
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== Solution ==
 
== Solution ==
 
== See Also ==
 
== See Also ==
 
*[[2005 AIME II Problems]]
 
*[[2005 AIME II Problems]]

Revision as of 23:16, 8 July 2006

Problem

A game uses a deck of $n$ different cards, where $n$ is an integer and $n \geq 6.$ The number of possible sets of 6 cards that can be drawn from the deck is 6 times the number of possible sets of 3 cards that can be drawn. Find $n.$

Solution

See Also

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