Difference between revisions of "2018 UNCO Math Contest II Problems/Problem 9"
m (→Problem) |
m (→Solution) |
||
| Line 17: | Line 17: | ||
b) <math>G(n) = G(n - 1) + G(n - 2); G(0) = 1 \text{ and } G(1) = 2</math> | b) <math>G(n) = G(n - 1) + G(n - 2); G(0) = 1 \text{ and } G(1) = 2</math> | ||
| − | c) <math>G(n + 1) = G(n) + G(n | + | c) <math>G(n + 1) = G(n) + G(n - 1)</math>. |
== See also == | == See also == | ||
Latest revision as of 21:02, 28 October 2023
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 | ||
