Difference between revisions of "2006 AMC 12A Problems/Problem 25"
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== Problem == | == Problem == | ||
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| + | How many non-empty subsets <math>S</math> of <math>\{1,2,3,\ldots ,15\}</math> have the following two properties? | ||
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| + | <math>(1)</math> No two consecutive integers belong to <math>S</math>. | ||
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| + | <math>(2)</math> If <math>S</math> contains <math>k</math> elements, then <math>S</math> contains no number less than <math>k</math>. | ||
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| + | <math> \mathrm{(A) \ } 277\qquad \mathrm{(B) \ } 311\qquad \mathrm{(C) \ } 376\qquad \mathrm{(D) \ } 377\qquad \mathrm{(E) \ } 405</math> | ||
== Solution == | == Solution == | ||
Revision as of 00:12, 11 July 2006
Problem
How many non-empty subsets 
of 
have the following two properties?
No two consecutive integers belong to .
If contains 
elements, then contains no number less than .
