Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2009 UNCO Math Contest II Problems/Problem 10

Revision as of 20:14, 19 October 2014 by Timneh (talk | contribs) (moved 2009 UNC Math Contest II Problems/Problem 10 to 2009 UNCO Math Contest II Problems/Problem 10: disambiguation of University of Northern Colorado with University of North Carolina)

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2009_UNCO_Math_Contest_II_Problems/Problem_10&oldid=65170"