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| − | == Problem ==
| + | #REDIRECT [[2006 AIME I Problems/Problem 2]] |
| − | 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>
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| − | == Solution ==
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| − | The smallest <math>S</math> is <math>1+2+ \ldots +90 = 91 \cdot 45 = 4095</math>. The largest <math>S</math> is <math>11+12+ \ldots +100=111\cdot 45=4995</math>. All numbers between <math>4095</math> and <math>4995</math> are possible values of S, so the number of possible values of S is <math>4995-4095+1=901</math>.
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| − | == See also ==
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| − | {{AIME box|year=2006|n=II|num-b=1|num-a=3}}
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| − | [[Category:Intermediate Geometry Problems]]
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| − | [[Category:Intermediate Algebra Problems]]
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