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2009 UNCO Math Contest II Problems/Problem 10

Revision as of 17:53, 19 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == Let <math>S=\left \{1,2,3,\ldots ,n\right \}</math>. Determine the number of subsets <math>A</math> of <math>S</math> such that <math>A</math> contains at least t...")
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Problem

Let $S=\left \{1,2,3,\ldots ,n\right \}$. Determine the number of subsets $A$ of $S$ such that $A$ contains at least two elements and such that no two elements of $A$ differ by $1$ when

(a) $n=10$

(b) $n=20$

(c) generalize for any $n$.


Solution

See also

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