Difference between revisions of "2006 AIME A Problems/Problem 2"
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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> | |
== Solution == | == Solution == |
Revision as of 12:56, 25 September 2007
Problem
Let set be a 90-element subset of and let be the sum of the elements of Find the number of possible values of
Solution
By the Triangle Inequality:
Also:
Combining these two inequalities:
The number of possible integer values for is the number of integers over the interval , which is .