# Problem #2169

 2169 How many non-empty subsets $S$ of $\lbrace 1,2,3,\ldots ,15\rbrace$ have the following two properties? $(1)$ No two consecutive integers belong to $S$. $(2)$ If $S$ contains $k$ elements, then $S$ contains no number less than $k$. $\mathrm{(A) \ } 277\qquad \mathrm{(B) \ } 311\qquad \mathrm{(C) \ } 376\qquad \mathrm{(D) \ } 377\qquad \mathrm{(E) \ } 405$ This problem is copyrighted by the American Mathematics Competitions.
Note: you aren't logged in. If you log in, we'll keep a record of which problems you've solved.