2006 AIME I Problems/Problem 2: Difference between revisions
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== Problem == | == Problem == | ||
Let set <math> \mathcal{A} </math> be a 90-element subset of <math> \{1,2,3,\ldots,100\}, </math> and let <math> S </math> be the sum of the elements of <math> \mathcal{A}. </math> Find the number of possible values of <math> S. </math> | Let [[set]] <math> \mathcal{A} </math> be a 90-[[element]] [[subset]] of <math> \{1,2,3,\ldots,100\}, </math> and let <math> S </math> be the sum of the elements of <math> \mathcal{A}. </math> Find the number of possible values of <math> S. </math> | ||
== Solution == | == Solution == | ||
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== See also == | == See also == | ||
* [[2006 AIME I Problems/Problem 1 | Previous problem]] | |||
* [[2006 AIME I Problems/Problem 3 | Next problem]] | |||
* [[2006 AIME I Problems]] | * [[2006 AIME I Problems]] | ||
* [[Combinatorics]] | * [[Combinatorics]] | ||
[[Category:Intermediate Combinatorics Problems]] | [[Category:Intermediate Combinatorics Problems]] | ||
be a 90-
and let 
be the sum of the elements of 
Find the number of possible values of 
. The largest S is 
. All numbers between 4095 and 4995 are possible values of S, so the number of possible values of S is 
.
