Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 2"
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2. Let <math>\star (x)</math> be the sum of the digits of a positive integer <math>x</math>. <math>\mathcal{S}</math> is the set of positive integers such that for all elements <math>n</math> in <math>\mathcal{S}</math>, we have that <math>\star (n)=12</math> and <math>0\le n< 10^{7}</math>. If <math>m</math> is the number of elements in <math>\mathcal{S}</math>, compute <math>\star(m)</math>. | 2. Let <math>\star (x)</math> be the sum of the digits of a positive integer <math>x</math>. <math>\mathcal{S}</math> is the set of positive integers such that for all elements <math>n</math> in <math>\mathcal{S}</math>, we have that <math>\star (n)=12</math> and <math>0\le n< 10^{7}</math>. If <math>m</math> is the number of elements in <math>\mathcal{S}</math>, compute <math>\star(m)</math>. | ||
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Revision as of 14:56, 24 July 2006
2. Let 
be the sum of the digits of a positive integer 
. 
is the set of positive integers such that for all elements 
in , we have that 
and 
. If 
is the number of elements in , compute 
.
