Difference between revisions of "2005 AIME I Problems/Problem 9"
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== Problem == | == Problem == | ||
| − | Twenty seven unit | + | Twenty seven unit [[cube (geometry) | cube]]s are painted orange on a set of four [[face]]s so that two non-painted faces share an [[edge]]. The 27 cubes are randomly arranged to form a <math> 3\times 3 \times 3 </math> cube. Given the [[probability]] of the entire [[surface area]] of the larger cube is orange is <math> \frac{p^a}{q^br^c}, </math> where <math> p,q, </math> and <math> r </math> are distinct [[prime number | prime]]s and <math> a,b, </math> and <math> c </math> are [[positive integer]]s, find <math> a+b+c+p+q+r. </math> |
== Solution == | == Solution == | ||
| − | + | {{solution}} | |
== See also == | == See also == | ||
| + | * [[2005 AIME I Problems/Problem 8 | Previous problem]] | ||
| + | * [[2005 AIME I Problems/Problem 10 | Next problem]] | ||
* [[2005 AIME I Problems]] | * [[2005 AIME I Problems]] | ||
Revision as of 12:25, 30 October 2006
Problem
Twenty seven unit cubes are painted orange on a set of four faces so that two non-painted faces share an edge. The 27 cubes are randomly arranged to form a 
cube. Given the probability of the entire surface area of the larger cube is orange is 
where 
and 
are distinct primes and 
and 
are positive integers, find 
Solution
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