2018 UNCO Math Contest II Problems/Problem 9
Problem
Call a set of integers Grassilian if each of its elements is at least as large as the number of elements in the set. For example, the three-element set is not Grassilian, but the six-element set is Grassilian. Let be the number of Grassilian subsets of . (By definition, the empty set is a subset of every set and is Grassilian.)
(a) Find , , and .
(b) Find a recursion formula for . That is, find a formula that expresses in terms of
(c) Give an explanation that shows that the formula you give is correct.
Solution
a)
b)
c) .
See also
2018 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |